Design and Analysis of Wireless-Optical Broadband Access Networks (WOBAN) By SUMAN SARKAR B.E. (Bengal Engineering and Science University, India) 2001 M.S. (University of California, Davis) 2005 DISSERTATION Submitted in partial satisfaction of the requirements for the degree of DOCTOR OF PHILOSOPHY in Computer Science in the OFFICE OF GRADUATE STUDIES of the UNIVERSITY OF CALIFORNIA DAVIS Approved: Dr. Biswanath Mukherjee Dr. Dipak Ghosal Dr. Xin Liu Committee in charge 2008 –i–
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Design and Analysis of Wireless-OpticalBroadband Access Networks (WOBAN)
By
SUMAN SARKARB.E. (Bengal Engineering and Science University, India) 2001
M.S. (University of California, Davis) 2005
DISSERTATION
Submitted in partial satisfaction of the requirements for the degree of
DOCTOR OF PHILOSOPHY
in
Computer Science
in the
OFFICE OF GRADUATE STUDIES
of the
UNIVERSITY OF CALIFORNIA
DAVIS
Approved:
Dr. Biswanath Mukherjee
Dr. Dipak Ghosal
Dr. Xin Liu
Committee in charge
2008
–i–
To my father: Late Priyabrata Sarkar, and mother: Mrs. Sipra Sarkar.
–ii–
Abstract
The growing customer demands for bandwidth-intensive services are accelerating
the need to design an efficient “last mile” access network in a cost-effective manner. Tra-
ditional “Quad-play” applications (which refer to a bundle of services with voice, video,
Internet, and wireless) and premium rich-media applications (e.g., multimedia, interactive
gaming, and metaverse) need to be delivered over the access network to the end users in
a satisfactory and economical way. Thus, besides its enormous transport capacity, today’s
access infrastructure should bring operational efficiencies, namely mobility and untethered
convenience to end users. Hence, this dissertation proposes and investigates a novel hybrid
4.3.1 Lagrangean Relaxation and Lower Bound of Primal Model (PM) . . 654.3.2 Primal Algorithm and Upper Bound of Primal Model . . . . . . . . 704.3.3 Computing Upper Bound (UB) and Lower Bound (LB) of Primal Model 71
4.4 Performance Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 734.4.1 PM vs. CH: Impact of Carrier-to-Interference (CI) Threshold, I . . 764.4.2 PM vs. CH: Impact of Wireless Channel Pool, F . . . . . . . . . . . 784.4.3 PM vs. CH: Impact of User Coverage Ratio, ρ . . . . . . . . . . . . 794.4.4 PM vs. CH: Impact of Non-Homogeneous Demography . . . . . . . 80
2.1 A hybrid wireless-optical broadband access network (WOBAN) architecture. 14
3.1 Performance of various schemes of ONU placement in a WOBAN. . . . . . 383.2 Average distance (in meters) of ONUs from their primary users. . . . . . . 393.3 Map of wireless routers in Wildhorse. . . . . . . . . . . . . . . . . . . . . . . 403.4 Map of wireless routers by their signal strengths. . . . . . . . . . . . . . . . 413.5 Average distance (in meters) of ONUs from their primary users in Wildhorse. 423.6 Placement of 3 ONUs in Wildhorse WOBAN by Greedy (Top left cone:
4.1 Primal Algorithm schematic (“T” means True, “F” means False). . . . . . . 724.2 Impact of channel interference on normalized deployment cost (with ρ = 1
and |F | = 50 channels). If I ≥ 18 dB, no feasible solution exists for CH. . . 774.3 Impact of available channel pool on normalized deployment cost (with ρ = 1
and I = 12 dB). If |F | < 35 channels, no feasible solution exists for CH. . . 784.4 Impact of user coverage ratio on normalized deployment cost (with I = 12
dB and |F | = 50 channels). . . . . . . . . . . . . . . . . . . . . . . . . . . . 794.5 Impact of non-homogeneous user coverage ratio on normalized deployment
cost (with I = 12 dB and |F | = 50 channels). If ρ > 0.8, no feasible solutionexists for CH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.1 A WOBAN’s upstream and downstream protocols. . . . . . . . . . . . . . . 835.2 San Francisco WOBAN and its front-end wireless mesh (SFNet). . . . . . . 855.3 Differential and asymmetric capacity assignment. . . . . . . . . . . . . . . . 905.4 Link-state predictions (LSPs) used at time intervals. . . . . . . . . . . . . . 93
–xi–
5.5 Average delay vs. load in SFNet. . . . . . . . . . . . . . . . . . . . . . . . . 955.6 Delay vs. load [for the furthest router/gateway pair (1, 25)] in SFNet. . . . 965.7 Comparing K-DARA (K > 1) path delays with PTRA delay [for the furthest
router/gateway pair (1, 25)] in SFNet. . . . . . . . . . . . . . . . . . . . . . 975.8 Average number of K-DARA (K > 1) paths under PTRA delays in SFNet. 975.9 Average hops vs. load in SFNet. . . . . . . . . . . . . . . . . . . . . . . . . 985.10 Hop distributions vs. load in SFNet. . . . . . . . . . . . . . . . . . . . . . . 985.11 Load balancing (or link congestion) vs. load in SFNet. . . . . . . . . . . . . 995.12 Actual vs. predicted packet intensities at high loads. . . . . . . . . . . . . . 1005.13 Actual vs. predicted packet intensities at low loads. . . . . . . . . . . . . . 100
2.1 A sample of municipal access networks. . . . . . . . . . . . . . . . . . . . . 182.2 Pros and cons of various placement schemes in WOBAN. . . . . . . . . . . 222.3 Pros and cons of various routing algorithms in the wireless part of a WOBAN. 26
3.1 Research activities on network placement. . . . . . . . . . . . . . . . . . . . 313.2 A small part of scanning results from Wildhorse. . . . . . . . . . . . . . . . 413.3 Wildhorse WOBAN user distributions (in hop count). . . . . . . . . . . . . 423.4 Simulation parameters for SA. . . . . . . . . . . . . . . . . . . . . . . . . . 473.5 Various components of WOBAN and PON expenditure. . . . . . . . . . . . 503.6 Device and fiber layout expenses (in normalized units). . . . . . . . . . . . . 503.7 ONU, WiFi, and WiMAX capacities. . . . . . . . . . . . . . . . . . . . . . . 513.8 WOBAN and PON setup expenditures (in normalized units). . . . . . . . . 513.9 Estimation of channel interference and number of BSs by CH. . . . . . . . . 53
The dominant broadband access network that is emerging from today’s research
and development activities is a point-to-multipoint optical network, known as Passive Op-
tical Network (PON). The basic configuration of a PON connects the telecom central office
(CO) to businesses and residential users by using one wavelength channel in the downstream
direction [from Optical Line Terminal (OLT) at CO to Optical Network Units (ONU)], and
another wavelength channel in the upstream direction [from ONUs to OLT]. A PON does
not have any active element in the signal’s path from source to destination; hence, it is
robust. The only interior elements used in such a network are passive combiners, couplers,
and splitters.
A PON (Figure 1.1) provides much higher bandwidth for data applications [than
current solutions such as digital subscriber line (DSL) and cable modem (CM)] as well as
deeper fiber penetration. Based on current standards [B/G/GFP-PON standards (see below
for details of these abbreviations)], the PON can cover a maximum distance of 20 km from
the OLT to the ONU. While fiber-to-the-building (FTTB), fiber-to-the-home (FTTH), or
even fiber-to-the-PC (FTTPC) solutions have the ultimate goal of fiber reaching all the way
to end user premises, fiber-to-the-curb (FTTC) may be the more economical deployment
scenario today [1, 2].
The traditional single-wavelength PON (also known as the time-division-multiplexed
Chapter 1: Introduction 2
PON or TDM-PON) combines the high capacity of optical fiber with the low installation
and maintenance cost of a passive infrastructure. The optical carrier is shared by means
of a passive splitter among all the users, so the PON topology is a tree, as in most other
distribution networks, e.g., those for power, video, etc. As a consequence, the number of
ONUs is limited by the splitting loss, and by the bit rate of the transceivers in the OLT
and in the ONUs. Current specifications allow for 16 ONUs at a maximum distance of 20
km from the OLT and 32 ONUs at a maximum distance of 10 km from the OLT [3].
The per-user cost of such a network can be low as the bandwidth (for EPON,
this bandwidth is typically up to 1 Gbps in current practice and expected to increase to
10 Gbps in the future; and for GPON, it is 2.5 Gbps in current practice and expected
to be 10 Gbps in future) is shared among all the end users. But, as end users demand
for more bandwidth, the need for upgrading the existing PON architectures [viz., Ethernet
PON (EPON), Gigabit PON (GPON)1, Broadband PON (BPON, based on ATM), Generic
Framing Procedure PON (GFP-PON), etc.] to incorporate multiple wavelengths is essential.
Incorporating multiple wavelengths in PON [by means of wavelength-division multiplexing
(WDM)] provides excellent scalability because it can support multiple wavelengths over the
same fiber infrastructure, it is inherently transparent to the channel bit rate, and, depending
on its architecture, it may not suffer power-splitting losses. Please see [5] for a review of
WDM-PON architectures.
The basic idea behind the WDM-PON (Figure 1.2) is to increase the bandwidth
of the PON by employing wavelength-division multiplexing (WDM), such that multiple
wavelengths may be supported by either or both the upstream and downstream directions.
WDM-PON research has received quite a lot of attention in the literature, and most current
research focuses on the remote node (RN) and ONU architectures.
The straightforward approach to build a WDM-PON is to employ a separate wave-
length channel from the OLT to each ONU, both in the upstream and downstream direc-
tions. This approach creates a point-to-point (P2P) link between the OLT and each ONU,
which differs from the point-to-multipoint (P2MP) topology of the traditional PON. In the1With the recent progress of PON technology, Verizon’s GPON+TV services may support multiple wave-
WDM-PON, each ONU can operate at a rate up to the full bit rate of a wavelength chan-
nel. Moreover, different wavelengths may be operated at different bit rates, if necessary;
hence, different types of services may be supported over the same network. This is clearly
an advantage of WDM-PON over the traditional PON [6,7].
There are various industry efforts to build PON architecture for commercial de-
ployment. In the United States, Verizon has introduced its “Fiber-to-the-Premises” archi-
tecture, called FiOS, to deliver high speed voice and data services to the home. FiOS service
consists of three consumer broadband speeds: up to 5 Mbps downstream and up to 2 Mbps
upstream (5 Mbps/2 Mbps), 15 Mbps/2 Mbps, and 30 Mbps/5 Mbps. FiOS network is
migrating from current BPON to future GPON architecture, thus moving towards higher
upstream/downstream speed and eliminating ATM [8]. Among other efforts, Novera Optics
has launched TurboLIGHT, a dense wavelength-division-multiplexed (DWDM) fiber-to-the-
X (FTTX) optical access technology, which allows flexible multimode transport capabilities
at different bit rates (125 Mbps to 1.25 Gbps) [9]. In Asia, a similar effort can be found
in WE-PON, which has a combined architecture of WDM (from CO to WDM device) and
TDM (from WDM device to ONU through splitters) with bit rates on the order of 100
Mbps [10].
1.2 Recent Trends in Wireless Access Networks
Another promising access solution is a wireless network. Recently, we have seen
tremendous growth in the research and deployment of various wireless technologies. There
are three major techniques that have been employed for wireless access networks worldwide,
viz., “Wireless Fidelity” (known as WiFi), “Worldwide Interoperability for Microwave Ac-
cess” (known as WiMAX), and “Cellular Network”. These technologies have their own
advantages and disadvantages.
WiFi is one of the most popular wireless technologies (standards: IEEE 802.11a/b/g) [11],
and it is mainly used for wireless local-area networks (WLAN). WiFi can operate in both
the “Infrastructure” and “Ad-Hoc” modes. In infrastructure mode, a central authority,
Chapter 1: Introduction 5
known as Base Station (BS) or Access Point (AP)2, is required to manage the network.
But, in ad-hoc mode, the users are self-managed and there is no concept of an adminis-
trator. WiFi technology can exploit the flexibility of “multi hopping”. WiFi offers low
bit rate (max 54/11/54 Mbps for 802.11a/b/g respectively) and limited range (typically
100 meters). In recent years, wireless mesh (standard: IEEE 802.11s) has evolved as a
cost-effective alternative (to fiber access network) in the federated and community network.
WiMAX (standard: IEEE 802.16) [12] is gaining rapid popularity. It is essentially
a point-to-multipoint broadband wireless access service. WiMAX can be used efficiently
for single-hop communication (for multi-hop, WiMAX suffers from higher delay and lower
throughput). It provides high bandwidth and uses less-crowded spectrum. Thus, WiMAX is
particularly suitable for wireless metropolitan-area networks (WMAN), because of its high
bit rate and long range. It can support data rates upto 75 Mbps in a range of 3-5 km, and
typically 20-30 Mbps over longer ranges. Transmission over longer distances significantly
reduces bit rates due to the fact that WiMAX does not work efficiently for non-line-of-sight
(NLOS) communications. WiMAX Base Stations (BS) can be placed indoor (installed
by customer) or outdoor (installed by network operator) to manage the wireless network.
Recently, WiMAX is being examined as an alternative for fixed wired infrastructures, viz.,
DSL and cable modem, to deliver “last mile” broadband access to users.
There are several industry efforts to build WiMAX architecture for commercial
deployment, and a few examples are stated below. In the United States, Sprint Nextel
holds the licence in 2.5 GHz band to build a nationwide wireless access network, which is
expected to cover 100 million US customers in 2008 [13]. Towerstream has deployed wireless
networks, which have bit rates of tens of Mbps, in several locations in the US [14]. Among
other regions, Intel WiMAX trials have been launched in several locations in Europe and
India in collaborations with local service providers [15].
Cellular technology is used for low-bit-rate applications (max 2 Mbps). A cellular
network is mainly used to carry voice traffic, and is not optimized for data traffic. In
addition, the data component of the cellular network, such as the High-Speed Downlink2Throughout this dissertation, we shall use the words Base Station (BS) and Access Point (AP) inter-
changeably.
Chapter 1: Introduction 6
Packet Access (HSDPA) and High-Speed Uplink Packet Access (HSUPA), jointly known
as High-Speed Packet Access (HSPA) in the 3G (3rd Generation) evolution can deliver
a downstream bandwidth of up to 14 Mbps and upstream bandwidth of up to 5 Mbps.
A more advanced version, namely HSPA+, will offer a downlink speed of up to 40 Mbps
and up to 10 Mbps in upstream direction. They use Federal Communications Commission
(FCC) regulated expensive spectrum (licensed band) with 3G [16] and B3G (Beyond 3rd
Generation), namely 4G (4th Generation) [17] standards. WiFi technology, on the other
hand, uses the free Industrial Scientific and Medical (ISM) band, while WiMAX uses both
licensed and ISM bands.
Several recent studies in the field of wireless access networks have focussed on the
integration of WiFi and cellular. This type of architecture exploits the advantages of both
WiFi and cellular [18]. An integrated cellular infrastructure with ad-hoc relaying at strategic
locations can provide better load balancing by diverting the traffic from a heavily-congested
cell to a neighboring relatively-less-congested cell, if possible. This type of architecture has
other benefits too. It is more flexible because it can extend the traditional cellular coverage.
It also helps in the interoperability of managing the two diverse technologies: ad-hoc and
cellular. Integration helps in improving the fault tolerance of the system, by improving its
reliability. It also improves the transmission rate by exploiting the additional bandwidth of
the ad-hoc network [19–21].
1.3 Radio-on-Fiber – A Precursor of WOBAN
Unlike WOBAN, which mainly focuses on the networking aspect of the wireless-
optical converged architecture, the radio-on-fiber (ROF) technology has its root in the
communication challenges of sending radio signals over fiber. The radio signals in ROF
can be effectively carried over an existing optical fiber infrastructure (saving “last mile”
costs) by means of the “Hybrid Fiber Radio” (HFR) enabling technology. Thus, challenges
with ROF (which are complementary to WOBAN’s research focus) are: (1) to design better
transmission equipments, (2) to improve the signal’s power gain, (3) to develop sophisticated
signal modulation/demodulation and up/down conversion techniques, etc.
Chapter 1: Introduction 7
Recent research works propose ROF-based technologies in millimeter-waveband
(mm-waveband) [22, 23], and demonstrate integrated broadband services in a ROF down-
stream link [24]. HFR helps to reduce the design complexity at the Remote Antenna
Units (RAU) (consequently leading to inexpensive and simple RAUs), because up/down-
conversion, multiplexing/demultiplexing, modulation/demodulation, etc. can be performed
at a central office (also known as HFR head end). It is also possible to transmit multiple
radio signals over the same fiber. The ROF-enabled access network may have different
topologies such as “optical star – radio point-to-point”, “optical tree – radio star”, “optical
star – radio cellular”, etc. Among various research efforts, the work in [25] proposes a dy-
namic wavelength allocation scheme for bursty traffic load for WDM fiber-radio ring access
The fault-tolerant property of a WOBAN may handle most of these failure scenar-
ios efficiently. If a gateway fails, then the traffic can be redirected to other nearby gateways.
Similarly, if an ONU fails, and as a consequence, one or multiple gateways fail, the packets
will be rerouted to other “live” gateways that are connected to a “live” ONU. An OLT
failure (and as a consequence, the failure of all ONUs connected to that OLT) is the most
severe. In this case, packets from a large portion of the WOBAN will need to be rerouted.
Thus, to tackle these problems, a “Risk-and-Delay Aware Routing Algorithm
(RADAR)”, which is an extension to DARA, has been developed (the details of which
can be found in Chapter 6). RADAR can handle the multiple failure scenarios. RADAR
differentiates each gateway in the WOBAN by maintaining a hierarchical risk group that
shows which PON group (ONU and OLT) a gateway is connected to. Each gateway is
indexed, which contains its predecessors (ONU and OLT indices as well) to maintain the
tree-like hierarchy of WOBAN. ONUs and OLTs are indexed in similar fashion. To reduce
packet loss, each router maintains a “Risk List (RL)” to keep track of failures. In the
no-failure situation, all the paths are marked “live”. Once a failure occurs, RL will be
updated and paths that lead to the failed gateway(s) will be marked “stale”. Thus, while
forwarding packets, the router will only choose a “live” path. The pros and cons of RADAR
Chapter 2: WOBAN Architecture and Research Challenges 28
are captured in Table 2.3.
2.6 Summary
In this chapter, we introduced an architecture and a vision for WOBAN, and
articulated why the combination of wireless and optical presents a compelling solution that
optimizes the best of both worlds. While it briefly touched upon the business drivers, the
main arguments focussed on design and deployment considerations.
We discussed network setup, network connectivity, and fault-tolerant character-
istics of the WOBAN. In network setup, we proposed and investigated the design of a
WOBAN where the back end is a wired optical network, the front end is configured by
wireless connectivity, and, in between, the tail ends of the optical part [known as Optical
Network Units (ONUs)] communicate directly with the wireless base stations (known as
“gateway routers”). We summarized algorithms to optimize the placement of ONUs in a
WOBAN deployment scenario. We also evaluated the pros and cons of the various routing
algorithms (network connectivity) in a WOBAN, including its fault-tolerant characteristics
and presented some novel concepts that are better suited for such hybrid networks.
29
Chapter 3
Network Planning and Setup for
WOBAN
3.1 Introduction
The network performance of WOBAN depends on its proper deployment. A
WOBAN deployment is more challenging than only an optical or a wireless access net-
work deployment. This is because of the design interplay between two very diverse access
technologies (optical and wireless). In addition, the network designer has to ensure that
both parts are well designed and neither part is over-designed (with excess resources) nor
under-designed (a resource bottleneck). However, the research on traditional access network
setup is an excellent pointer to begin with.
3.1.1 Related Literature
Although a few research activities are reported on WOBAN design [31–35], re-
search on traditional access network placements can be a good starting point. Thus, Ta-
ble 3.1 summarizes the research on network setup, where the architecture is mainly focused
on the wireless network. We observe that the placement research can be broadly divided
into two categories: indoor and outdoor locations. For both categories, several techniques
have been employed, e.g., iterative methods (viz., quasi-Newton in [50], linear regression
Chapter 3: Network Planning and Setup for WOBAN 30
and least square in [56], etc.), pruning-searching techniques (viz., Hooke-Jeeves in [50],
Nelder-Mead in [51], etc.), and combinatorial optimizers (viz., genetic algorithm in [54],
tabu search in [58], etc.). Various metrics have been used for network optimization, ranging
from distance (in [52]) to signal strength (in [53]). Some studies also focus on the trial-and-
error deployment of BSs so that no void region (a region with little or no signal coverage)
exists. A campus-wide access network setup is captured in [55].
Chapter 3: Network Planning and Setup for WOBAN 31
Tab
le3.
1:R
esea
rch
acti
viti
eson
netw
ork
plac
emen
t.
Res
earc
hW
ork
Obje
ctiv
eSet
ting
Cost
Model
Optim
izati
on
Contr
ibuti
ons
(in
bri
ef)
Sher
ali
etal.
[50]
Optim
um
pla
cem
ents
ofB
ase
Sta
tions
for
min
imiz
ing
the
tota
lco
stof
net
work
setu
p.
Outd
oor
Sig
nalst
rength
Hooke-
Jee
ves
,Q
uasi
-New
ton,H
ill-cl
imbin
gM
inis
um
,M
inim
ax,co
mbin
ati
on
model
;C
aptu
res
single
and
multip
leT
xpro
ble
ms.
Wri
ght
[51]
Indoor
Sig
nalpro
pagati
on
Nel
der
-Mea
dD
irec
tSea
rch
Gen
eric
model
wit
hatt
enuati
on;
Fin
ds
loca
lopti
mum
.M
olina
etal.
[52]
Outd
oor
Dis
tance
Gre
edy,
Gen
etic
,G
reed
y+
Gen
etic
Optim
ized
cellula
rco
ver
age;
Com
bin
ato
rialappro
ach
.H
url
ey[5
3]
Outd
oor
Sig
nal,
Dis
tance
,Tra
ffic
Sim
ula
ted
Annea
ling
Mult
iple
cost
sappro
ach
;C
ellhandover
consi
der
ed.
Nagy
etal.
[54]
Indoor
Motl
ey-K
eenan
path
loss
Gen
etic
Alg
ori
thm
Em
pir
icalm
odel
;H
igh
com
ple
xity.
Hills
[55]
Indoor
Sig
nalst
rength
Tri
al-and-e
rror
Cylindri
caldes
ign
appro
ach
;D
eplo
yed
inC
arn
egie
Mel
lon.
Chen
etal.
[56]
Indoor
Bahl’s
path
loss
Lin
ear
Reg
ress
ion,Lea
stSquare
Both
signal-st
rength
and
loca
tion
aw
are
nes
s;G
ener
icm
odel
wit
hatt
enuati
on.
Kam
enet
skym
etal.
[57]
Outd
oor
Sig
nalst
rength
Uniform
,P
runin
g,Sim
ula
ted
Annea
ling
Em
pir
icalm
odel
;M
inis
um
and
Min
imax
appro
ach
es.
Batt
itiet
al.
[58]
Outd
oor
Sig
nalst
rength
Tabu,H
ill-cl
imbin
g,Sim
ula
ted
Annea
ling
Loca
liza
tion
+si
gnal-co
ver
age
model
;Show
str
ade-
off
bet
wee
ntw
om
etri
cs.
Chapter 3: Network Planning and Setup for WOBAN 32
The rest of this chapter is organized as follows. In Section 3.2, we propose and
investigate the characteristics of an algorithm, which finds suitable locations to deploy
multiple ONUs in a WOBAN. This is a Greedy Algorithm based on “local optimization”.
To obtain some representative data on locations of wireless users in a typical residential
neighborhood, we have conducted a survey on the distribution and types of wireless routers
in the Wildhorse neighborhood of North Davis, CA. Section 3.3 reports a small part of
this data and illustrative numerical examples to show the performance of our algorithm.
In Section 3.4, we study the multiple-ONU placement problem using a global optimization
technique, namely Simulated Annealing algorithm. We find that the results from local
optimization are quite close to those obtained from the global optimizer. After determining
suitable locations to deploy ONUs, we explore the expenditure of WOBAN setup, and
compare this with a wired access solution, viz., a PON all the way to each user. Noting
that WOBAN is based on complex interactions of the design inter-play between two diverse
technologies, Section 3.6 captures the design aspects of both the wireless front end and the
optical back end, and proposes a joint optimization algorithm. Section 3.7 summarizes this
chapter.
To begin, we first develop a simple (greedy) algorithm to deploy multiple ONUs
in WOBAN, with much lower processing requirements than iterative solvers and optimizers
discussed below. Unlike some of the approaches in Table 3.1, where discontinuous design
models may lead the iterative solvers and optimizers to get trapped, our algorithm does not
suffer from any non-convergence. Next, we introduce the design methodology of Greedy
Algorithm, and later we will build on it to achieve a complete WOBAN deployment (see
Section 3.5 and 3.6 for details).
3.2 Placement of Multiple ONUs in WOBAN
The network performance largely depends on the deployment of ONUs. Proper
deployment of ONUs is critical to minimize the overall expenditure of a WOBAN setup.
To tackle this problem, we first investigate a greedy algorithm (Greedy) (see Algorithm 1)
with no backtracking for placing multiple ONUs in the network. Given the locations of
Chapter 3: Network Planning and Setup for WOBAN 33
the wireless users, our goal is to find the suitable placement of multiple ONUs to minimize
the average distance between wireless users and their closest ONU. So, Greedy is mainly
focused on the average distance (wireless users to ONU) optimization in the WOBAN’s
wireless front end (and the results from Greedy will be used for our joint optimization
algorithm later in Section 3.6). Next, we introduce the cost metric for ONU deployment.
3.2.1 Cost Metric for ONU Deployment
Our primary goal is to place multiple ONUs (say N of them) properly in a ge-
ographic area where the users’ locations are known, e.g., in a residential neighborhood.
Assume that (Xi, Yi) is the position (“cartesian” coordinates) of i-th ONU, which will serve
users at (xj , yj), where j ∈ (1, 2, ..., k′i). We model the cost to deploy the i-th ONU as the
average “Euclidean” distance from that ONU to its users as follows:
CONUi =1k′i∗
k′i∑j=1
√(xj −Xi)2 + (yj − Yi)2
. (3.1)
3.2.2 Greedy Approach
We start with a given distribution of wireless users. Since WOBAN is primarily
a broadband access solution for residential and business premises, user mobility is not a
major concern. We consider a number of locations as possible candidates to place the
ONUs. These initial locations could be chosen randomly or deterministically. The initial
deterministic placement could be achieved by dividing the neighborhood into multiple non-
overlapping regions and then placing the ONUs at the “centers” of each region. Then,
we find the distances of all ONUs with respect to a user (whose coordinates are known
beforehand). For each user, we form an ordered set (in ascending order), with the user’s
distances from ONUs as the set’s elements. Then, we identify the primary ONU, which is
the closest (minimum distance from the user). We obtain a set of users for primary ONUs;
we call these users “premium users” for that ONU, and suitably place each primary ONU
with respect to its premium users. The details of the algorithm are shown in Algorithm 1.
Chapter 3: Network Planning and Setup for WOBAN 34
3.2.3 Notations
We list the notations used as follows:
• (xj , yj): User j’s X/Y-coordinates,
• k: Total users in the network,
• (Xi, Yi): ONU i’s X/Y-coordinates,
• N : Number of ONUs,
• dij : Distance between ONU i and user j,
• SDj : Set of ONUs for user j (The elements of this set are the distances between
user j and all the initial ONU locations in the network. This is an ordered set where
elements are in ascending order. From this set, we will choose a user’s primary ONU.),
• ONUPrimaryij : Primary ONU i (minimum-distance ONU) for user j,
• SUi: Set of premium users for a primary ONU i (the elements of this set are the
coordinates of users with minimum distance from ONU i, compared to any other
ONU), and
• k′i: Premium users for ONU i (where∑N
i=1 k′i = k).
Based on the model in Section 3.2.1, this algorithm tries to achieve an efficient
solution in polynomial time.
3.2.4 Running Time
We determine the running time of this algorithm as follows. Running time for line
2 of phase 1 (finding distances) is k ∗ O(N). Running time for line 3 of phase 1 (sorting
ONUs) is k ∗O(NlogN). Running time for line 4 of phase 1 (finding minimum) is k ∗O(1).
Running time for line 1 of phase 2 (finding users) is N ∗ O(k′i). Running time for line
2 of phase 2 (finding mean) is N ∗ O(1). So, the total running time of our algorithm is
k ∗O(N) + k ∗O(NlogN) + k ∗O(1) + N ∗O(k′i) + N ∗O(1) = O(kN + kNlogN + Nk′i) =
Chapter 3: Network Planning and Setup for WOBAN 35
Algorithm 1 Greedy Algorithm (for suitable deployment of multiple ONUs in a WOBAN)Input : Locations of users, (xj , yj).Output : Locations of ONUs, (Xi, Yi).Phase 1: Identify Primary ONUs
1. Given locations of k users, (xj , yj),∀j ∈ (1, 2, 3, ..., k), consider N ran-dom/deterministic points, (Xi, Yi),∀i ∈ (1, 2, 3, ..., N), as candidates for initial ONUplacements.
2. Find the distances between a user j and all the ONUs, dij =√(xj −Xi)2 + (yj − Yi)2,∀i ∈ (1, 2, 3, ..., N). Repeat the same for all other
users, i.e., ∀j ∈ (1, 2, 3, ..., k).
3. For user j, sort the distances in ascending order and put them in the sets, SDj ={dij : dij ≤ di′j ,∀(i, i′) ∈ (1, 2, 3, ..., N), i 6= i′}. Repeat the same for all other users,i.e., ∀j ∈ (1, 2, 3, ..., k).
4. Identify a primary ONU for each user, where ONUPrimaryij = mini{SDj}.
Phase 2: Find Placement of Primary ONUs
1. Obtain the set of users (call them “premium users”) for each primary ONU for whichthe distances between the ONU and its users are minimum (compared to all otherONUs), SUi = {(xj , yj) :
√(Xi − xj)2 + (Yi − yj)2 is min}, ∀j ∈ (1, 2, 3, ..., k′i), k
′i ≤
k, for a particular ONU i and ∀i ∈ (1, 2, 3, ..., N).
2. For a set of premium users, (xj , yj),∀j ∈ (1, 2, 3, ..., k′i), place ONUi at the mean of
the users’ X/Y-coordinates. Therefore, (Xi, Yi) =
(∑k′ij=1 xj
k′i,
∑k′ij=1 yj
k′i
). Repeat the
same for all other ONUs, i.e., ∀i ∈ (1, 2, 3, ..., N).
Chapter 3: Network Planning and Setup for WOBAN 36
O(kNlogN). It is expected that, in a WOBAN, the number of ONUs will be relatively
small compared to the number of users. Since k >> N in practical cases, this algorithm
will run in O(k) time, which is linear in the number of users in the network.
3.2.5 Analysis
In this algorithm, we start with a divide-and-conquer approach to partition the
network. After identifying the primary ONUs, we try to minimize the average distance
between the ONU and its users. This problem of finding the minimum distance does not
have any closed-form solution. But we will show that, for a uniform random distribution of
wireless users, the chance of obtaining the minimum cost is higher for the Greedy Algorithm
(compared to other schemes of ONU placements, viz., random and deterministic placements)
with a placement which considers the mean as the optimization metric.
The cost of this algorithm is defined as the average distance for all the ONUs over
those users for whom the ONUs are the primary ONUs. So, the cost for a particular ONU
at (X, Y ) can also be expressed as:
CX,Y = E[√
(x−X)2 + (y − Y )2] (3.2)
=∫ (√
(x−X)2 + (y − Y )2)
f(x, y)dxdy, (3.3)
where E[.] stands for the expected value and f(x, y) denotes the probability density function
of (x, y).
Now, CX,Y will be minimized at (X ′, Y ′) = (∫
xfx(x)dx,∫
yfy(y)dy), the mean of
the distribution, where f is random and uniformly distributed around (x, y), and fx(x) and
fy(y) are the marginal distributions of x and y, respectively.
If users at (xj , yj),∀j ∈ (1, 2, 3, ..., k′i) are independent and identically distributed
(i.i.d.) with density f , then C∗X,Y = 1
k′i∗(∑k′i
j=1
√(xj −X)2 + (yj − Y )2
)approximates
CX,Y for any (X, Y ). Therefore, if (X∗, Y ∗) minimizes C∗X,Y , then (X∗, Y ∗) is close to
(X ′, Y ′) (the mean of the distribution) in probability for large k′i. This justifies our choice
to place the ONU at the mean of the X/Y-coordinates of its premium users.
Now, we will show that the local minimum of our cost function is also the global
Chapter 3: Network Planning and Setup for WOBAN 37
minimum in this case. To do so, we need to find the second-order partial derivatives of our
cost function, C∗X,Y :
DXX =∂2C∗
X,Y
∂2X(3.4)
=1k′j
k′j∑i=1
(yi − Y )2
((xi −X)2 + (yi − Y )2)32
(3.5)
Similarly,
DY Y =∂2C∗
X,Y
∂2Y(3.6)
=1k′j
k′j∑i=1
(xi −X)2
((xi −X)2 + (yi − Y )2)32
(3.7)
And
DXY = DY X =∂2C∗
X,Y
∂X∂Y(3.8)
=1k′j
k′j∑i=1
−(xi −X)(yi − Y )
((xi −X)2 + (yi − Y )2)32
(3.9)
So,
DXX + DY Y > 0 (3.10)
DXXDY Y −D2XY ≥ 0 (3.11)
Since the matrix of second-order partial derivatives of C∗X,Y is non-negative definite
(n.n.d.), our cost function is a convex function in (X, Y ) (necessary and sufficient condition
for a function to be convex). So, the local minimum here coincides with the global minimum.
To find the exact global minimum, we need to solve the Jacobian of the equations,
which will not produce a closed-form solution. This is where Greedy is useful in finding
the location of ONUs close to a global minimum point. Thus, we can achieve an efficient
placement through Greedy. Our analysis is supported by our performance study reported in
the following section, where Greedy outperforms other simple schemes of ONU placements
Chapter 3: Network Planning and Setup for WOBAN 38
Figure 3.1: Performance of various schemes of ONU placement in a WOBAN.
the experiment to place three ONUs in the Wildhorse WOBAN. As expected, Greedy with
initial deterministic placement performs better as we can see the typical cost for three-ONU
placements for various schemes in Figure 3.5.
Figure 3.6 shows the placement of the three ONUs (black triangles) in Wildhorse
WOBAN (as returned by Greedy). Their locations are (Latitude, Longitude): (38.5650N,
-121.7197W), (38.5677N, -121.7254W), and (38.5690N, -121.7171W).
Given this optimal placement, we find the single-hop and multi-hop distribution of
wireless users (see Table 3.3) with respect to each ONU (assuming a WLAN radio capability
of 100 meters).
Chapter 3: Network Planning and Setup for WOBAN 43
Figure 3.6: Placement of 3 ONUs in Wildhorse WOBAN by Greedy (Top left cone: ONU1,Bottom center cone: ONU2, Top right cone: ONU3. Colored dots are residential wirelessusers).
The problem of finding the optimum solution with the cost metric as in Eqn. (1)
does not have any closed-form solution. Although Greedy produces lower costs, it may
be a sub-optimal solution. Thus, in the next section, we reformulate our problem as a
global optimization problem and resort to a popular combinatorial optimization algorithm
— “Simulated Annealing (SA)” — to solve the problem. We show that, although SA can
improve the chances of reaching the global optimum, Greedy performs quite well at a lower
processing requirement, compared to global optimizer.
3.4 Global Optimization of Placements of Multiple ONUs in
WOBAN
Greedy (Algorithm 1) is a heuristic, which performs local optimization of an in-
dividual ONU after the identification of premium users for that ONU. The solution is not
globally optimal. For global optimal, we need a better approach.
Our next approach is to optimize the placement of ONUs globally. We study
a combinatorial-optimization technique, Simulated Annealing. We start with an initial
Chapter 3: Network Planning and Setup for WOBAN 44
solution returned by Greedy and then perturb it by slightly displacing one of the high-cost
ONUs (viz., the ONU with overall maximum average distance to the users it serves, i.e., the
premium users) to see if there is an overall cost improvement. After multiple “successful”
iterations, we hope to achieve the “system equilibrium”. Then, no more perturbation is
expected to produce better results. We compare the solution produced by Greedy with
those produced by SA.
3.4.1 Simulated Annealing (SA)
First proposed by Kirkpatrick, Gellat, and Vecchi [48] in 1983, SA is one of the
most-widely-used combinatorial optimization techniques. Researchers from many diverse
fields have successfully been using SA for optimization. SA is a generalization of the “Monte-
Carlo” method and is known as a probabilistic meta-algorithm (because the basic block of
this algorithm is derived from the Monte-Carlo method). The concept of SA comes from
how liquid freezes or metal recrystalizes, known as the annealing process. This algorithm
has five phases: (1) Initialization, (2) Perturbation, (3) Cost calculation, (4) Acceptance,
and (5) Update, as shown in Algorithm 2 [60].
SA Convergence:
- Inner loop criteria: Given T (temperature), number of iterations until new solutions
stops improving.
- Outer loop/ stopping criteria: when T ∼ 0 (ground/frozen state).
3.4.2 Applying SA to Multiple-ONU Placement Problem of WOBAN
– Initialization Phase: Our search space will be the users’ network, where
objects are equivalent to ONUs, and Sini is the initial placement of ONUs, e.g., the one
returned by the Greedy Algorithm (see Algorithm 1). The purpose of this global optimiza-
tion is to find the minimum average distance of all the users (not only the premium users)
with respect to multiple ONUs. So, apart from an individual ONU cost, we also define the
Chapter 3: Network Planning and Setup for WOBAN 45
Algorithm 2 Simulated Annealing (for optimal deployment of multiple ONUs in aWOBAN)
- Initialization Phase: T = Initial annealing temperature, B = Boltzmann’s constant,Sini = Initial placement of objects, F = Cost function, Cini = Initial cost, andk ∈ [0, 1] = Rate of cooling.
- Perturbation Phase: Generate moves randomly, i.e., relocate objects from one placeto another randomly. After perturbation, we get Snew = New placement of objects.
- Cost-Calculation Phase: Calculate new cost of placements after perturbation,where Cnew = New cost after perturbation.
- Acceptance Phase:
1. Change of cost, dC = Cnew − Cini.
2. Cost function, F (dC, T ) = min(1, e−
dCB∗T
).
3. If dC is negative, F = 1; ACCEPT new placement, Snew. Update initial cost bynew cost, Cini = Cnew.If dC is positive, F ∈ [0, 1]. Generate a random number, r ∈ [0, 1].If r < F , ACCEPT new placement, Snew, update cost, Cini = Cnew; else RE-JECT.
- Update Phase: Update T by its rate of cooling, T = k∗T . Go back to PerturbationPhase for a new move.
Chapter 3: Network Planning and Setup for WOBAN 46
overall network cost as follows:
CiniONUi
= CPrimaryONUi
, (3.12)
Cinioverall =
N∑i=1
CiniONUi
. (3.13)
Equation 3.12 captures the cost of ONUi, which is the cost of premium users
(same as in Eqn. 3.1, CONUi = CPrimaryONUi
) for which the ONU will act as a primary ONU.
Therefore, the overall cost of placing multiple ONUs (Eqn. 3.13) is the sum of the individual
costs of all N ONUs.
– Perturbation Phase: We will relocate the ONUs by a small random input. We employ
a rectangular grid to model the neighborhood’s geography, and move an ONU at most a
single unit only to up, down, left, and right of its coordinates. No diagonal move is allowed.
After perturbation of ONUs, we get Snew = New random placement ONUs.
– Cost-Calculation Phase: We calculate the new cost of ONU placements after pertur-
bation, i.e., CnewONUi
and Cnewoverall.
– Acceptance Phase: 1) If CnewONUi
≤ CiniONUi
, then F = 1, and we ACCEPT the new place-
ment of ONUs, Snew, and update the network costs, CiniONUi
= CnewONUi
and Cinioverall = Cnew
overall.
2) If CnewONUi
> CiniONUi
, then F ∈ [0, 1]. So, we accept the ONU relocation with a certain
probability.
– Update Phase: We update the annealing temperature, T .
3.4.3 Illustrative Numerical Examples: Greedy vs. SA
We study the multiple-ONU placement problem in WOBAN using SA to observe
how the optimum placement could be achieved globally, and how Greedy performs compared
to SA. We have the same range of inputs, varying the number of ONUs (2, 3, 4, 5), area
in sq-meters (1000x1000, 2500x2500, 5000x5000, 7500x7500, 10000x10000), and number of
nodes (100, 250, 500, 750, 1000). Each configuration is repeated 25 times (for a total of
2500 experiments). Simulation parameters for SA have been chosen as shown in Table 3.4
(using our experience after experimenting with various values for these parameters).
In all experiments, SA returns lower WOBAN deployment cost than Greedy (which
Chapter 3: Network Planning and Setup for WOBAN 47
Table 3.4: Simulation parameters for SA.
Initial Annealing Temperature, T 10Boltzmann’s Constant, B 0.01Cooling Rate, k 0.95Inner Loop 100 per TGround State Temperature, T 0.005Outer Loop 190Total Iteration 19000 per move (perturbation)
Figure 3.7: Cost improvement (in meters) in WOBAN for individual ONU deployment withSA (in the test network).
is expected since SA’s starting point is Greedy’s solution). The cost reduction (from SA to
Greedy) for individual ONUs typically varies from 10% to as low as 0.05%. The overall cost
improvement from SA over Greedy is typically under 3%. Thus, we infer that, although SA
returns better solution, Greedy produces quite accurate results as well.
We present an illustrative numerical example of how much SA could improve the
deployment cost vs. Greedy in a test network with 100 users (uniformly and randomly
located) over 1000x1000 sq-meters of area. We deploy four ONUs in the network. Figure 3.7
shows that SA indeed improves the cost of individual ONU deployment (e.g., largest cost
saving from SA is for ONU #1, 6.38% improvement, and smallest cost saving is for ONU
#2, 0.05% improvement) as well as the overall cost of deployment (2.70% improvement).
Chapter 3: Network Planning and Setup for WOBAN 48
Figure 3.8: Cost improvement (in meters) in Wildhorse WOBAN for individual ONU de-ployment with SA.
Figure 3.9: Relocation of 3 ONUs in Wildhorse WOBAN with SA compared to Greedy(Top left: ONU1, Bottom center: ONU2, Top right: ONU3).
Chapter 3: Network Planning and Setup for WOBAN 49
Figure 3.8 captures a similar result for Wildhorse WOBAN, where SA improves the
costs of deployment of three individual ONUs (and, in turn, the overall cost of deployment)
over Greedy. However, the cost improvement of SA over Greedy is marginal.
Figure 3.9 plots the three ONUs placed by SA compared to Greedy in the Wild-
horse WOBAN as described in Section 3.3.1. We observe the solution returned by Greedy
(ONUs indicated by cones) and how the ONUs are relocated by SA (ONUs indicated by
squares) in a practical scenario of 310 residential Wildhorse users (indicated by colored dots).
Locations of ONUs returned by SA are (Latitude, Longitude): (38.5649N, -121.7198W),
(38.5677N, -121.7254W), and (38.5689N, -121.7172W).
Knowing the placement of multiple ONUs by Greedy Algorithm, next we will
compute the expenditure of a WOBAN setup, and compare this with a fully wired access
solution, viz., PON all the way to each user. We argue that WOBAN is a cost-effective
alternative compared to other approaches.
3.5 Cost Comparison of WOBAN and PON Setup in Wild-
horse
Having found the proper placements for multiple ONUs, we compare the expendi-
tures of WOBAN vs. PON solutions in Wildhorse, Davis.
We consider that an OLT is placed in the city’s (Davis) hot-spot, which is located
at the center of the city with an area of nearly 16 square miles. Optical fiber installation is
expensive (USD 100,000 per mile in metropolitan area), and it is reported that about 85%
of this amount is tied to trenching and installing a new duct [61]. The rest (about 15%) of
the expense involves the cost of new fiber and raw materials.
A WOBAN setup involves OLT at the hot-spot, and fiber is laid out from the
OLT to ONUs (which, in turn, drive wireless BSs/routers). ONUs are placed in Wildhorse
according to our Greedy algorithm. In the United States, an estimated 95% of localities are
within 1-1.5 km of fiber-optic infrastructure [61]. So, the Wildhorse locality of Davis is taken
to be within an estimated distance of about 1 km of fiber duct infrastructure. Thus, from
OLT in Davis’ hot-spot to ONUs in Wildhorse, most of the fiber duct is assumed to exist,
Chapter 3: Network Planning and Setup for WOBAN 50
and the new duct in about the last half of a mile (toward ONUs) only needs to be trenched.
From ONUs, wireless technology (either WiFi or WiMAX) provides the connectivity to the
end users in Wildhorse (so, no need for fiber at all).
In a PON setup, OLT-to-ONU infrastructure is similar to a WOBAN. However,
unlike WOBAN, fiber is laid out from ONUs to each user’s home (end-to-end fiber solution).
Again, we consider, from OLT to ONUs, most of the fiber duct has already been trenched,
and the new duct only in about the last half of a mile (toward ONUs) needs to be trenched.
Besides, from ONUs, all new fiber duct needs to be trenched for the fiber drop to each
user’s home.
Table 3.5 shows major components involved for WOBAN and PON setup in brief,
and Table 3.6 shows the expenses of various devices and fiber layout, normalized to the cost
of one ONU unit, which is taken to be USD 100 at the time of this article.1
Table 3.5: Various components of WOBAN and PON expenditure.
OLT-to-ONU fiber (for both WOBAN and PON): half-a-mile new trenching.ONU-to-user fiber (for PON only): all new trenching.
Table 3.6: Device and fiber layout expenses (in normalized units).
Device Cost (1 ONU unit)ONU 1 [62]OLT 50 [62]Fiber (trenching + material + labor and installation) 1000/mile [61]WiFi BS/Router 60 [63]WiMAX BS/Router 100 [64]Customer Premise Equipment (CPE) 1Note: The expenditure reported here is normalized to the cost of one ONU unit.
Note: At the time of writing this dissertation, one ONU unit costs 100 USD.Number of Wildhorse users = 310
Table 3.7 shows present and future (expected) capacities of ONU, WiFi, and
WiMAX devices, and Table 3.8 captures the expenditure of corresponding WOBAN and1The normalized cost is less sensitive to ups and downs of the absolute cost.
Chapter 3: Network Planning and Setup for WOBAN 51
PON solutions. Note that, in a WOBAN solution, we explore the possibilities of both the
WiFi front end and the WiMAX front end. The cost of each solution (for a single Wildhorse
user for one Mbps of bandwidth) reported here is normalized to an estimated present cost
of PON solution.
Table 3.7: ONU, WiFi, and WiMAX capacities.
Device Capacity (Mbps)Present Future
ONU 2500 10000WiFi 54 100 [65]WiMAX 100 1000 [66]
Table 3.8: WOBAN and PON setup expenditures (in normalized units).
Our computation estimates the cost of present PON solutionper Wildhorse user per Mbps of bandwidth to be USD 2.27.
Thus, the present cost of WOBAN with WiFi front endsolution would be USD 0.3304× 2.27 = USD 0.75
for a single user to get one Mbps of bandwidth, and so on.Note: The computations are based on our design criteria,
and the device prices we have chosen.
From Table 3.8, based on our assumptions, we observe that WOBAN is a cost-
effective solution compared to a full PON solution, and it will continue to remain so in the
future. Between WOBAN solutions, as expected, WOBAN with WiMAX setup emerges as
a better choice compared to WOBAN with WiFi.
We also studied the feasibility of an emerging WiMAX access solution from the
CO (an all-wireless access solution, unlike WOBAN and PON), the results of which are not
reported here. We found that, in current scenario, PON is a better solution than WiMAX
access. But, in future, the expenses for WiMAX and PON are found to be similar (not
reported here) [WiMAX (IEEE 802.16m) and PON capacities are expected to reach 1 and
10 Gbps, respectively]. Note that, due to its higher transport capacity, PON will still be
preferred among users with higher bandwidth requirement. Keeping this in mind, we expect
Chapter 3: Network Planning and Setup for WOBAN 52
WOBAN solution (cost effective as well as higher capacity) to dominate the last-mile access
in the future.
A WOBAN is a marriage of two powerful techniques. Thus, to capture the chal-
lenges behind a complete WOBAN setup, we propose and investigate a joint optimization
algorithm, which considers design aspects of both the wireless front end, such as avoiding
interference among neighboring BSs, and the optical back end, such as minimizing expensive
fiber layout, simultaneously.
3.6 Joint Optimization of WOBAN: Combined Heuristic (CH)
We have optimized the placements of multiple ONUs so that users’ average dis-
tance from their premium ONU gets minimized. This is essentially focused on the wireless
front-end optimization. The efficient fiber layout in the back end (from OLT to ONUs) has
not been considered. Also, it assumes an ideal situation with no interference among wireless
BSs (or wireless routers). Therefore, this section involves proposing and investigating the
characteristics of a joint optimization algorithm, which considers the design interplay be-
tween both optical and wireless domains together (and the results from Greedy will be used
for our joint optimization algorithm to place ONUs). A proper pre-deployment optimization
strategy can actually save expensive optical and wireless resources needed for a “greenfield”
deployment2 of this type of network. Thus, we propose a Combined Heuristic (CH) model
that focuses on the placements of BSs (on the basis of interference), placements of ONUs
(as returned by Greedy Algorithm), and the minimum-cost fiber layout from OLT/CO to
ONUs in the back end simultaneously (see Algorithm 3).
Note that an additional challenge in deploying WOBAN lies in co-channel in-
terference among neighboring BSs, which are in close proximity. Co-channel interference
arises when two neighboring BSs use the same wireless channel to communicate at the same
time. This will reduce the maximum number of users a BS and its ONU can support. The
co-channel interference will deteriorate the signal quality. If the signal quality is below a
certain threshold (called Carrier-to-Interference threshold or CI threshold), then no trans-2The “greenfield” deployment of a network considers that no prior infrastructure exists.
Chapter 3: Network Planning and Setup for WOBAN 53
mission is possible. In order to deal with the co-channel interference, CH carefully plans
the placements of nearby BSs.
The Combined Heuristic (CH) models the BS’s “footprint” (or transmission area)
as a hexagonal cell (similar to the concept of modeling a cellular architecture) [67]. Given
the number of available wireless channels and the CI threshold, CH determines the number
of BSs needed for proper communications without interference.
In CH, based on the channel reuse criteria, a cell and its neighboring cells can not
use the same channel due to interference. The set of neighboring cells that do not use the
same channel is known as a cluster. For example, if a cluster size is 7, each cell and its six
neighboring cells should use different channels, and the same channel can only be reused
beyond these cells. The channel reuse distance is√
3NR, where N is the cluster size and
R is the cell radius (or transmission radius of the BS). Assuming that only surrounding
BSs can interfere with each other, Table 3.9 estimates the number of BSs needed to serve
a number of users (for example 800 wireless users) with 50 available wireless channels that
can be assigned to these users.
Table 3.9: Estimation of channel interference and number of BSs by CH.
In Table 3.9, cluster size (N) is computed by N = u2 + uv + v2, where u and v
are non-negative integers. Assuming an BS can interfere only with its six surrounding BSs,
and the wireless signal attenuation factor is 4, then CI can be computed by CI= (√
3N)4
6 .
When all the BSs in the same cluster share the available channels, each BS can get at
most 50/N number of channels. Therefore, we need at least(
800N50
)number of BSs to serve
all 800 users. This is the minimum number of BSs computed on the basis of co-channel
interference threshold. CH deploys these BSs uniformly, determines their transmission
radius, and assigns channels to them so that there is no CI violation. After deploying BSs,
CH determines the number of ONUs needed to support BSs and deploys ONUs according
Chapter 3: Network Planning and Setup for WOBAN 54
to our Greedy Algorithm (see Algorithm 1). Finally, CH finds a minimum-cost spanning
tree (MST) to lay fiber from OLT to all the ONUs, and calculates the total WOBAN setup
cost based on the design.
Algorithm 3 Combined Heuristic (CH) (for joint optimization in WOBAN in a “greenfield”deployment)
1. Begin
2. Construct a channel interference table (see Table 3.9).
3. Derive minimum # of BSs, based on CI threshold (see Table 3.9).
4. Deploy these BSs uniformly in the area.
5. Assign channels to BSs to serve users.
6. Determine transmission radius (R) of each deployed BS.
7. If (All users are within BSs’ “footprint”)
8. Go to Step 13.
9. Else
10. Deploy additional BSs.
11. Assign channels to them without violating existing CI constraints.
12. End If
13. Deploy ONUs according to Greedy Algorithm (see Algorithm 1).
14. Construct a Minimum-cost Spanning Tree (MST) from OLT to ONUs to lay fiber.
15. Calculate design cost, based on # of BSs, # of ONUs, and fiber layout.
16. End
3.6.1 Illustrative Numerical Examples: CH
We placed 800 users randomly in an area of 5 × 5 square-miles. We assumed
an OLT to be located at (0, 0). We chose WiMAX as the front end wireless solution for
WOBAN. There are 50 available channels, and each channel operates at 20 MHz. In non-
line-of-sight (NLOS) WiMAX communication, when the channel operates at 20 MHz, the
maximum transmission radius can reach up to 5 miles [68, 69]. The maximum capacity for
each BS and ONU was set as 1 Gbps and 10 Gbps, respectively. Device and fiber layout
Chapter 3: Network Planning and Setup for WOBAN 55
costs are chosen according to Table 3.6.
Figure 3.10 shows the overall expenditure of a “greenfield” deployment of the
WOBAN by our joint optimization algorithm. The user coverage ratio captures what frac-
tion of users among the population needs to be served. With low user coverage ratio, it
is intuitive that fewer BSs and ONUs would be needed. In Fig. 3.10, we observe that the
WOBAN deployment cost is less for a lower user coverage ratio. The threshold of CI is set
at 12 dB, and the number of available channels is chosen as 50.
Note that WOBAN deployment cost is normalized to one ONU cost, which is taken
to be USD 100 at the time of this study.
Figure 3.10: WOBAN setup cost (normalized to one ONU unit cost) by Combined Heuristic(CH).
We will report more experimental results on CH in our next chapter and compare
the solution of CH with a constraint programming model.
3.7 Summary
This chapter investigated the problem of optimal placements of multiple ONUs in
a WOBAN. We first studied a simple algorithm (Greedy) for placing the multiple ONUs.
We formulated and analyzed the solution. We conducted a survey of existing wireless users
Chapter 3: Network Planning and Setup for WOBAN 56
in the Wildhorse neighborhood of North Davis, and then compared the performance of
various schemes (Greedy vs. random vs. deterministic) and network configurations. We
demonstrated a suitable placement of 3 ONUs in a real neighborhood of wireless users, viz.,
Wildhorse, Davis, with our Greedy algorithm.
We also investigated the problem of multiple-ONU placement using a combinato-
rial optimization algorithm, viz., simulated annealing (SA). We measured the accuracy of
Greedy vs. global optimizer. We found that Greedy performs very well in minimizing the
network cost, but at much lower processing requirements.
After getting the proper locations for ONUs, we compared the expenditures of a
WOBAN vs. a full wired access solution, namely PON. We demonstrated that WOBAN
is a cost-effective broadband access network alternative. To capture the challenges behind
a complete WOBAN setup, we proposed and investigated the characteristics of a joint
optimization algorithm [Combined Heuristic (CH)]. CH expounds on the design aspects of
both the wireless front end, such as avoiding interference among neighboring BSs, and the
optical back end, such as minimizing expensive fiber layout.
57
Chapter 4
Constraint Programming Model
for WOBAN Deployment
4.1 Introduction
Our prior work in Chapter 3 reported on simple, yet efficient approaches, viz.
greedy algorithm, simulated annealing, and combined heuristic for WOBAN deployment.
In these approaches, minimizing average distance (from ONU to users) is the optimization
metric, and other aspects of WOBAN deployment (such as ONU and BS capacities, user as-
signment, channel assignment, etc.) were not considered. (These terms will become clearer
later in this chapter.) Therefore, a sophisticated deployment approach should capture the
design interplay between various aspects of a WOBAN. Additionally, a “good” estimation
model of deployment cost of a WOBAN should be very important to a network designer.
To tackle this challenging problem, in this chapter, we propose and investigate the
characteristics of a constraint programming model (called Primal Model or PM) with the
deployment cost as an optimization metric. We identify six sets of constraints, viz., user
assignment constraints, BS installation constraints, ONU installation constraints, capacity
constraints, channel assignment constraints, and signal-quality and interference constraints.
For analytical tractability of this PM, we relax a few constraints (“Lagrangean Relaxation”)
to transform the problem to the corresponding “Lagrangean Dual” problem. Then, we
Chapter 4: Constraint Programming Model for WOBAN Deployment 58
solve the dual problem to obtain a lower bound on the primal problem (i.e., PM without
relaxation). We also develop an algorithm (called Primal Algorithm) to solve the PM and
obtain its upper bound. By measuring the “duality gap”, which is the difference between
the solution to the primal problem and the solution to its Lagrangean dual problem, we
verify the accuracy of our formulation. Then, we explore how the “Combined Heuristic
(CH)”, a joint deployment algorithm developed in Chapter 3, performs compared to this
optimal analytical model.
The rest of the study is organized as follows. In Section 4.2, we briefly discuss
WOBAN’s design aspects that needs to be considered. In Section 4.3, we present the ana-
lytical formulation (Primal Model) and its solution approach by “Lagrangean Relaxation”
and Primal Algorithm. Section 4.4 contains performance studies of the PM and Section 4.5
summarizes this work.
4.2 Design Criteria for WOBAN
With the advances in wireless technologies, IEEE 802.11a/b/g (WiFi) deploy-
ments, which are very common, can support up to 54 Mbps today; and the emerging IEEE
802.16 (WiMAX) can support much higher data rates (∼ 100 Mbps) over a long distance.
In WOBAN, gateway BSs are associated with ONUs with fiber; so each user can connect to
the back end PON infrastructure via wireless channels. Then, WOBAN can save a major
part of the deployment cost, which is the high cost of laying fiber in the “last mile” from
CO to user. In addition, due to high ONU capacity (e.g., 1 Gbps to 10 Gbps), one ONU can
support multiple BSs; and a BS, in turn, can support multiple users via wireless channels.
WOBAN can also leverage a wireless network’s flexibility; i.e., the “anytime-anywhere”
approach.
In the WOBAN architecture, the deployment cost of the optical part of this net-
work is much higher than its wireless counterpart. Besides the deployment cost, the deploy-
ment time for the optical part of WOBAN is longer than its wireless part. Therefore, to
keep minimum fiber penetration, the wireless part of the network should provide coverage
as far as possible. In other words, one ONU needs to support more wireless BSs. However,
Chapter 4: Constraint Programming Model for WOBAN Deployment 59
this kind of design strategy must be careful to meet the following criteria.
- How to cope with the increasing user traffic demands:
As the user’s traffic demand grows, we need to deploy additional BSs to serve this
demand. However, due to the capacity constraint of an ONU, the number of BSs that
an ONU can support is limited. Therefore, unless carefully planned, the increasing
traffic demand may not be properly served.
- How to avoid co-channel interference among BSs:
The frequency spectrum in a wireless network is a limited and valuable resource. If
two adjacent BSs (or BSs in close proximity) use the same channel to serve their users,
they will incur co-channel interference. Since the co-channel interference deteriorates
the signal quality, it reduces the maximum number of users a BS and an ONU can sup-
port. If the signal quality is below a certain threshold (called Carrier-to-Interference
threshold or CI threshold), then users’ information (such as data packets) will be
dropped. In order to deal with the co-channel interference, channel assignment for
users communicating with BSs should be carefully planned in a WOBAN design.
Note that there is a tradeoff between WOBAN’s deployment cost and its perfor-
mance. Hence, how to minimize the deployment cost without degrading the performance
is a challenging task. Given the user traffic demands and the signal quality requirements,
several decisions should be made (details of which are elaborated in Section 4.3).
- BS location and its transmission radius:
That is, where to deploy the BSs and how to determine their coverage area (or assign
transmission radius) to satisfy the user traffic demand and avoid interference at the
same time.
- User homing decision:
That is, which BS should serve a user to satisfy user’s bandwidth requirement.
- Carrier-to-Interference ratio for channel assignment:
A BS’s channel assignment should avoid co-channel interference, which is captured by
Chapter 4: Constraint Programming Model for WOBAN Deployment 60
Carrier-to-Interference ratio (CI ratio). Unlike the conventional approach to assign
different non-overlapping channels to nearby BSs, which may result in poor channel
utilization and throughput, we tackle this issue with a more sophisticated approach
utilizing Carrier-to-Interference (CI) ratio. CI ratio is also linked with signal quality
and bit-error rate (BER). The higher the CI ratio, the lower is the BER and vice
versa (see Section 4.4 for more information).
- ONU location and fiber link deployment:
The deployment of the optical part of the network should minimize the deployment
cost and meet the BS’s traffic demands.
4.3 Mathematical Formulation for Optimal Placement of BSs
and ONUs
This study focuses on the optimal placement of BSs and ONUs in the front end,
and the fiber layout from BSs to ONUs and from ONUs to OLT/CO in the back end of a
WOBAN. In our mathematical formulation of this optimization problem, we consider the
cost of ONUs and BSs, though our performance studies (in Section 4.4) indicate that the
cost of laying fiber in a WOBAN is more significant than the costs of various devices. Also
note that more ONUs can lead to additional OLT installation cost, because an OLT can
generally drive a fixed number of ONUs. Therefore, additional OLTs will increase the cost
of a WOBAN solution considerably as OLTs are expensive.
We propose and investigate a “Primal Model (PM)” formulation, which is a pre-
deployment network-optimization scheme, where the cost of WOBAN design is minimized
(by placing reduced number of BSs and ONUs, and planning an efficient fiber layout).
We also examine the interference among multiple BSs, and explore several installation and
assignment constraints that have to be satisfied for a better-quality access solution and
increased coverage. Our proposed model (PM) for WOBAN placement and its solution
approach by “Lagrangean Relaxation” are shown below.
Chapter 4: Constraint Programming Model for WOBAN Deployment 61
Given Parameters:
L: set of possible locations for BSs1,
O: set of possible locations for ONUs,
Θi (Bi): installation cost of a BS at location i,
Λk (Uk): installation cost of an ONU at location k,
Φik (Zik): fiber installation cost from BS i to ONU k,
T : set of users,
Kr: traffic demand of user r,
F : set of available wireless channels,
A: upper bound on number of channels assigned to a BS,
Ei: maximum capacity of BS at location i,
ρ: fraction of users served by BSs (user coverage ratio),
Dri: distance between user r and BS at location i,
Ψ (Dri): supported bandwidth (in Mbps) to user r from BS i with distance Dri,
Γ: discrete set of possible transmission radius of BS,
J ′: upper bound of decision variable Jk,
R′: upper bound of decision variable Ri,
I: threshold of Carrier-to-Interference (CI) ratio, and
G: an arbitrarily large number.
1Here ”locations” mean cross-points on a square grid.
Chapter 4: Constraint Programming Model for WOBAN Deployment 62
Decision Variables:
Bi: 1, if a BS is installed at location i, and 0 otherwise,
Uk: 1, if an ONU is installed at location k, and 0 otherwise,
Zik: 1, if an ONU at location k is connected to a BS at location i, and 0 otherwise,
Xji: 1, if channel j is assigned to BS at location i, and 0 otherwise,
Yri: 1, if user r is assigned to BS at location i, and 0 otherwise,
Jk: capacity of ONU at location k,
Ri: transmission radius of BS at location i, and
Iii′: interference factor of BS at locations i′ on BS at location i (Iii′ =(
Ri′Dii′
)4where Dii′
is the distance between BSs at i and i′).
Objective Function of Primal Model:
CPM = Min
(∑k∈O
Λk (Uk) +∑i∈L
Θi (Bi) +∑i∈L
∑k∈O
Φik (Zik)
)(4.1)
The objective (CPM ) is to minimize the sum of the following items: installation
cost for all ONUs required, plus installation cost for all BSs required, plus cost of connecting
BSs to an ONU by fiber. These three items are the major costs involved in configuring a
WOBAN. As discussed before, for analytical tractability, we relax a few challenging con-
straints (constraints are described later) in Section 4.3.1 to transform the primal model
(CPM ) to the corresponding Lagrangean dual problem (CLR).
Constraints:
Below are the constraints that need to be satisfied in the Primal Model. The goal of the
first set of constraints is to enforce user assignment constraints. Constraint 1 captures the
binary decision variable Yri. Each user is at most associated with only one BS (Constraint
Chapter 4: Constraint Programming Model for WOBAN Deployment 63
2), and at least ρ (ρ ≤ 1) fraction of total number of users needs to be served by BSs
(Constraint 3).
1. Yri = 0 or 1 ∀r ∈ T, i ∈ L,
2.∑
i∈L Yri = 1 ∀r ∈ T , and
3.∑
r∈T
∑i∈L Yri ≥ ρ|T | ∀r ∈ T, i ∈ L.
The goal of the second set of constraints is to enforce BS installation constraints. Constraint
4 specifies that the decision variable Bi must be binary. A BS must be installed first before
a user can be assigned to it (Constraint 5). In addition, the distance between user r and
BS i must be within the transmission radius of BS i (Constraint 6). The non-negativity
constraints of decision variable Ri are captured by Constraints 7 and 8. Constraint 9 is
used to enforce that the transmission radius of a BS should be a discrete set.
4. Bi = 0 or 1 ∀i ∈ L,
5. Yri ≤ Bi ∀r ∈ T, i ∈ L,
6. DriYri ≤ Ri ∀r ∈ T, i ∈ L,
7. Ri ≤ R′Bi ∀i ∈ L,
8. 0 ≤ Ri ∀i ∈ L, and
9. Ri ∈ Γ ∀i ∈ L.
The goal of the third set of constraints is to enforce channel assignment constraints of BS.
Constraint 10 specifies that the decision variable Xji must be binary. In WiFi or WiMAX
technology, the channel can be CDMA codes or TDMA time slots in wireless frequency
bands. Therefore, Constraint 11 indicates that the number of channels assigned to each BS
is large enough to serve its users. Constraint 12 indicates that BS must be installed first
before channel assignment. Constraint 13 indicates that the number of channels assigned
to a BS should not exceed the upper bound of channels assigned to any BS.
10. Xji = 0 or 1 ∀j ∈ F, i ∈ L,
Chapter 4: Constraint Programming Model for WOBAN Deployment 64
11.∑
r∈T Yri ≤∑
j∈F Xji ∀i ∈ L,
12. Xji ≤ Bi ∀j ∈ F, i ∈ L, and
13.∑
j∈F Xji ≤ A ∀i ∈ L.
The fourth set of constraints captures the ONU installation constraints. Constraints 14 and
15 specify that the decision variables Zik and Uk, respectively, must be binary. Constraint
16 indicates that an ONU must be installed first before any BS can be connected to it.
Each BS should be connected to only one ONU, which can be captured by an equality∑k∈O Zik = Bi, where ∀i ∈ L. This equality can be broken into two inequalities such as
Constraints 17 and 18.
14. Zik = 0 or 1 ∀i ∈ L, k ∈ O,
15. Uk = 0 or 1 ∀k ∈ O,
16. Zik ≤ Uk ∀i ∈ L, k ∈ O,
17.∑
k∈O Zik ≤ Bi ∀i ∈ L, and
18. Bi ≤∑
k∈O Zik ∀i ∈ L.
The fifth set of constraints enforces capacity constraints of BSs and ONUs. Constraint
19 enforces that the maximum bandwidth of user r from BS i satisfies the user’s traffic
demand. Constraint 20 indicates that a BS should be able to manage its users’ aggregate
traffic demands. Constraint 21 enforces that the capacity of each ONU is large enough to
serve all traffic introduced by its associated BSs. The non-negativity constraints of decision
variable Jk are captured by Constraints 22 and 23.
19. Kr ≤ Ψ(Dri) Yri ∀r ∈ T, i ∈ L,
20.∑
r∈T Ψ(Dri) Yri ≤ Ei ∀i ∈ L,
21.∑
i∈L EiZik ≤ Jk ∀k ∈ O,
22. Jk ≤ J ′Uk ∀k ∈ O, and
Chapter 4: Constraint Programming Model for WOBAN Deployment 65
23. 0 ≤ Jk ∀k ∈ O.
The goal of the sixth set of constraints is to enforce signal quality constraints for each user.
Since co-channel interference will significantly impact the signal quality, we need to take this
into account when we decide on the channel assignment for each BS. In Constraint 24, the
left-hand side is the total co-channel interference introduced by other BSs using the same
channel j to BS at i. In Constraint 24, when Xji = 0, the right-hand side will be equal to
G (a very large number). This makes Constraint 24 to be always satisfied. However, when
Xji = 1, the right-hand side will be equal to 1I . Hence, we can guarantee the signal quality
to be at least the threshold of acceptable CI ratio. Constraints 25 is the non-negativity
constraint of decision variable Iii′ .
24.∑
i′∈L,i′ 6=i Iii′Xji′ ≤ G +(
1I −G
)Xji ∀i ∈ L, j ∈ F , and
25. 0 ≤ Iii′ ∀(i, i′) ∈ L, i 6= i′.
4.3.1 Lagrangean Relaxation and Lower Bound of Primal Model (PM)
This Primal Model (PM) formulation is very challenging since we need to carefully
plan the locations of BSs and ONUs, the transmission radius of BSs, the channel assignment
of BSs, the assignment of users to BS, and the assignment of BSs to ONU in order to satisfy
the traffic requirement and signal-quality requirement of users at minimum cost.
We apply the Lagrangean Relaxation (LR) method to relax some of the constraints
of our formulation. For analytical tractability, we relax those constraints that make the PM
hard. After the relaxation, we get the Lagrangean dual problem. The solution to this
dual problem is the lower bound to the primal problem. On the other hand, by developing
the Primal Algorithm, we can obtain feasible solutions which give the upper bound to the
primal problem. The Primal Algorithm (see Section 4.3.2) is designed such that it can
obtain the upper bound of the primal problem quickly. By measuring the duality gap, i.e.,
the gap between the upper bound and the lower bound of our model, we can determine how
optimal the solutions are.
Next, we relax the ten Constraints 5, 6, 11, 12, 17, 18, 20, 21, 22, and 24. The
intuition behind relaxing these ten constraints is that they make the Primal Model “hard”
Chapter 4: Constraint Programming Model for WOBAN Deployment 66
to solve, and after relaxation, the Lagrangean dual model will be analytically tractable.
The more we relax these constraints to make the Primal Model simpler, the larger will be
the duality gap. Then, the obtained solution to the primal problem will be too far from
its optimal solution. On the other hand, if we relax too few constraints, we may not be
able to solve the Lagrangean dual problem optimally. Then, the solution obtained to the
dual problem will not produce the true lower bound of the primal problem. Hence, how to
relax the minimum number of constraints to get the correct and tight duality gap between
the lower bound and the upper bound solutions is very important in Lagrangean relaxation
scheme. Next, we will show how relaxing the above-mentioned ten constraints will provide
an optimal solution to the our Lagrangean dual problem and a tighter duality gap.
So, the Lagrangean dual problem (CLR) becomes:
CLR (µ) = Min∑k∈O
Λk (Uk) +∑i∈L
Θi (Bi) +∑i∈L
∑k∈O
Φik (Zik) ... (4.2)
+∑i∈L
∑r∈T
µ1ir (Yri −Bi) +
∑i∈L
∑r∈T
µ2ir (DriYri −Ri) ...
+∑i∈L
µ3i
∑r∈T
Yri −∑j∈F
Xji
+∑i∈L
∑j∈F
µ4ij (Xji −Bi) ...
+∑i∈L
µ5i
(∑k∈O
Zik −Bi
)+∑i∈L
µ6i
(Bi −
∑k∈O
Zik
)...
+∑i∈L
µ7i
(∑r∈T
Ψ(Dri) Yri − Ei
)+∑k∈O
µ8k
(∑i∈L
EiZik − Jk
)...
+∑k∈O
µ9k
(Jk − J ′Uk
)+∑i∈L
∑j∈F
µ10ij
∑i′∈L,i′ 6=i
Iii′Xji′ −G−(
1I−G
)Xji
,
subject to Constraints 1, 2, 3, 4, 7, 8, 9, 10, 13, 14, 15, 16, 19, 23, and 25. Note that the
µn’s (µn ≥ 0,∀n ∈ [1, 10]) are known as “Lagrangean multipliers”.
We can decompose CLR into five independent subproblems (viz., CS1, CS2, CS3,
CS4, and CS5) and the terms with given parameters Ei and G. Subproblems are the smaller
blocks of problems for a large problem, such as CLR, and each subproblem contains one or
Chapter 4: Constraint Programming Model for WOBAN Deployment 67
multiple decision variable(s). So, Eqn. (4.2) becomes:
CLR (µ) = CS1 + CS2 + CS3 + CS4 + CS5 −∑i∈L
µ7i Ei −
∑i∈L
∑j∈F
µ10ij G. (4.3)
The five subproblems are as follows.
- Subproblem 1: for Bi and Ri
CS1 = Min∑i∈L
Θi (Bi)−∑i∈L
∑r∈T
µ1irBi −
∑i∈L
∑j∈F
µ4ijBi... (4.4)
−∑i∈L
(µ5
i − µ6i
)Bi −
∑i∈L
∑r∈T
µ2irRi,
subject to Constraints 4, 7, 8, and 9.
We can further decompose Subproblem 1 into |L| independent subsubproblems.
So, for BS at location i ∈ L, Subproblem 1 becomes:
Min Θi (Bi)−
∑r∈T
µ1ir +
∑j∈F
µ4ij + µ5
i − µ6i
Bi −∑r∈T
µ2irRi, (4.5)
subject to Constraints Bi = 0 or 1, Ri ≤ R′Bi, 0 ≤ Ri, and Ri ∈ Γ.
We can observe that, if we assign Bi = 0, then Ri = 0 and the objective value
of the subproblem is zero as well. On the other hand, if we assign Bi = 1, we can as-
sign Ri = R′ and this will lead to the smallest objective value (since the coefficient of
Ri is negative for a non-negative µ2ir). Then, the objective value is equal to Θi (Bi) −(∑
r∈T µ1ir +
∑j∈F µ4
ij + µ5i − µ6
i
)−∑
r∈T µ2irR
′. If this objective value is smaller than
zero, then the optimal solution is to assign Bi = 1 and Ri = R′; otherwise, the optimal
solution is to first assign Bi = 0 and then Ri = 0. The time complexity of solving this
subproblem is on the order of (|T |+ |F |) for each BS i.
- Subproblem 2: for Uk and Zik
CS2 = Min∑k∈O
Λk
(Uk − µ9
kJ′Uk
)+∑i∈L
∑k∈O
(Φik (Zik) +
(µ5
i − µ6i + µ8
kEi
)Zik
), (4.6)
Chapter 4: Constraint Programming Model for WOBAN Deployment 68
subject to Constraints 14, 15, and 16.
Similarly, we can further decompose Subproblem 2 into |O| independent subsub-
problems. So, for ONU at location k ∈ O, Subproblem 2 becomes:
Min Λk (Uk)− µ9kJ
′Uk +∑i∈L
(Φik (Zik) +
(µ5
i − µ6i + µ8
kEi
)Zik
), (4.7)
subject to Constraints Zik = 0 or 1 ∀i ∈ L, Uk = 0 or 1, and Zik ≤ Uk ∀i ∈ L.
When Uk = 0, all the corresponding decision variables Zik will be zero. Then, the
objective value of the subproblem will be zero as well. If Uk = 1, then some of the Zik’s
will be one. In this case, we will only select those Zik’s that have negative coefficient, i.e.,(µ5
i − µ6i + µ8
kEi
)< 0. Consider, for i ∈ L′, L′ ⊆ L, ω =
∑i∈L′
(µ5
i − µ6i + µ8
kEi
)Zik < 0.
Now, if Λk (Uk) − µ9kJ
′Uk +∑
i∈L′ Φik (Zik) + ω < 0, then we will assign Uk = 1, Zik = 1
∀i ∈ L′, and Zik = 0 ∀i /∈ L′, where L′ ⊆ L. Otherwise, we will get optimal solution at
Uk = 0 and Zik = 0 ∀i ∈ L. The time complexity of solving Subproblem 2 is on the order
of (|L|) for each ONU k.
- Subproblem 3: for Jk
CS3 = Min∑k∈O
(µ9
k − µ8k
)Jk, (4.8)
subject to Constraint 23.
Similarly, we can further decompose Subproblem 3 into |O| independent subsub-
problems. So, for ONU at location k ∈ O, Subproblem 3 becomes:
Min(µ9
k − µ8k
)Jk, (4.9)
subject to Constraint 0 ≤ Jk.
For each ONU k, if the coefficient of Jk is negative, i.e.,(µ9
k − µ8k
)< 0, then we
will assign Jk to its maximum value, i.e., Jk = J ′ to minimize the objective value of the
subproblem, else assign Jk = 0. The time complexity of solving Subproblem 3 is on the
order of (1) for each ONU k.
Chapter 4: Constraint Programming Model for WOBAN Deployment 69
- Subproblem 4: for Yri
CS4 = Min∑i∈L
∑r∈T
(µ1
ir + µ2irDri + µ3
i + µ7i Ψ(Dri)
)Yri, (4.10)
subject to Constraints 1, 2, 3, and 19.
For each user r ∈ T , since the possible number of BS locations is finite and fixed,
we can exhaustively examine each BS. Then, we identify the set of BSs that can satisfy the
maximum bandwidth requirement.
Among those BSs, we choose the one with the smallest(µ1
ir + µ2irDri + µ3
i + µ7i Ψ(Dri)
)value. Then, we will select ρ|T | number of users to be served by those BSs. The time com-
plexity of solving this subproblem is on the order of (|T ||L|).
- Subproblem 5: for Iii′ and Xji
CS5 = Min∑i∈L
∑j∈F
(µ4
ij − µ3i −
(1I−G
)µ10
ij
)Xji +
∑i∈L
∑j∈F
∑i′∈L,i′ 6=i
µ10ij Iii′Xji′ , (4.11)
subject to Constraints 10, 13, and 25.
After performing variable changing (Xji′ as Xji), we can decompose Subproblem 5
into |L| independent subsubproblems. So, for BS at location i ∈ L, Subproblem 5 becomes:
Min∑j∈F
µ4ij − µ3
i −(
1I−G
)µ10
ij +∑
i∈L,i6=i′
µ10i′jIi′i
Xji, (4.12)
subject to Constraints Xji = 0 or 1 ∀j ∈ F ,∑
j∈F Xji ≤ A, and 0 ≤ Ii′i.
The transmission radius of each BS is a discrete and finite set. So, for each
transmission radius assignment, the interference factor Ii′i can be precomputed. Therefore,
Xji is the only decision variable in Subproblem 5. Since the number of channels assigned
to the BS at location i can not exceed A, we can choose at most A channels. Being a finite
set, we can exhaustively try all possible transmission radius assignments to determine the
minimum cost one. The scheme for solving Subproblem 5 optimally is as follows, with the
time complexity on the order of (|L||Γ|).
Chapter 4: Constraint Programming Model for WOBAN Deployment 70
I. Initialize set S = Null .
II. Until all transmission radius assignments have been taken into account, for a transmis-
sion radius Ri, calculate Ii′i, and do the following.
III. For channel j, calculate coefficient(µ4
ij − µ3i −
(1I −G
)µ10
ij +∑
i∈L,i6=i′ µ10i′jIi′i
).
IV. For all possible channel assignments in j ∈ F ,
calculate∑
j∈F
(µ4
ij − µ3i −
(1I −G
)µ10
ij +∑
i∈L,i6=i′ µ10i′jIi′i
). Find which of these chan-
nel assignments produces the smallest coefficient.
Assume for a particular channel assignment j ∈ ξ, the coefficient will be the minimum,
smin =∑
j∈ξ
(µ4
ij − µ3i −
(1I −G
)µ10
ij +∑
i∈L,i6=i′ µ10i′jIi′i
).
V. S = S ∪ {smin}.
VI. Change the transmission radius Ri ← (Ri + ∆(Ri)) ∈ Γ. Go back to Step II.
VII. After getting all the smallest coefficient values for possible Ri’s, find Min (S) and let
the corresponding channels Xji = 1 ∀j ∈ ξ.
Note that the Lagrangean Relaxation technique helps us to successfully solve a
non-convex formulation of Subproblem 5.
According to the weak Lagrangean duality theorem [70, 71] (which says “for any
given set of nonnegative multipliers, the optimal objective function value of the Lagrangean
dual problem is a lower bound on the optimal objective function value of the corresponding
primal problem”), solving CLR (µ) will give the lower bound (LB) of CPM . Based on above
observations for each subproblem, we can solve the Lagrangean dual problem (CLR (µ))
optimally by using the subgradient method to get the tightest lower bound (LB) [72,73] (see
Section 4.3.3 for details).
4.3.2 Primal Algorithm and Upper Bound of Primal Model
Though the solution to the Lagrangean dual problem (CLR (µ)) is not an exact
solution (since some of the constraints of the PM have been relaxed), it can serve as a
Chapter 4: Constraint Programming Model for WOBAN Deployment 71
good starting point to get a feasible solution. The basic idea of the Primal Algorithm is to
install the BSs that can serve more users under the capacity constraints and interference
constraints until at least a fraction of the total number of users is covered (Constraint 3).
Then, we will deploy the minimum number of ONUs to satisfy the traffic demands from
BSs. Figure 4.1 shows the schematic of the Primal Algorithm, which will give the upper
bound (UB) of CPM .
We identify the sequence of channels to be assigned to users in order not to violate
the co-channel interference constraints in Step 2 of the algorithm. This is because users
at close proximity should be assigned non-interfering channels simultaneously to reduce
cross-talk; the same channel can only be reassigned to users far apart from each other
(channel reuse). The non-negative Lagrangean multiplier µ10ij has a physical significance of
co-channel interference violation cost. Therefore, we can determine the sequence of channel
assignment for BS i by sorting µ7ij in ascending order.
In Step 4, we examine the capacity constraint of BS (i.e., Constraint 20). In Step 5,
we examine the co-channel interference constraint (i.e., Constraint 24). If these constrains
are satisfied, then we assign one channel to the user; otherwise, we continue to examine
the other unvisited (unassociated) users. In Step 8, if Constraint 3 is not satisfied, we add
a new BS to cover unvisited users. After Constraint 3 is satisfied, we can assign ONUs
to cover all the traffic demands from installed BSs (Constraint 21). After the ONUs are
identified, we construct a minimum-cost spanning tree (MST) to layout fibers from OLT to
reach all ONUs and BSs.
4.3.3 Computing Upper Bound (UB) and Lower Bound (LB) of Primal
Model
Next, we show how to compute the UB (solution produced by Primal Algo-
rithm, see Section 4.3.2) and the LB (solution produced by Lagrangean relaxation, see
Section 4.3.1) of our PM formulation. We use the subgradient method as given below, where
quiescence age is incremented if CLR (µ) does not improve. When quiescence age becomes
quiescence threshold, step size coefficient (or δ) becomes halved for the next iteration. The
Chapter 4: Constraint Programming Model for WOBAN Deployment 72
Figure 4.1: Primal Algorithm schematic (“T” means True, “F” means False).
Chapter 4: Constraint Programming Model for WOBAN Deployment 73
complexity of this method for each iteration is on the order of (|L|(|L||Γ|+ |F |log|F |+ |T |)).
4.4 Performance Study
We conducted several computational experiments to test the solution quality and
effectiveness of our approach. In this study, we set max iteration and quiescence threshold
as 1000 and 30, respectively (using our experience after experimenting with various values
for these parameters). We initialized step size coefficient (or δ) as 2.
We placed 800 users randomly in an area of 5× 5 square-miles. We assumed OLT
to be located at (0, 0). We chose WiMAX as the front-end wireless solution for WOBAN.
There are 50 available channels, and each channel operates at 20 MHz. In non-line-of-
sight (NLOS) WiMAX communication, when the channel operates at 20 MHz, we can get
a maximum data rate of 75 Mbps with a maximum transmission radius of 5 miles [68].
WiMAX supports adaptive modulation schemes to adjust its data rates as needed inside
a BS’s coverage area. More sophisticated modulation scheme (e.g., 64 QAM) are used in
inner-most zone of the coverage area to provide better signal quality, which, in turn, leads to
higher throughput and lower BER. On the other hand, moderate modulation schemes (e.g.,
QPSK, BPSK, etc.) are adopted in the outer zones of a BS’s coverage area [69]. Table 4.1
shows typical values of Carrier-to-Interference ratios (CI) in order to ensure a BER of 10−6
Note: The expenditure reported here is normalized to the cost of one ONU unit.Note: At the time of writing this dissertation, one ONU unit cost is taken as 100 USD.
From Table 4.2, we infer that Θi (Bi) for each BS i and Λk (Uk) for each ONU k are
set to 10000 USD and 100 USD (US Dollar), respectively [62, 64]. Φik (Zik) for connecting
BS i and ONU k is determined by the cost of laying fiber, which is chosen to be 100000
USD/mile [61,75]. [For the sake of completeness of this study, we also show the normalized
cost of an OLT and a WiMAX Customer Premise Equipment (CPE). Note that the CPE
cost will be borne by customers, not the WOBAN designers.]
We assume that all ONUs connect to one OLT, located at (0, 0). We connect the
OLT and ONUs/BSs through a minimum-cost spanning tree with OLT as the root.
In Sections 4.4.1 and 4.4.2, we set the user coverage ratio, ρ = 1, and observe
how a WOBAN’s deployment cost varies due to CI threshold (I) and available wireless
channels (F ), respectively. In Section 4.4.3, we study the impact of user coverage ratio ρ on
deployment cost of WOBAN. In Section 4.4.4, we examine how the WOBAN’s deployment
cost varies in a non-homogeneous demography, where a majority of users is clustered in
a small area, and the remaining users are far away. By observing the duality gap (see
Figs. 4.2, 4.3, 4.4, and 4.5) of Primal Model (PM), we can infer a WOBAN’s optimum
deployment cost; this is because the optimum cost is upper and lower bounded by UB and
LB, respectively. Also, we compare the cost returned by the PM to the joint optimization
heuristic captured by CH (discussed in Chapter 3). The complexity of CH is on the order2The normalized cost is less sensitive to ups and downs of the absolute cost.
Chapter 4: Constraint Programming Model for WOBAN Deployment 76
of (|L|(|L||Γ|+ |F |+ |T |)).
4.4.1 PM vs. CH: Impact of Carrier-to-Interference (CI) Threshold, I
Intuitively, the higher the distance between a BS and a user, the lower will be
the signal quality and higher will be the noise/interference. So, to serve all users with
satisfactory channel quality, we need sufficient numbers of BSs and ONUs. In other words,
we need to deploy enough BSs (and ONUs) to accommodate all the users if CI threshold
is higher. In Table 4.3, we show the number of BSs and ONUs needed for different CI
thresholds. Note that, when CI threshold is set to be 18 dB or higher, Combined Heuristic
(CH) could not find feasible solutions.
Table 4.3: Number of BSs and ONUs.
CI theshold (dB) 0 3 6 9 12 15 18 20Primal Model (PM).
BSs 21 26 32 39 48 58 70 86ONUs 3 3 4 4 5 6 7 9
Combined Heuristic (CH).BSs 23 30 36 49 71 99 NA NAONUs 3 3 4 5 8 10 NA NA
NA stands for Not Applicable.
In Fig. 4.2, we examine the solution quality of our formulation with respect to
different CI thresholds (i.e., I in Section 4.3). UB is the upper bound solution through
the Primal Algorithm and LB is the lower bound solution with CLR (µ). There are three
important observations. First, the cost increase at higher CI threshold is not very significant
(though we need significantly more number of BSs and ONUs at higher CI threshold as
in Table 4.3). This is because the fiber layout cost (100000 USD/mile) dominates the
equipment costs of BSs and ONUs. Also, ONUs and BSs will be diversely placed as users
are randomly distributed. Therefore, for smaller number of BSs and ONUs, the total fiber
length in the minimum-cost spanning tree is comparable to the larger number of deployed
BSs and ONUs. This is the reason why the deployment costs do not shoot up while deploying
large numbers of ONUs and BSs.
Second, the UB increases with higher CI threshold, but the LB does not increase
Chapter 4: Constraint Programming Model for WOBAN Deployment 77
Figure 4.2: Impact of channel interference on normalized deployment cost (with ρ = 1 and|F | = 50 channels). If I ≥ 18 dB, no feasible solution exists for CH.
significantly. This is because the co-channel interference constraint (Constraint 24) was
relaxed in formulating the dual problem. Hence, the LB is not very sensitive to CI threshold.
Third, observe that the cost estimation by PM always outperforms the Combined
Heuristic (CH), especially at higher CI threshold. This is because, in the first phase, CH
estimates the minimum number of BSs required, distributes them homogeneously in the
area, and tries to cover as many users as possible by tuning the transmission radius. But
apart from these BSs, we may need additional BSs to take care of other constraints such
as traffic demand. At higher co-channel interference constraint, the transmission radius of
the additional BSs need to be small in order to satisfy existing CI constraints. This results
in the deployment of a larger number of additional BSs. Note that CH does not produce a
feasible solution for CI threshold of 18 dB or higher. This is due to the fact that a stringent
CI threshold makes the deployment of additional BSs (which are needed to cover all the
users and their traffic demands) difficult without violating the CI constraints of existing
BSs, leading to an infeasible solution.
Note that WOBAN deployment cost is normalized to one ONU cost, which is taken
to be USD 100 at the time of this study.
Chapter 4: Constraint Programming Model for WOBAN Deployment 78
4.4.2 PM vs. CH: Impact of Wireless Channel Pool, F
In some of the WiMAX standards (such as IEEE 802.16-2004), the frequency
spectrum is not free. Therefore, we need to utilize channels efficiently to satisfy the traffic
demands. In Fig. 4.3, we study the impact of total number of available channels on the
solution quality where the CI threshold is set at 12 dB.
Figure 4.3: Impact of available channel pool on normalized deployment cost (with ρ = 1and I = 12 dB). If |F | < 35 channels, no feasible solution exists for CH.
We observe that, when the channel resource is scarce, we need to deploy more
BSs and ONUs to cover all the users. This leads to higher deployment cost compared to
when the channel resource is rich. For example, when there are 20 channels, WOBAN’s
deployment cost is upper bounded by 75000 ONU unit cost; but when there are 50 channels,
deployment cost is reduced to around 45000 ONU unit cost for UB. Therefore, the solution
quality is better when channel resource is rich than when it is scarce.
Also note that the LB is less sensitive to channel resources compared to the UB.
This is because we relax channel assignment constraints (Constraints 11 and 12), which
indicates that the number of channels assigned to each BS is large enough to serve its users.
The solution quality of the Primal Model is always superior to that of CH for all
types of channel resources (rich or scarce). Furthermore, when channel resource is scarce
Chapter 4: Constraint Programming Model for WOBAN Deployment 79
(i.e., less than 35 channels), CH can not find a feasible solution. This is due to the fact
that the number of limited channels will incur severe co-channel interference, leading to an
infeasible solution.
4.4.3 PM vs. CH: Impact of User Coverage Ratio, ρ
Another interesting property is the impact of user coverage ratio. With low user
coverage ratio, it is intuitive that fewer BSs and ONUs would be needed to satisfy the
traffic demand. In Fig. 4.4, we observe that the deployment cost is decreasing with respect
to smaller user coverage ratio ρ. The threshold of CI is set at 12 dB, and the number of
available channels is chosen as 50.
Figure 4.4: Impact of user coverage ratio on normalized deployment cost (with I = 12 dBand |F | = 50 channels).
Also note that the solution quality is better for smaller ρ. For example, when
ρ = 0.5, the duality gap is 26.17% compared to 35.35% at ρ = 1.0. Again, the solution
quality of the PM outperforms CH for all coverage ratios.
Chapter 4: Constraint Programming Model for WOBAN Deployment 80
4.4.4 PM vs. CH: Impact of Non-Homogeneous Demography
In a practical situation, the user population density may not be evenly distributed.
More often than not, it is expected to be significantly non-homogeneous and clustered, where
a majority of users resides in a small area. Hence, we study what fraction of the WOBAN
deployment cost is needed to serve the extreme users (who are far away and/or isolated).
For this study, we partition the test network (area of 5× 5 square-miles) into 100
equal grids, where each grid is of 0.5× 0.5 square-miles area. We select 20 grids randomly
(called hot-spots) and distribute 80% of the users in these hot-spots. The remaining 20% of
the users are scattered over other parts of the network. Therefore, 80% of the users reside
in only 20% of the area. Figure 4.5 shows the WOBAN deployment cost with this uneven
user coverage ratio (ρ).
Figure 4.5: Impact of non-homogeneous user coverage ratio on normalized deployment cost(with I = 12 dB and |F | = 50 channels). If ρ > 0.8, no feasible solution exists for CH.
There are three important observations. First, the deployment cost is almost linear
to the user coverage ratio till we serve the nearest 80% of the users (ρ ≤ 0.8). After that,
the cost grows superlinearly. This is expected because the farthest 20% of the users are
scattered over a larger area, leading to higher deployment cost (due to more expense for
longer fiber layout).
Chapter 4: Constraint Programming Model for WOBAN Deployment 81
Second, as expected, the PM outperforms CH, especially for higher user coverage
ratio. CH can not produce a feasible solution after 80% user-coverage ratio, because users’
population in hot-spots is too dense to be served by the minimum number of BSs (as
calculated from Table 3.9 in Chapter 3). Therefore, we need additional BSs, but it is hard
to deploy them in a small area without violating the CI constraints of existing BSs. Thus,
some users in hot-spots do not get served, leading to an infeasible solution.
Third, the vast majority (80%) of users can be served at a cost of approximately
35000 ONU units (cost at mid-point of the duality gap at ρ = 0.8). The cost for serving
all 100% of users, however, is approximately 75000 ONU units (mid-point of duality gap at
ρ = 1). Thus, we observe that more than 50% of the deployment cost is used to serve the
20% of users who are far away (or outliers). The additional cost is mainly due to expensive
fiber layout.
4.5 Summary
In this chapter, we proposed and investigated the characteristics of an analytical
model (called Primal Model) for optimum placements of Base Stations (BS) and Optical
Network Units (ONU) so that the WOBAN deployment cost is minimized. We devel-
oped several constraints that need to be satisfied for optimality: BS and ONU installation
constraints, their capacity constraints, user assignment constraints, channel assignment
constraints, and channel interference constraints. For analytical tractability of the primal
problem, we used the “Lagrangean Relaxation” technique to relax some of the harder con-
straints, and obtained the corresponding Lagrangean dual problem. We solved this dual
problem to obtain the lower bound of the PM. We also developed a Primal Algorithm and
found an upper bound of the PM. We verified the solution quality with respect to a set of
chosen metrics such as user coverage ratio, number of channels, and channel interference
threshold. Specifically, we measured the “duality gap” between the upper and lower bounds
(UB and LB, respectively) of the PM, and compared the primal solutions to a Combined
Heuristic (CH), discussed in Chapter 3. We found that the PM outperformed CH in all
these metrics, and CH could not find a feasible solution in several challenging scenarios.
82
Chapter 5
WOBAN Connectivity and
Routing
5.1 Introduction
Once a WOBAN is deployed, how to create a mesh topology in the front end and
how to route information (data packets) through it are important problems. In a typical
WOBAN, an end user, e.g., a subscriber with wireless devices at individual homes (scattered
over a geographic area) sends a data packet to one of its neighborhood wireless routers. This
router then injects the packet into the wireless mesh of the WOBAN. The packet travels
through the mesh, possibly over multiple hops, to one of the gateways (and to the ONU)
and is finally sent through the optical part of the WOBAN to the OLT/CO. In the upstream
direction of the wireless front end (from a wireless user to a gateway/ONU), the WOBAN
is an anycast network, i.e., an end user can try to deliver its packet(s) to any one of the
gateways (from which the packet will find its way to the rest of the Internet). In the optical
back end, the upstream part of a WOBAN (from an ONU to a OLT/CO) is a multi-point
media-access network, where ONUs are deployed in a tree network with respect to their OLT
and they contend for a shared upstream resource (or bandwidth). But in the downstream
direction of the wireless front end (from a gateway/ONU to a wireless user), this network
is a unicast network, i.e., a gateway will send a packet to only its specific destination (or
Chapter 5: WOBAN Connectivity and Routing 83
Figure 5.1: A WOBAN’s upstream and downstream protocols.
user). In the optical back end, the downstream (from a OLT/CO to an ONU) of a WOBAN
is a broadcast network, where a packet, destined for a particular ONU, is broadcast to all
ONUs in the tree and processed selectively only by the destination ONU (all other ONUs
discard the packet), as in a standard PON. Figure 5.1 captures a WOBAN’s upstream and
downstream transmit modes.
Note that the wireless links in the front end mesh of a WOBAN may have asym-
metric and differential capacities. This is because of how a router connects to other routers
in its neighborhood; e.g., if a router is associated with two other routers, and the wire-
less channel is time-division multiplexed, then on average, each link (associated with that
router) will get half of the capacity to other routers. Also the effective link capacity from
router A to router B may be different than that from router B to router A, because routers
A and B may have different numbers of neighbors.
This chapter explores the routing properties of WOBAN. Although it compares
several performance metrics among routing algorithms, the study primarily focuses on
packet delay (latency) in the front end (wireless mesh) of the WOBAN, i.e., the packet
delay from the router to the gateway (attached to ONU) and vice versa. The packet delay
could be significant as the packet may travel through several routers in the mesh before
finally reaching the gateway (in the upstream direction) or to the user (in the downstream
Chapter 5: WOBAN Connectivity and Routing 84
direction). The larger the mesh of the WOBAN, the higher is the expected delay. Con-
sequently, we propose “Delay-Aware Routing Algorithm (DARA)” as a proactive routing
scheme where we model each wireless router as a queue and predict the wireless link states
(using link-state prediction or LSP) periodically [49]. Based on the LSP information, we
assign weights to the wireless links. Links with higher predicted delays are given higher
weights. Then, we compute the path with the minimum predicted delay from a router to
any gateway and vice versa. While traveling upstream/downstream, a router/gateway will
send its packet along the computed path only if the predicted delay is below a predeter-
mined threshold, referred to as the delay requirement for the mesh; otherwise, we will not
admit the packet into the mesh. We also study how choosing a path from a set of paths
(whose delays are below the delay requirement) can alleviate congestion and achieve better
load balancing.
A common vision of a next-generation converged (fixed and wireless) network is
that of the IP-based end-to-end (between the end nodes) network for connectivity and rout-
ing, which enables devices to access common services over one or more networks seamlessly.
In a WOBAN-like network, end terminal mobility can also be supported at the IP layer
by one of the three dominant approaches, namely Mobile IP, Migrate, and Host Identity
Protocol (HIP) [76], which is beyond the scope of this discussion.
5.1.1 San Francisco WOBAN: A Community Wireless Mesh
We consider a part of the city of San Francisco, California, from approximately
(N 37◦46′43.39′′, W 122◦26′19.22′′ (Golden Gate Avenue and Divisadero Street intersec-
tion)) to (N 37◦46′51.78′′, W 122◦25′13.27′′ (Golden Gate Avenue and Van Ness Avenue
intersection)) and from (N 37◦47′32.57′′, W 122◦26′28.90′′ (Divisadero Street and Pacific
Avenue intersection)) to (N 37◦47′41.39′′, W 122◦25′23.71′′ (Van Ness Avenue and Pacific
Avenue intersection)) (see Fig. 5.2) for our performance study. This is approximately a
one square-mile area in downtown San Francisco with an estimated population of around
15, 000 residents, where San Francisco has an area of nearly 47 square-miles with a popula-
tion of around 745, 000; so the population of SFNet in Fig. 5.2 is quite representative of San
Francisco’s population density. The wireless part of our San Francisco WOBAN (henceforth
Chapter 5: WOBAN Connectivity and Routing 85
Figure 5.2: San Francisco WOBAN and its front-end wireless mesh (SFNet).
called “SFNet”) is a mesh that consists of a number of point-to-point or point-to-multipoint
WiFi routers1. SFNet is envisioned as a part of an on-going effort to deploy the San Fran-
cisco community mesh. In SFNet, we distribute 25 wireless routers in one square-mile area.
Five of these 25 routers are designated as gateways to the optical back end of WOBAN and
placed at the edges of SFNet. We carefully choose the number (as well as distribution) of
routers and gateways in SFNet to match the solution provider’s current deployment status,
where typically 25− 30 routers are needed to serve one square-mile of area.
The rest of this chapter is organized as follows. In Section 5.2, we briefly review
the current routing schemes in these networks and similar research efforts. In Section 5.3,
In Link-State Advertisement (LSA) (see Algorithm 5), each router/gateway will
periodically advertise its link conditions. Smaller the LSA period, less is the possibility of
“stale” advertisement (where an advertisement becomes “stale” when the link state changes
significantly after the last advertised information). However, LSA in smaller intervals leads
to the problem of sacrificing a significant portion of the network’s bandwith in advertise-
ment, which could have otherwise been used for data packets. Therefore, we can increase
the LSA intervals suitable for WOBAN to preserve the bandwidth for packets and predict
the link conditions (called Link-State Prediction) (see Section 5.3.2) between the intervals
to avoid “stale” information. These Link-State Predictions (LSP) can also capture the
burstiness of data packets in the access network.
In Link-Weight Assignment (LWA) (see Algorithm 5), we assign link weights in
such a manner that the links with more delay get higher weights.
5.3.1 Achieving Load Balancing
DARA works on the principle of delay optimization along paths from a router
to a gateway in the front end of WOBAN. If every packet in the mesh wants the path
with minimum weight (alternatively, the path with minimum delay), then some links in the
Chapter 5: WOBAN Connectivity and Routing 91
Algorithm 5 Delay-Aware Routing Algorithm (DARA)
- Link-State Advertisement (LSA): For each link i, advertise periodically currentpacket intensity (λi), effective link capacity (Ci), and time stamp (tn).
- Link-State Prediction (LSP): For each link i, estimate packet intensity (λesti ) to
be used until next LSA gets advertised (see Section 5.3.2).
- Link-Weight Assignment (LWA): Assign weight of each link i as: Wi = Qi =(1
µCi+ 1
2µCi+ ρi
µCi−λesti
).
- Path Computation:
1. Compute K minimum-weight paths (K > 1),(∑
i∈PkWi
), from the source
router to the gateway or vice versa, where Pk is the k-th path for k ∈ [1,K]. Wecall these paths as K-DARA paths.
2. Derive a set of paths, F (called “feasible paths”), that satisfy the delay require-ment of the packet.
3. Among F , choose one path.
- Admission Control:
1. Admit a new packet in the mesh only if its delay requirement (Treq) satisfies the
minimum delay among the feasible paths F , MinPk∈F
(∑i∈Pk
Wi
)≤ Treq.
2. Else reject the packet.
Chapter 5: WOBAN Connectivity and Routing 92
mesh may attract more packets (overload situation) compared to the other links. This may
adversely affect the operation of the network as many packets might get rejected due to the
link congestions in some parts of the network (had they chosen some other path, they would
have still satisfied their delay requirement). This is why we compute K minimum-weight
paths, instead of only computing the minimum-weight path to leverage greater flexibility
in choosing the paths.
Delays for K-DARA paths are bounded between the minimum delay and the max-
imum delay that satisfies the delay requirement of the packet. Let Tpkt denotes the delay of
a packet whose delay requirement is Treq in the mesh, then Tpkt is shown to be as follows:
Tpkt =
MinPk∈F
∑i∈Pk
Wi
,MaxPk∈F
∑i∈Pk
Wi
≤ Treq (5.1)
where Pk is the k-th path with k ∈ [1,K].
We may achieve better load balancing by choosing paths described above. DARA
will also help us relieve network congestion. Let γ denote the average system arrivals and
Tsys denote the average system delay in the mesh, then Tsys can be defined as below (where
E denotes the connectivity in the mesh):
Tsys =1γ
∑i∈Pk
λiWi +∑
i6∈Pk,i∈E
(λi
µCi+
λi
2µCi+
λiρi
µCi − λi
) (5.2)
=1γ
∑i∈Pk
λiWi +∑
i6∈Pk,i∈Em
(ρi +
ρi
2+
ρ2i
1− ρi
) (5.3)
where Pk is the k-th path with k ∈ [1,K].
5.3.2 Analysis of Link-State Predictions
Link-State Predictions (LSP) need to be quite accurate to capture the current
network conditions and the packet burstiness. We use “weighted moving average (WMA)”
to estimate the packet intensity. Let λi(tn) denote the measured packet intensity that gets
advertised (through LSA) in the mesh at time tn for link i, and let λesti (tn−1) denote the
Chapter 5: WOBAN Connectivity and Routing 93
Figure 5.4: Link-state predictions (LSPs) used at time intervals.
estimated (or predicted) packet intensity for the same link at the previous time instant tn−1
(and used for time interval [tn−1, tn))(see Fig. 5.4). So, LSP will compute the estimated
packet intensity for the next time instant, tn (and to be used for time interval [tn, tn+1)) as
follows:
λesti (tn) =
(3α
3α + 1
)∗(λi(tn) + λest
i (tn−1))∗ S
1−α1+α , (5.4)
where α is the “decaying index” of WMA and S is the number of samples used for pre-
dictions. Decaying index has a physical significance. It captures if a link is highly loaded
or not. If a link is highly loaded, α = ∞. Then Eqn. (5.4) estimates the current intensity
based on all previous samples. On the other hand, if a link is lightly (or moderately) loaded,
we set α = 1, and and the estimations are as follows:
Following Eqns. (5.5), (5.6), and (5.7), we observe that only 10% of λi(0) remains present in
packet intensity computations (or 90% of the past samples are “forgotten” after only eight
time periods).
Chapter 5: WOBAN Connectivity and Routing 94
5.3.3 Analysis of Throughput
Till now, we approximately modeled each router to be a M/M/1 queue with
infinite capacity. This assumption is reasonably accurate for light to moderate loads as
storage devices are inexpensive and compact. But for a more realistic throughput analysis,
we now consider each router/gateway to be an M/M/1/B queue with finite queue size B.
Throughput of the WOBAN can be computed by measuring the number of dropped
packets over a certain time period. Packets will start dropping if a router’s queue is filled
up and a new packet arrives. The packet-loss probability for a router R′ is ΦR′B and has a
closed-form equation:
ΦR′B =
1− λ′′nµC
1−(
λ′′nµC
)B+1
(λ′′nµC
)B
(5.8)
and a similar expression for ΦO′B exists for gateway O′ with λ′j as the packet arrival metric.
Now, a packet could traverse g hops from a router to a gateway in the mesh.
Assuming each router as an independent M/M/1/B queue (independence assumption is
valid if we consider that a large number of packets is passing through each router), the
packet-loss probability Lpkt could be computed as follows:
Lpkt = 1−g−1∏n=1
(1− ΦR′
nB
)(1− Φ
O′j
B
)j ∈ [1, |O|]. (5.9)
We have |V | routers and gateways (where |V | = |R|+ |O|) with average packet arrivals as
λ′′n and λ′j , then the total packet arrival in the system per unit time is(∑B
s=1 ΦR′s
)λ′′n|R|+(∑B
s=1 ΦO′s
)λ′j |O| = λ′′n|R|+ λ′j |O|.
The number of dropped packets will be ΦR′B λ′′n|R|+ ΦO′
B λ′j |V | (assuming indepen-
dence of packet loss in each router). So, system throughput ∆(T ) over a time-period T is
as follows:
∆(T ) =(1− ΦR′
B
)λ′′n|R|T +
(1− ΦO′
B
)λ′j |O|T. (5.10)
Chapter 5: WOBAN Connectivity and Routing 95
Figure 5.5: Average delay vs. load in SFNet.
5.4 Performance Study
We compare how delay-aware routing algorithm (DARA) performs vis-a-vis MHRA,
SPRA, and PTRA. We took SFNet as our test setting. Packet arrivals are independent.
Packet lengths are independent and exponentially distributed. We modeled a wireless
router’s capacity to be 11 Mbps (i.e., WiFi IEEE 802.11b), and chose the delay thresh-
old as 25 ms. Each of our simulation experiments was run for 100,000 packet arrivals, and
results averaged over all these runs are reported below.
Figure 5.5 shows that DARA outperforms MHRA, SPRA, and PTRA with respect
to average transfer delay. We observe that, at low loads (till the normalized load of 0.40)2,
MHRA and SPRA perform comparably with DARA. This is expected because both MHRA
and SPRA work on the shortest-path principle. So, at low loads, these two algorithms have
higher probability to find the shortest paths with less delay. But as load increases, DARA’s
performance improves significantly compared to MHRA and SPRA. DARA performs much
better than PTRA at all loads. At a very high load of 0.95, the average transfer delay for
DARA improves nearly 30% from its nearest competitor, namely PTRA.2A link load is computed by dividing the link’s packet arrival rate by the service rate. The networkwide
normalized load (referred to as “load” in our discussions here) is computed by averaging over all the linkloads.
Chapter 5: WOBAN Connectivity and Routing 96
Figure 5.6: Delay vs. load [for the furthest router/gateway pair (1, 25)] in SFNet.
Figure 5.6 compares individual path delays among the four schemes. We choose
the furthest origin/gateway pair (1, 25) in the mesh [see Fig. 5.2 for (1, 25) pair in SFNet],
because a packet will travel multiple hops and the delay will be cumulative in each hop.
We find that DARA performs much better than all the other schemes. The performance
improves at high loads. We also observe that, after a load of 0.50, PTRA delay shoots up
and overtakes SPRA delay.
Figure 5.7 shows how many paths one can find between minimum DARA delay
and PTRA delay for the same origin/gateway pair (1, 25). As described in Section 5.3.1,
we find K-DARA paths (K > 1) (a set of paths whose delay is less than the PTRA delay).
At low loads, we get two such paths as PTRA performs quite well. But at high loads (0.50
and beyond), we can find several such paths. In Fig. 5.8, we plot how many such K-DARA
paths on average exist whose delays are less than the PTRA delay.
Figure 5.9 shows the average hop counts of all four schemes. Expectedly, MHRA
and SPRA produce the minimum average number of hops, but DARA performs comparably
with them (particularly at a low load, till 0.40, DARA performs very well). DARA performs
much better than PTRA for all loads. In Fig. 5.10, we plot the percentage distribution of
path lengths for each of these schemes. We observe that DARA performs well, because
Chapter 5: WOBAN Connectivity and Routing 97
Figure 5.7: Comparing K-DARA (K > 1) path delays with PTRA delay [for the furthestrouter/gateway pair (1, 25)] in SFNet.
Figure 5.8: Average number of K-DARA (K > 1) paths under PTRA delays in SFNet.
Chapter 5: WOBAN Connectivity and Routing 98
Figure 5.9: Average hops vs. load in SFNet.
Figure 5.10: Hop distributions vs. load in SFNet.
Chapter 5: WOBAN Connectivity and Routing 99
Figure 5.11: Load balancing (or link congestion) vs. load in SFNet.
unlike PTRA, DARA tries to pack many packets in fewer hops (1− 3 hops). DARA has a
maximum of ten hops in this example, but only 0.025% of packets will get routed along the
10-hop paths.
Figure 5.11 captures how these schemes perform in terms of load balancing and
link congestion. We plot the traffic difference, which is the difference between the maximum
and the minimum packet intensities for links in the mesh for MHRA, SPRA, DARA, and
PTRA paths. Smaller the difference, better will be the load balancing (or less will be the
link congestion) and vice versa. In this performance metric also, DARA performs much
better than MHRA and SPRA. MHRA and SPRA find the shortest paths and thereby
poorly balance the load. Consequently, they congest a part of the mesh. Both DARA
and PTRA perform well and are comparable to each other. Till the load of 0.75, DARA
performs better than PTRA. After that, PTRA performs better.
Figures 5.12 and 5.13 capture the accuracy of our LSP. We plot the LSA values
for packet intensities in wireless links against the predicted values by LSP. We observe that,
both at high and low loads, the predicted values by LSPs are quite accurate. At high
loads, predicted values are on average 0.1% off the range of LSA values. Even at higher
LSA intervals, LSPs perform well (except during the transient phase where the LSP values
Chapter 5: WOBAN Connectivity and Routing 100
Figure 5.12: Actual vs. predicted packet intensities at high loads.
Figure 5.13: Actual vs. predicted packet intensities at low loads.
Chapter 5: WOBAN Connectivity and Routing 101
oscillate before settling down after a certain time period, see subplots 2 and 3 of both
figures). The maximum difference between LSA and LSP values is 15.58%. Similarly, at
low loads, LSP values are on average below 1% off the range of LSA values.
We also observe the increasing bandwidth consumption for LSAs if we decrease
the LSA period in Table 5.1. For LSA periods of 60, 30, 15, and 7.5 seconds, the bandwidth
consumptions due to LSAs in San Francisco WOBAN (SFNet) are 1.54%, 3.07%, 6.15%,
and 12.31%, respectively of total bandwidth. For the mesh in WOBAN, it is very important
to keep the LSA period high enough so that the total bandwidth consumption due to LSA
is low. So, in between the higher LSA periods, LSP will predict link states. Thus, LSP
saves WOBAN bandwidth with accurate predictions of link states.
Table 5.1: LSA’s bandwidth consumption.
Computed for San Francisco WOBAN.LSA period Bandwidth consumption1 min. 1.54%30 secs. 3.07%15 secs. 6.15%7.5 secs. 12.31%
5.5 Summary
This chapter focused on the WOBAN’s front-end wireless mesh connectivity (rout-
ing properties). We reviewed several routing algorithms, which are currently being used to
carry packets in the front end. Then, we proposed and investigated the characteristics of
“Delay-Aware Routing Algorithm (DARA)” that minimizes the average packet delay in the
wireless front end of a WOBAN. Our numerical examples showed that DARA achieves better
load balancing and less congestion compared to tradional approaches such as minimum-hop
routing algorithm (MHRA) and shortest-path routing algorithm (SPRA). In addition to
minimizing delay, DARA also improves on the average hop count compared to the predic-
tive throughput routing algorithm (PTRA), a popular protocol used in several deployments
for the wireless front end of a WOBAN.
102
Chapter 6
WOBAN Fault Tolerance and
Restoration
6.1 Introduction
WOBAN architecture exhibits fault-tolerant behavior and can restore the net-
work against possible failure scenarios. Due to its multi-domain hierarchical architecture,
WOBAN can experience multiple failures. The failures can be of several types:
- Gateway failure: If a wireless gateway fails, the wireless routers need to reassociate
themselves with other “live” gateways.
- ONU failure: If an ONU fails, the connection from its gateways (and their associated
routers down the hierarchy) should be reprovisioned to other neighboring ONUs.
- OLT failure: This failure is more damaging (since an OLT at the top the hierarchy
drives several ONUs/gateways), but less frequent (due to its protection from natural
calamities and human errors because of its location inside the CO). Consequently,
multiple ONUs fail. In this failure, traffic from a large portion of the area needs to
be rerouted.
- Fiber cut: Failure due to fiber cut between upstream (ONU/gateways) and down-
stream (OLT) components. Hence, paths between CO and PON groups will be non-
Chapter 6: WOBAN Fault Tolerance and Restoration 103
functional.
Packet loss may also occur due to any combination of the failure scenarios in WOBAN
architecture, viz., gateway failure, ONU failure, and/or OLT failure.
WOBAN has a self-healing property to combat these failures. We propose “Risk-
and-Delay Aware Routing Algorithm”, called RADAR, to exploit this property. The rest
of the chapter is organized as follows. Section 6.2 describes RADAR. Section 6.3 exam-
ines how efficiently RADAR can exploit WOBAN’s risk awareness and self-healing prop-
erty. In Section 6.4, we report how RADAR minimizes packet loss vs. traditional routing
- Link-State Advertisement (LSA): For each link i, advertise periodically currentpacket intensity (λi), effective link capacity (Ci), and time stamp (tn).
- Link-State Prediction (LSP): For each link i, estimate packet intensity (λesti ) to
be used until next LSA gets advertised (see Section 5.3.2 in Chapter 5 for details).
- Link-Weight Assignment (LWA): Assign weight of each link i as: Wi = Qi =(1
µCi+ 1
2µCi+ ρi
µCi−λesti
).
- Path Computation:
1. Compute K minimum-weight paths (K > 1),(∑
i∈PkWi
), from the source
router to the gateway or vice versa, where Pk is the k-th path for k ∈ [1,K].
2. Derive a set of paths, F (called “feasible paths”), that satisfy the delay require-ment of the packet.
3. Among F , choose one path.
- Risk List Update: Maintain a Risk List (RL) table in each router based on F.Update RL at next LSA.
- Path Selection: Among paths in RL, choose a “live” path. (See Section 6.3 fordetails.)
6.3 Analysis of RADAR
We explain how WOBAN exhibits risk awareness and self-healing properties. To
handle failures, RADAR exploits these properties through its periodic “Risk List Update”
and a suitable “Path Selection” mechanism.
6.3.1 Risk Awareness
To reduce packet loss, each router maintains a “Risk List (RL)” to keep track of
failures. An RL in each router contains six fields, viz. path number (PN), Primary Gateway
Group (PGG), Secondary Gateway Group (SGG), Tertiary Gateway Group (TGG), path
status (PS) (“live” or “stale”), and corresponding path delay (PD). The primary gateway
Chapter 6: WOBAN Fault Tolerance and Restoration 105
Figure 6.1: An illustration of RADAR.
for a router is the gateway with the minimum delay path. PGG contains paths with
the primary gateway and the gateways connected to the same ONU as with the primary
gateway. SGG contains paths with gateways that are connected to different ONUs but the
same OLT as with the PGG. TGG contains paths with gateways that are connected to a
different OLT (and consequently a different ONU). Figure 6.1 illustrates the risk awareness
and self-healing mechanisms of RADAR.
There are a number of gateways at the edges of the front end of a WOBAN.
Furthermore, at the optical back end, there are different OLTs, and each OLT supports
multiple ONUs. Each gateway will be assigned a gateway id, viz. CBvAwu , where CBvAw
u
stands for the u-th gateway (denoted by C), associated with the v-th ONU (denoted by B),
which, in turn, is connected to the w-th OLT (denoted by A) at the back end. For example,
gateway id CB16A21 will be assigned to the 1st gateway associated with the 16th PON group
(or ONU) of the 2nd OLT (see Fig. 6.1).
A router may find multiple paths for a packet satisfying its delay requirement in
the mesh. Now, if a router finds five minimum-weight paths, then F = 5. Consider that the
Chapter 6: WOBAN Fault Tolerance and Restoration 106
also reduce the packet loss for multiple failure scenarios, viz., gateway failure, ONU failure,
and OLT failure.
115
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