Korea Advanced Institute of Science and Technology Network Systems Lab. Wireless Mesh Network Professor Song Chong Network Systems Laboratory EECS, KAIST [email protected]
Korea Advanced Institute of Science and Technology Network Systems Lab.
Wireless Mesh Network
Professor Song ChongNetwork Systems Laboratory
EECS, [email protected]
Korea Advanced Institute of Science and Technology Network Systems Lab.
Architecture, Applications & Protocols
Korea Advanced Institute of Science and Technology Network Systems Lab.
WMN ArchitectureWMNs (Wireless Mesh Networks) consist of: mesh routers and mesh clientsMesh routers
Conventional wireless AP (Access Point) functionsAdditional mesh routing functions to support multi-hop communicationsUsually multiple wireless interfaces built on either the same or different radio technologies
Mesh clientsCan also work as a router for client WMN Usually one wireless interface
Classification of WMN architectureInfrastructure/Backbone WMNsClient WMNsHybrid WMNs
Korea Advanced Institute of Science and Technology Network Systems Lab.
Infrastructure/Backbone WMNsInfrastructure/Backbone WMNs
Korea Advanced Institute of Science and Technology Network Systems Lab.
WMN CharacteristicsMulti-hop wireless network
Extend coverage with lower transmission powerProvide non-line-of-sight (NLOS) connectivity
Ad hoc network with self-forming, self-healing, and self-organization capability
Low upfront investmentEasy deploymentFault tolerance
Minimal mobilityMesh routers have minimal mobilityMesh clients can be stationary or mobile
Korea Advanced Institute of Science and Technology Network Systems Lab.
WMN CharacteristicsWireless internetwork
Internetwork of heterogeneous wireless networks (e.g., Wi-Fi networks, WiMax networks, cellular networks, Zig-Bee networks etc.)
Traffic patternMost traffic is user-to-gateway or gateway-to-userIn ad hoc networks, most traffic is user-to-user
Not an energy-limited networkMesh routers are usually AC-poweredEnergy efficiency is not an issue in protocol design
Korea Advanced Institute of Science and Technology Network Systems Lab.
WMN AdvantageVery low installation and maintenance cost.
No wiring! Wiring is always expensive/labor intensive, time consuming, inflexible.
Easy to provide coverage in outdoors and hard-to-wire areas.
Ubiquitous access.
Rapid deployment.Self-healing, resilient, extensible.
Korea Advanced Institute of Science and Technology Network Systems Lab.
Application ScenariosBroadband home networking
Korea Advanced Institute of Science and Technology Network Systems Lab.
Application ScenariosCommunity and neighborhood networking
Korea Advanced Institute of Science and Technology Network Systems Lab.
Application ScenariosEnterprise networking
Korea Advanced Institute of Science and Technology Network Systems Lab.
Application ScenariosMetropolitan area networking
Korea Advanced Institute of Science and Technology Network Systems Lab.
Application ScenariosPublic safety
Korea Advanced Institute of Science and Technology Network Systems Lab.
Application ScenariosSensor networking for environment monitoring (e.g., meteorological observatory network)
Beacon (Seosoo-Do)
Deukjeuk-Do
Sunmi-Do
Jaweol-Do
Deujeuk Buoy
Inchon MO
Muei-Do
Youngjong-Do
Bu-Do
Daebu-Do
YoungHung-Do
Palmi-Do
Korea Advanced Institute of Science and Technology Network Systems Lab.
Application ScenariosTransportation systemsBuilding automationsHealth and medical systemsSecurity surveillance systemsSpontaneous networking
Korea Advanced Institute of Science and Technology Network Systems Lab.
Market Opportunities
Municipalities,Public Safety
23%
Education15%
Warehousing andIndustrial
25%
Hospitality25%
Healthcare12%
Hotels, malls, conventions
Hospitals,Nursing homes
Access, security, surveillance
Asset tracking, RFID, sensor nets, dispatch
Access, campus,mobile classroom
Estimated $1B market by 2009 [source: IDC, ABI]
Korea Advanced Institute of Science and Technology Network Systems Lab.
Industry PlayersFiretideIntelKiyonLocust WorldMesh DynamicsMicrosoftMotorola /Mesh NetworksNokia RooftopNortel Networks
Packet HopSkyPilot NetworksStrix SystemsTropos Networks
Not a comprehensive list.Technical details usually proprietary.Solutions typically based on standard802.11, single or multiple radios, standard routing solutions.
Korea Advanced Institute of Science and Technology Network Systems Lab.
Commercial Technologies
Same as for client access
1 802.11b/g5210 MetroMesh Router
Tropos Networks
Up to 3 802.11aUp to 3 802.11b/gOWS 3600Strix Systems
1 802.11a 1 802.11bWireless AP 7220Nortel
Same as for client access
1 802.11a/b/g HotPort 3203Firetide
1 802.11a 1 802.11b/g Aironet 1500Cisco
Up to 3 proprietary 5GHz
1 802.11b/g BelAir 200BelAir Networks
Radios for backhaul
Radios for client access
ProductVendor
Korea Advanced Institute of Science and Technology Network Systems Lab.
Service ModelsPrivate ISP (paid service)City/county/municipality effortsGrassroots community effortsMay be shared infrastructure for multiple uses
Internet accessGovernment, public safety, law enforcementEducation, community peer-to-peer
Korea Advanced Institute of Science and Technology Network Systems Lab.
WMN Testbed StudiesField Testbeds
Technology For All – Houston, Texas (non-profit)Mesh network for low income residences, libraries, and small businesses
Research Testbeds Microsoft, MIT, UIUC, Stony Brook, UCSD, Rice, UCSB, KAIST …)
Report card so far
A+ connectivity, deployability, economics
C performance
I service model, security, protocols, …
Korea Advanced Institute of Science and Technology Network Systems Lab.
Capacity of WMN under 802.11 MAC [Jun03]
Assume each node has external load GAssume MAC layer capacity is BBottleneck collision domain
Collision domain by link 2-3{2-3, GW-1, 1-2, 3-4, 4-5}Traffic: 4G+5G+6G+7G+8G = 30G
Throughput per node: G ≤ B/30
Korea Advanced Institute of Science and Technology Network Systems Lab.
Capacity of WMN under 802.11 MAC
The collision domain of link 17-18 is the bottleneck with traffic of 97GThroughput per node: G≤B/97
Korea Advanced Institute of Science and Technology Network Systems Lab.
Link Quality Measurement in Indoor WMN [Morris03]
Packet delivery ratio for individual links for a 29 node (406 links) indoor mesh network shown.Links widely vary in loss characteristics. Also, many asymmetric links.
Delivery ratio in one direction
Delivery ratio in the other direction
Korea Advanced Institute of Science and Technology Network Systems Lab.
Link Quality Measurement in Outdoor WMN [Morris04]
Korea Advanced Institute of Science and Technology Network Systems Lab.
Routing ProtocolsRevisit ad hoc network routing protocolsTwo main thrusts
Proactive routingBased on traditional distance vector (DV) or link states (LS) routing protocolsAlways maintain shortest-path routesDSDV, OLSR, TBRPF
Reactive (on-demand) routingDiscover and maintain routes only “on-demand”Save routing loadAODV, DSR
Special considerations in WMNWMN routers differ from MANET routers
Power supplyMobility
Separation of WMN routers and clients
Korea Advanced Institute of Science and Technology Network Systems Lab.
Routing MetricsLQSR (Link Quality Source Routing) [Daves04]
DSR with link quality metrics• Hop count • per-hop RTT• per-hop packet pair• ETX (Expected Transmission Count)
Lessons• ETX metric performs best in static scenarios.• Hop count metric performs best in mobile scenarios.• RTT performs worst.• PacketPair metric suffers from self-interference on
multi-hop paths.
Korea Advanced Institute of Science and Technology Network Systems Lab.
ETX: Expected Transmission Count [Morris03]
ETX of a link = Expected no. of transmissions required to send a packet over that link.Assumes a link layer ACK (e.g., 802.11) -> link has to work in both directions.
ETX of path = sum of link ETXs
rf ddETX
×=
1
fd = forward delivery ratio (measurement based)
rd = reverse delivery ratio (measurement based)
Korea Advanced Institute of Science and Technology Network Systems Lab.
ETT: Expected Transmission Time [Davies04-2]
Adjust ETX for bandwidth.Probe size = S, link bandwidth = B
Each transmission lasts for S/B time.
ETT = (S/B)*ETXCan add channel access delay to this.
This delay includes any channel sensing delay, backoff.
Cost of path = sum of constituent link ETTs.
Korea Advanced Institute of Science and Technology Network Systems Lab.
Extremely Opportunistic Routing (ExOR) [Morris05]
Source broadcasts each packet without intended receiver.Learn the set of nodes which actually received the packet.The receiver in the set that is closest (in terms of ETX) to thedestination is selected to forward the packet.This continues until the destination receives the packet.
ExOR provides more throughput than conventional routingEach transmission has more independent chances of being received and forwarded (broadcast gain)Take advantage of transmissions that reach unexpectedly far (opportunistic gain)ETX: In ExOR, (1-(1-0.25)^4)^-1+1 = 2.46
In conventional routing, 4+1 = 5
Korea Advanced Institute of Science and Technology Network Systems Lab.
TCP over Wireless TCP interprets any packet loss as a sign of congestion.
TCP sender reduces congestion window.
On wireless links, packet loss can also occur due to random channel errors, handoffs or route changes.
Not due to congestion.Reducing window may be too conservative.Leads to poor throughput.
How to distinguish loss due to congestion from loss due to other wireless/mobility reasons?
Korea Advanced Institute of Science and Technology Network Systems Lab.
TCP on Mutihop Wireless [Gerla99,Holland99]
First sign of problem: TCP throughput drops with increase in #hops. Reasons:
Each hop adds additional self-contention.Also, more delay, more variability in delay, and more chance of packet loss.
Korea Advanced Institute of Science and Technology Network Systems Lab.
Impact of MAC Unfairness [Knightly04]
320.5 320.5 320.5
2 20
1247
3 27 40.7
1000
38.5 48
11771058.7
988
0
400
800
1200
1600
TA(1) TA(2) TA(3) TA(4) Total
Goo
dput
[kb/
sec]
Obj. Basic RTS/CTS
ACK Traffic
Ethe
rnet
Ethe
rnet
Ethe
rnet
Ethe
rnet
TAP1 TAP2 TAP3 TAP4
Notations: Obj = objective throughput
for fair sharingBasic = no RTS/CTS
Two longer flows starve Similar effect regardless whether RTS/CTS are used
Korea Advanced Institute of Science and Technology Network Systems Lab.
Multi-hop Wireline Network
Network Utility Maximization
― Link capacity is given and constant― Rate allocation problem
( )
( )
max
s.t. ,
0
sr s
s ls S l
U r
r c l
r∈
≤ ∀
≥
∑
∑
1r
2r 3r
1c 2c
Korea Advanced Institute of Science and Technology Network Systems Lab.
Functional DecompositionLagrangian function
Dual problem
Dual decomposition― Flow control at source
― Congestion price at link
TCP is an approximation of this dual decomposition
( ) ( )( )
, = s l s ls l s S l
L r U r r c∈
⎛ ⎞λ − λ −⎜ ⎟
⎝ ⎠∑ ∑ ∑
( )min max ,rL r
λλ
( ) 1
( ) ( )max s s l s lr s l L s l L s
U r r r U −
∈ ∈
⎛ ⎞ ⎛ ⎞′− λ ⇒ = λ⎜ ⎟ ⎜ ⎟
⎝ ⎠ ⎝ ⎠∑ ∑ ∑
( ) ( )min ll s l s l
l s S l s S lr c r c
λ∈ ∈
⎛ ⎞λ − ⇒ λ = −⎜ ⎟⎝ ⎠
∑ ∑ ∑g
Korea Advanced Institute of Science and Technology Network Systems Lab.
Multi-hop Wireless Network
Long-term Network Utility Maximization
― Link capacity is time-varying and a function of resource control― Joint rate, power allocation and link scheduling
( )
( )
, , max
s.t. ,
sR P I sU R
R F P I∈
∑
1R
2R 3R
( )1 , ,C P I h ( )2 , ,C P I h : power allocation: link scheduling: channel state
PIh
Korea Advanced Institute of Science and Technology Network Systems Lab.
Functional DecompositionFor a realization of channelsLagrangian function
Dual problem
Dual decomposition― Flow control at source
― Scheduling/power control at link
― Congestion price at link
Joint MAC and transport problemDistributed scheduling/power control is a challenge
( ) ( ) ( )( )
, , , = , ,s l s ls l s S l
L r P I U r r C P I h∈
⎛ ⎞λ − λ −⎜ ⎟
⎝ ⎠∑ ∑ ∑
( ), ,
min max , , ,r P I
L r P Iλ
λ
( ) 1
( ) ( )max s s l s lr s l L s l L s
U r r r U −
∈ ∈
⎛ ⎞ ⎛ ⎞′− λ ⇒ = λ⎜ ⎟ ⎜ ⎟
⎝ ⎠ ⎝ ⎠∑ ∑ ∑
( ) ( )( ) ( )
min , , , ,ll s l s ll s S l s S l
r C P I h r C P I hλ
∈ ∈
⎛ ⎞λ − ⇒ λ = −⎜ ⎟⎝ ⎠
∑ ∑ ∑g
( ),
max , ,l lP I lC P I hλ∑
Korea Advanced Institute of Science and Technology Network Systems Lab.
Per-link Queueing Case
User 0
User 2
)( 11 xU
)( 00 xU
)( 22 xU
cA=1 cB=1
subject to μa is the fraction oftime link A is used
Korea Advanced Institute of Science and Technology Network Systems Lab.
Functional DecompositionCongestion control (sources and nodes)
MAC or scheduling (network)
Korea Advanced Institute of Science and Technology Network Systems Lab.
Per-flow Queueing Case
User 0
User 1
User 2
)( 11 xU
)( 00 xU)( 22 xU
cA=1 cB=1
subject to
μa0 is the fraction oftime link A is used foruser 0
Korea Advanced Institute of Science and Technology Network Systems Lab.
Functional DecompositionCongestion control (sources)
MAC or scheduling (network)
x0 μa0 μb0
x1 μa1 x2 μb2
pa0 pb0
pa1 pb2
Korea Advanced Institute of Science and Technology Network Systems Lab.
Notations
( )ab tμ
{0,1,2, }t∈ L
a
b
Assume slotted time N nodes, L linksLink (a, b) is distinct from link (b, a)
is the matrix of transition rates offered over each link (a, b) during slot t (in units of bits/slot)
( ) [ ( )]abt tμΜ =
Korea Advanced Institute of Science and Technology Network Systems Lab.
Link Transmission Rate FunctionThe link transmission rates are determined by a link transmission rate function
The topology state process represents all uncontrollable properties of the network that influence the set of feasible transmission ratesFor example, time-varying channel conditions due to- user mobility- fading- weather- other external environmental factors
( , )I SC( ) ( ( ), ( ) )
where s(t) = network topology state during slot tI(t) = link control action taken by the network according to a policy during slot t
t I t s tΜ = C
( )s t ∈S
( )s t
Korea Advanced Institute of Science and Technology Network Systems Lab.
Link Transmission Rate FunctionThe link control input represents all of the possible resource allocation options available in the link/MAC layer under a given topology state
Examples- might specify the particular set of links chosen for activation
during slot t- might represent the matrix of power values allocated for
transmission over each data link- might represent the channel (or subcarrier) allocation
decisions for every data link
Note that
( )I t
( )s t( )( ) s tI t I∈
( )I t
( )I t
( )I t
( ) ( ( ), ( ) )ab abt C I t s tμ =
Korea Advanced Institute of Science and Technology Network Systems Lab.
Assume topology state is constant, i.e., stationary nodes and time-invariant channels etc.
The objective is to schedule interference-free link activation
Let be the set contains all sets of links that can be simultaneously activated without inter-link interference, called feasible link activation sets or independent setsThen, if
Note the difficulty in distributed implementation
Example: Static Multihop Wireless Network( )s t
( )I t
I
( ) ,I t I∈if ( ) 1
( ( ), )0 if ( ) 0ab ab
abab
C I tC I t s
I t=⎧
= ⎨ =⎩
Korea Advanced Institute of Science and Technology Network Systems Lab.
Interference Model
2r
1 2 3 4
5
node
link
5 2
1 3
4
1r
Network connectivity graph G
Conflict graph CG
- Links in G = nodes in CG- CG-Edge if links in G interfere with each other
Korea Advanced Institute of Science and Technology Network Systems Lab.
Maximal clique model
- Clique = complete subgraph of CG- Maximal clique = clique not a subset of any other- Only one node in a clique can be active at a time- Network utility maximization (NUM) problem
Interference Model
2
1max ( )i
iU r
=∑
5 2
1 3
4
2
3
1 1 2 1 2 2
1 2 3 5
1 2 1 2 1 2
2 3 4
subject to clique constrainsts
1
1
r r r r r rc c c cr r r r r rc c c
+ ++ + + ≤
+ + ++ + ≤
Korea Advanced Institute of Science and Technology Network Systems Lab.
Interference ModelLimitations of maximal clique model- Link activation schedule to achieve clique capacity is not
always feasible- Not easy to find a clique in a distributed manner
- The maximal throughput in the Pentagon CG is 40% per node. But, the clique constraints allow 50% per node.
1 2
5
4
3 1 2 2 3 3 4 4 5 5 1
Pentagon CG
Maximal cliques
Korea Advanced Institute of Science and Technology Network Systems Lab.
Interference ModelMaximal independent set model
- Only one maximal independent set can be active at a time-- NUM problem
{1, 4}, {2}, {3}, {4, 5}
5 2
1 3
4
CGMaximal independent sets
( )I t I∈ { }where {1, 4}, {2}, {3}, {4, 5}I =
2
1max ( )i
iU r
=∑
1 1
1 2 2
1 2 3 41 2 3
41 2 4
52
4
1
subject to independent set constraints00 000 000 0
0 00 0 0
1ii
r cr r c
a a a ar r ccr r ccr
a=
⎡ ⎤⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥+ ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥≤ + + ++⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥+ ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦⎣ ⎦ ⎣ ⎦
=∑
Korea Advanced Institute of Science and Technology Network Systems Lab.
Example: Ad-hoc Network with Interference
The transmission rate function for link l
where p(t) represents the power allocation vector
SINR interference model
where
= background noise intensity at each receiver= attenuation factor from the transmitter of link k to
the receiver of link l
( ( ), ( ) ) ( ( ), ( ) )l lC I t s t C p t s t=
( ( ), ( ) ) log(1 ( ( ), ( )) )l lC p t s t SINR p t s t= +
0
( ) ( ( ))( ( ), ( ))( ) ( ( ))
l lll
k klk Lk l
p t s tSINR p t s tN p t s t
αα
∈≠
=+∑
0N( ( ))kl s tα
Korea Advanced Institute of Science and Technology Network Systems Lab.
Example: Ad-hoc Network with Interference
NUM at particular state s [Chiang05]
is a nonconcave function of pAssuming high SINR regime, i.e,
can be converted into a concave function of pthrough a log transformation (geometric programming)
Joint optimization of congestion control and power control
,
( )
max ( )
subject to( , ) ,
where
ip r i
i li I l
U r
r C p s l∈
≤ ∀
∑
∑
( , )lC p slog(1 ( , )) log( ( , ))l lSINR p s SINR p s+ ≈
( , )lC p s
0
( )( , ) log(1 ( , )) log 1( )
l lll l
k klk Lk l
p sC p s SINR p sN p s
αα
∈≠
⎛ ⎞⎜ ⎟⎜ ⎟= + = +⎜ ⎟+⎜ ⎟⎝ ⎠
∑
Korea Advanced Institute of Science and Technology Network Systems Lab.
Example: Ad-hoc Network with Interference
Lagrangian function
Dual problem
Dual decomposition
( ),
min max , ,r pL r p
λλ
( )( )
( , , ) ( ) ,i i l i li l i I l
L r p U r r C p s∈
⎛ ⎞λ = − λ −⎜ ⎟
⎝ ⎠∑ ∑ ∑
( )max ( )i i i lr i i l L i
U r r∈
− λ∑ ∑ ∑ Transport layer problem
Physical layer problem( )max ,l lp lC p sλ∑
Korea Advanced Institute of Science and Technology Network Systems Lab.
Example: Ad-hoc Network with Interference
AlgorithmFlow control at source
Power control at link
Congestion price at link
1
( )i l
l L ir U
+
−
∈
⎡ ⎤⎛ ⎞′= λ⎢ ⎥⎜ ⎟
⎢ ⎥⎝ ⎠⎣ ⎦∑
( )( ) ( ),( )
( ) ( )k k
kk kk
t SINR p t sm t
p t sλ ⋅
=α
( )( 1) ( ) ( ) ( )( )l
l l kl kk Llk l
tp t p t s m tp t ∈
≠
⎛ ⎞λ⎜ ⎟+ = + γ − α⎜ ⎟⎜ ⎟
⎝ ⎠∑
( )( )
( 1) ( ) ( ) ( ),l l i li I l
t t r t C p t s+
∈
⎡ ⎤⎛ ⎞λ + = λ + γ −⎢ ⎥⎜ ⎟
⎢ ⎥⎝ ⎠⎣ ⎦∑
Korea Advanced Institute of Science and Technology Network Systems Lab.
Example: Ad-hoc Network with Interference
InterpretationBalancing transport and physical layers
Physical layer
λr C
Transport layer
Source NodeFlow Control
Transmit LinkPower Controlλλ
Intermediate Congst. Price
r
Korea Advanced Institute of Science and Technology Network Systems Lab.
Long-term Capacity RegionTime-varying achievable rate region
Long-term rate region
: long-term rate region(can be shown to be convex)F
1R
2R
F
1r
2r
1r
2r
1r
2r
t
: long-term rate of user iR i
Korea Advanced Institute of Science and Technology Network Systems Lab.
Long-term NUM
Utility function [Mo00]
Network Utility Maximization (NUM)
max ( )
where = long-term rate of user i= long-term capacity region
iR F i
i
U R
RF
∈∑
( )11 , if 0 & 1
1log , if 1
ii i
i
RU RR
−α⎧⎪ α < α ≠= ⎨ −α⎪ α ≠⎩
α→0: throughput maximizationα=1: proportional fairness (PF)α→∞: max-min fairness
Korea Advanced Institute of Science and Technology Network Systems Lab.
Maximization of sum of weighted rates
Both problems yield an unique and identical solution if we set , where is the optimal solution of the long-
term NUM problem.
Sum of Weighted Rates (SWR)
max i iR F iRω
∈∑
*'( )i iU Rω = *iR
2R
1R
F
*2R
*1R
1 2( ) ( )U R U R J+ =
01 1 2 2R R Kω ω+ =
Korea Advanced Institute of Science and Technology Network Systems Lab.
Gradient-based Scheduling
Assuming stationarity and ergodicity, we have
The long-term NUM problem can be solved if we solve with at each state sThe resource allocation problem during slot t
where Ri(t) is the average rate of user i up to time t and is the replacement of Ri
* which is unknown a priori
Convergence of Ri(t) to Ri* can be proved by
stochastic approximation theory [Kush04] or fluid limit technique [Stol05].
( )max maxi i s i iR F r F si i
R E rω ω∈ ∈
⎡ ⎤= ⎢ ⎥
⎣ ⎦∑ ∑ where rate of user at state
( ) capacity region at state ir i s
F s s==
( )max i ir F s i
rω∈
∑ *'( )i iU Rω =
( )( )
max '( ( )) ( )
subject to ( ) ( )
i ir t iU R t r t
r t F s t∈
∑
Korea Advanced Institute of Science and Technology Network Systems Lab.
Transport and Network Layer Queueing1 2
3
45
transportlayer
networklayer
(3)1A
(4)1A
(3)5A
(1)4A (1)
4R (1)4U
= set of commodities in the network= the amount of new commodity c data that
exogenously arrives to node i during slot t= the amount of commodity c data allowed to enter the
network layer from the transport layer at node i during slot t= the backlog of commodity c data stored in the
network layer queue at node i during slot t
K( ) ( )ciA t
( ) ( )ciR t
( ) ( )ciU t
( and )i N c K∈ ∈
Korea Advanced Institute of Science and Technology Network Systems Lab.
Dynamic Control for Network Stability
The stabilizing dynamic backpressure algorithm [Tassiulas92]
- An algorithm for resource allocation and routing whichstabilizes the network whenever the vector of arrival rateslies within the capacity region of the network
Resource allocation- For each link , determine optimal commodity and optimal weight by
- Find optimal resource allocation action by solving
)(* tCab)(* tabω
]0,[max)(
)]()([maxarg)(
))(())((*
)()(
}),|({
*
** tCb
tCaab
cb
ca
Lbacab
abab
c
UUt
tUtUtC
−=
−=∈
ω
)(
*
)(
)(.
))(),(()(max
ts
abababtI
ItIts
tstICt
∈
⋅∑ω
),( ba
)(* tI
Korea Advanced Institute of Science and Technology Network Systems Lab.
Dynamic Control for Network Stability
Routing- For each link such that , offer a transmission rate of to data of commodity .
The algorithm requires in general knowledge of thewhole network state. However, there are importantspecial cases where the algorithm can run in adistributed fashion with each node requiringknowledge only of the local state information oneach of its outgoing links.
Interpretation- The resulting algorithm assigns larger transmission rates to links with larger differential backlog, and zero transmissionrates to links with negative differential backlog.
),( ba 0)(* >tabω))(,)(()( ** tstICt abab =μ )(* tCab
Korea Advanced Institute of Science and Technology Network Systems Lab.
Dynamic Control for Infinite Demands
AssumptionInfinite backlog at every transport layer queue
Cross-layer control algorithm [Neely05]Flow control at node i
Each time t, set Ri(c)(t) to
( )( ) ( ) ( )arg max ( )i
c c ci i nr c
VU r r U t⎡ ⎤−⎣ ⎦∑ 0 : control parameterV >
( )( ) 1( ) max ,0
cc ii
UR t UV
−⎡ ⎤⎛ ⎞′= ⎢ ⎥⎜ ⎟⎝ ⎠⎣ ⎦
Korea Advanced Institute of Science and Technology Network Systems Lab.
Dynamic Control for Infinite Demands
Routing and resource allocationSame as previous
Algorithm performance
Tradeoff between utility and delayControl parameter V determines the tradeoff
( )1
( )
0
1limsup ( )t
ci
t iU O V
t
−
→∞ τ=
τ ≤∑∑
{ } ( )1
( ) *
, 0 ,
1 1liminf ( )t
ci it i c i c
U E R U R Ot V
−
→∞τ=
⎛ ⎞ ⎛ ⎞τ ≥ − ⎜ ⎟⎜ ⎟ ⎝ ⎠⎝ ⎠∑ ∑ ∑
Stability
Optimality
Korea Advanced Institute of Science and Technology Network Systems Lab.
References[Kum03] K. Kumaran and L. Qian, “Uplink Scheduling in CDMA Packet-Data Systems,” IEEE INFOCOM 2003.[Mo00] J. Mo and J. Walrand, “Fair End-to-End Window-Based Congestion Control,” IEEE/ACM Trans. Networking, Vol. 8, No. 5, pp. 556-567, Oct. 2000.[Kush04] H. J. Kushner and P. A. Whiting, “Convergence of Proportional-Fair Sharing Algorithms Under General Conditions,” IEEE Trans. Wireless Comm., vol. , no., 2004.[Stol05] A. L. Stolyar, “On the Asymptotic Optimality of the Gradient Scheduling Algorithm for Multiuser Throughput Allocation,” Operations Research, vol. 53, no. 1, pp. 12-25, Jan. 2005.[Neely05] M. J. Neely et al., “Fairness and Optimal Stochastic Control for Heterogeneous Networks,” IEEE INFOCOM 2005.[Jun03] J. Jun, ML Sichitiu, The nominal capacity of wireless mesh networks, IEEE Wireless Communications 10 (5), 2003.[Morris03] D. Decouto, D. Aguayo, J. Bicket, and R. Morris, "A high-throughput path metric for multi-hop wireless networks", in Proceedings of MobiCom, 2003.[Morris04] Daniel Aguayo, John Bicket, Sanjit Biswas, Glenn Judd, Robert Morris, Link-level Measurements from an 802.11b Mesh Network, SIGCOMM 2004, Aug 2004.[Daves04] R. Draves, J. Padhye, and B. Zill. The architecture of the Link Quality Source Routing Protocol. Technical Report MSR-TR-2004-57, Microsoft Research, 2004.
Korea Advanced Institute of Science and Technology Network Systems Lab.
References
[Daves04-2] R. Draves, J. Padhye, and B. Zill. Routing in Multi-radio, Multi-hop Wireless Mesh Networks. ACM MobiCom, Philadelphia, PA, September 2004.[Morris05] Sanjit Biswas and Robert Morris, Opportunistic Routing in Multi-Hop Wireless Networks, SIGCOMM 2005, August 2005.[Chiang05] M. Chiang, “Balancing Transport and Physical Layers in Wireless Multihop Networks: Jointly Optimal Congestion Control and Power Control,”IEEE J. Sel. Areas Comm., vol. 23, no. 1, pp. 104-116, Jan. 2005.[Tassiulas92] L. Tassiulas and A. Ephremides, “Stability Properties of Constrained Queueing Systems and Scheduling Policies for Maximum Throughput in Multihop Radio Networks,” IEEE Trans. Automatic Control, vol. 37, no. 12, Dec. 1992.[Gerla99] M. Gerla, K. Tang, and R. Bagrodia, "TCP Performance in Wireless Multihop Networks," IEEE WMCSA 1999.[Holland99] G. Holland and N. Vaidya. Analysis of TCP performance over mobile ad hoc networks. In Proc. of MobiCom, 1999.[Knightly04] V. Gambiroza, B. Sadeghi and E. Knightly, “End-to-End Performance and. Fairness in Multihop Wireless Backhaul Networks”, in Proceedings of ACM. MobiCom’04, Philadelphia, PA, September 2004.