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Research ArticleAdvanced Load Balancing Based on Network Flow
Approach inLTE-A Heterogeneous Network
Shucong Jia, Wenyu Li, Xiang Zhang, Yu Liu, and Xinyu Gu
Beijing University of Posts and Telecommunications, Beijing
100876, China
Correspondence should be addressed to Shucong Jia;
[email protected]
Received 20 February 2014; Accepted 21 April 2014; Published 20
May 2014
Academic Editor: Lin Zhang
Copyright © 2014 Shucong Jia et al. This is an open access
article distributed under the Creative Commons Attribution
License,which permits unrestricted use, distribution, and
reproduction in any medium, provided the original work is properly
cited.
Long-term evolution advanced (LTE-A) systems will offer better
service to users by applying advanced physical layer
transmissiontechniques and utilizingwider bandwidth. To further
improve service quality, lowpower nodes are overlaidwithin amacro
network,creating what is referred to as a heterogeneous network.
However, load imbalance among cells often decreases the network
resourceutilization ratio and consequently reduces the user
experience level. Load balancing (LB) is an indispensable function
in LTE-Aself-organized network (SON) to efficiently accommodate the
imbalance in traffic. In this paper, we firstly evaluate the
negativeimpact of unbalanced load among cells through Markovian
model. Secondly, we formulate LB as an optimization problem whichis
solved using network flow approach. Furthermore, a novel algorithm
named optimal solution-based LB (OSLB) is proposed.Theproposed OSLB
algorithm is shown to be effective in providing up to 20% gain in
load distribution index (LDI) by a system-levelsimulation.
1. Introduction
Nowadays, smart phone and tablet users are growing rapidly.The
remarkable explosion of mobile internet traffic requireswireless
communication systems to support higher datarate. Various kinds of
transmission techniques in wirelesspropagation environment were
applied to meet the growingdemand, such as the high-order multiple
input multiple out-put (MIMO) [1] and the heterogeneous network,
where somelower power nodes are overlaid within a macro
network.Long-term evolution advanced (LTE-A), which was
stan-dardized by the 3rd generation partnership project (3GPP)[2],
is a promising wireless communication system to providehigh date
rate and spectral efficiency. The bandwidth of LTE-A can be up to
100MHz by using carrier aggregation tech-nology, which guarantees
effective bandwidth allocation to auser through concurrent
utilization of radio resources acrossmultiple carriers and
efficient carrier scheduling schemes [3].To improve the service
quality of cell edge users, some lowpower nodes can be deployed at
the edge of a cell, creatingwhat is referred to as a heterogeneous
network. Besidesthe transmission techniques mentioned above, some
othertechniques (e.g., coordinated multipoint transmission and
reception) are applied to improve the performance of
LTE-Asystem. However, there are still some challenges in deployinga
real LTE-A system. For example, in LTE-A, the trafficrequest of
some cells may be far higher than an acceptablelevel, named as
“hotspots,” while some of the other cells mayhave extra resources
to serve more users, which would resultin load unbalance and user
dissatisfaction. As the topology ofthe LTE-A heterogeneous network
is more complex, networkplanning and optimization bring a heavy
burden to LTE-A network operators. Self-optimizing network (SON) is
asolution to relieve the burden by selecting and adjustingthe key
parameters in the LTE-A system automatically [4].Load balancing
(LB), which hands off some users of a heavypayload cell to
neighboring comparatively less loaded cells,has been widely
discussed to increase the network resourceutilization.
2. Related Work
There are a great deal of articles which analyze the
loadbalancing problem of cellular networks. To equalize loadamong
cells, power control algorithms were proposed in [5],which have
reduced (or risen) the transmission power to
Hindawi Publishing CorporationInternational Journal of Antennas
and PropagationVolume 2014, Article ID 934101, 10
pageshttp://dx.doi.org/10.1155/2014/934101
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2 International Journal of Antennas and Propagation
contract (or expand) the coverage of heavy (or low)
payloadcells. By controlling beam, coverage patterns of
“commonsignals,” sizes, and shapes of cells can be
automaticallyadjusted to balance cell load [6]. In [7], the
cell-specificoffset was adjusted automatically based on payloads of
thesource cell and the neighboring cells. A two-layermobility
LBalgorithmwas discussed in [8], where the overloaded cell
canchoose a target cell by considering the situation of its two
layersurrounding cells. Authors in [9] selected the appropriate
LBmethod from handover parameter control and cell coveragecontrol
according to the situation. To cope with the potentialping-pong
load transfer and low convergence issues, authorsin [10] proposed a
game-theoretic solution to the SONLB. In [11], a multidomain LB
framework was proposed,which focuses on reducing the radio resource
cost andmitigating the cochannel interference across domains in
theheterogeneous network. In [12], authors proposed an antcolony
self-optimizing method for LB. In the method, firstthe load of all
cells is estimated; then some users are selectedto be handed over
to the neighbor cells according to thestimulation intensity of all
users in the cell. But none of theabove researches analyzes either
the optimal target cell for aheavily loaded cell or the optimal
number of users that shouldbe transferred between two cells.
There are a lot of articles which analyze wireless
networkthrough aMarkovian model. In [13], the blocking
probabilityof different types of service in a network is
calculated. Theauthors of [14] performed a stochastic performance
analysisof a finite-state Markovian channel shared by multiple
usersand derived delay and backlog upper bounds based on
theanalytical principle behind stochastic network calculus.
In this paper, we firstly evaluate the negative impact ofload
imbalance among cells through a Markovian model.Secondly, we
present a mathematical model for LB andintroduce the network flow
approach to derive the optimalsolution. Finally, we present a novel
LB algorithm basedon the optimal solution. Compared with the
previous LBalgorithms, our method can not only lighten the load of
thebusy cells but also avoid handover to much traffic to a
lowpayload target cell and change the target cell into a busy
cell.
The rest of this paper proceeds as follows: the scenario ofa
LTE-A heterogeneous network is described in Section 3. InSection 4,
we evaluate the negative impact of load imbalanceamong cells
through a Markovian model. In Section 5, weformulate LB as an
optimization problem, analyze loadbalancing based on the network
flow approach, and introducea novel LB algorithm in an LTE-A
heterogeneous network.In Section 6, a system-level simulation model
is presentedand the simulation results are analyzed. The paper
draws aconclusion in Section 7.
3. The Scenario
The scenario we considered is a heterogeneous network com-posed
of macrocells and picocells whose coverage is providedby macrobase
stations (Macro eNBs) and picobase stations(pico eNBs),
respectively [16], as shown in Figure 1. Thecombination of one
macrocell and some picocells overlaid
PicoeNB
PicoeNB
PicoeNB
PicoeNB
MacroeNB
MacroeNBMaUE
MaUE
MaUE
MaUE
PiUE
PiUE
Figure 1: The heterogeneous network.
within themacrocell can be named as cell.Theusers served bya
macro eNB are referred to as macrousers (MaUEs) and theusers served
by a pico eNB are referred as picousers (PiUEs).The system
bandwidth of each cell is equal and the frequencyspectrums of each
cell are divided among macrocell and thepicocells to avoid
interference between a MaUE and a PiUE.
4. Impact of Load Imbalance
In this section, we evaluate the negative impact of
loadimbalance among cells through a Markovian model. Tosimplify the
analysis, we consider the load imbalance betweentwo cells (cell 1
and cell 2). The arrival of user is assumedas a Poisson process and
the arrival rate of user in cell 𝑖 isassumed as 𝜆
𝑖. We assume that users are equally distributed
across three locations: macrocell center, macrocell edge,
andpicocell. We assume that the arrival rate of center users ofcell
1 is 𝜆
11, the arrival rate of edge users of cell 1 is 𝜆
12, and
the arrival rate of picousers of cell 1 is 𝜆13. Parameters 𝜆
21,
𝜆22, and 𝜆
23are the same meanings for cell 2. We assume
that the service time of users follows negative
exponentialdistribution. The service rate of all users in cell 𝑖 is
assumedas 𝜇𝑖. The signal to interference and noise ratio of cell
center
users is larger than that of cell edge users, so the
transmissionrate of one physical resource block (PRB) for a cell
edge useris smaller than that of a cell center user [17].
Therefore, weassume that the number of physical resource blocks
(PRBs)needed by a center user is one, the number of PRBs neededby
an edge user is four, and the number of PRBs needed bya picouser is
two. The total number of PRBs of each cell isassumed to be 100.
Then the PRBs occupied by users in cell𝑖 can be evaluated by a
three-dimensional Markovian model,as shown in Figure 2.
The state (𝑐, 𝑑, 𝑒) denotes that the number of PRBsoccupied by
cell center users of cell 𝑖 is 𝑐, the number of PRBsoccupied by
cell edge users of cell 𝑖 is 𝑑, and the number ofPRBs occupied by
picousers of cell 𝑖 is 𝑒.The number of PRBsoccupied by total users
of cell 𝑖 is 𝑐 + 𝑑 + 𝑒, which can notbe larger than the total
number of PRBs of each cell, that is,100. If the free PRB number in
a cell is no smaller than thenumber of PRBs required by a user, the
cell will allocate thePRBs to the user. Otherwise, the requirement
from the userwill be rejected. The probability that 𝑛 PRBs are used
by all
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International Journal of Antennas and Propagation 3
c, d, 0
c, d, e − 2
0, d, e c − 1, d, e c + 1, d, ec, d, e
c, 0, e
c, d − 4, e
c, d, e + 2
c, d + 4, e
𝜆i1 𝜆i1
𝜆i2
𝜆i2
𝜆i3
𝜆i3
𝜇i
𝜇i
𝜇i
𝜇i
𝜇i
𝜇i
...
...
...
· · · · · ·· · ·
· · ·· · ·
· · ·
Figure 2: The three-dimensional Markovian model for the PRB
occupation of cell 𝑖.
users can be respected by the stationary distribution 𝑞(𝑛)
in[13]; 𝑞(𝑛) is determined by the recursive formula as follows:
𝑞 (𝑛) =
𝑆
∑
𝑠=1
𝑎𝑠⋅ 𝑏𝑠
𝑛⋅ 𝑞 (𝑛 − 𝑏
𝑠) 𝑛 = 0, 1, . . . , 𝑁, (1)
where 𝑞(𝑛) = 0 for 𝑛 < 0 and ∑𝑁𝑛=1𝑞(𝑛) = 1. 𝑆 is the
number
of service types, that is, the dimension of the model. In
ourcase, there are three service types: the service of
macrocellcenter user, the service ofmacrocell edge user, and the
serviceof picocell user. 𝑎
𝑠= 𝜆𝑠/𝜇𝑠is the type 𝑠 offered load. 𝑏
𝑠is the
number of PRBs required by type 𝑠.𝑁 is the total number ofPRBs
of an LTE cell.
The blocking probability 𝑃𝑏𝑠
of type 𝑠 user can be calcu-lated as
𝑃𝑏𝑠
=
𝑁
∑
𝑛=𝑁−𝑏𝑠+1
𝑞 (𝑛) 𝑠 = 1, 2, . . . , 𝑆. (2)
Using formulas (1) and (2), we can calculate the
blockingprobability of users in case of different traffic densities
andload distributions.
For example, we consider two load distribution scenariosbetween
two cells. In the first scenario, we assume that thetotal arrival
rate of users in cell 1 is three times larger thanthe arrival rate
of users in cell 2. In the second scenario, weassume that the total
arrival rate of users in cell 1 is equal tothe total arrival rate
of users in cell 2. Besides, we assumethat the arrival rate of
total users, that is, users in cell 1with the addition of users in
cell 2, is equal in the two loaddistribution scenarios. Moreover,
the resource requirementand the service ratio are assumed to be the
same in the twoload distribution scenarios and the total number of
PRBsof each cell is 100. Some detail parameters are presented
in
0 4 8 12 16 20
Bloc
king
pro
babi
lity
Arrival ratio of total users (1/s)
Balanced load distribution scenarioUnbalanced load distribution
scenario
10−6
10−5
10−4
10−3
10−2
10−1
100
Figure 3: The blocking probability of users in two load
distributionscenarios versus the arrival rate of total users.
Table 1. Using formulas (1) and (2), we calculate the
blockingprobability of user in two load distribution scenarios as
thearrival rate of total users 𝜆total increasing from 1 to 20,
asshown in Figure 3.
From Figure 3, we can see that although the total trafficis the
same in the two load distribution scenarios, theblocking
probability of users in case of unbalanced loaddistribution is
larger than the blocking probability of usersin case of balanced
load distribution. So we need using LBto hands off some users of
heavily loaded cell to neighboringcomparatively less loaded cells,
for the purpose of improvingnetwork performance.
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4 International Journal of Antennas and Propagation
Table 1: The Markovian model parameters.
Scenario User type 𝜆 𝜇 𝑏𝑠
The center user of cell 1 0.25∗𝜆total 0.2 1
Unbalanced load distribution scenario
The edge user of cell 1 0.25∗𝜆total 0.2 4The picouser of cell 1
0.25∗𝜆total 0.2 2
The center user of cell 2 0.083∗𝜆total 0.2 1The edge user of
cell 2 0.083∗𝜆total 0.2 4The picouser of cell 2 0.083∗𝜆total 0.2
2
Balanced load distribution scenarioThe center user of cell 1 or
2 0.167∗𝜆total 0.2 1The edge user of cell 1 or 2 0.167∗𝜆total 0.2
4The picouser of cell 1 or 2 0.167∗𝜆total 0.2 2
5. LB Based on Network Flow Approach
As described in Section 4, load imbalance between twoadjacent
cells will affect the resource utilization of the twocells. If
there aremore cells in a system, the problem of how tobalance the
load among cells is more complex. In this section,we formulate the
LB problem as an optimization problem andsolve the problem using
network flow approach.
5.1. LB Problem Formulation and Analysis. We consider anetwork
consisting of 𝑛 cells and several users. Among the 𝑛cells, the
number of physical resource blocks (PRBs) neededby a cell 𝑘 to
support the traffic of users in the cell 𝑘 is denotedby𝑁𝑘. Due to
traffic distribution imbalance,𝑁
𝑘varies in size.
We assume a scenario like Figure 4, where cells A and C haveone
user, and cells B and D have three users. In Figure 4, weassume
each user needs the same number of PRBs to keepthe analysis simple.
Two LB schemes are shown in Figure 4.In scheme 1, a user in cell B
is switched to cell C. After the LB,the numbers of users in four
cells are 1, 2, 2, and 3, respectively.In scheme 2, a user in cell
B is switched to cell A and a userin cell D is switched to cell C.
After the LB, the number ofusers in each cell is 2. It is obvious
that scheme 2 is betterthan scheme 1.
From the example we think that LB should be analyzedamong
multiple cells rather than just between two cells. Ifthere are 𝑛
cells, we need to switch user among cells to make𝑁𝑘approaching𝑁 =
(1/𝑛)∑𝑛
𝑘=1𝑁𝑘.𝑁 is the average number
of PRBs needed by a cell. However, switching among cellshas some
signaling overhead, and the switched user’s signalquality may
decrease. Therefore, in LB, we should minimizethe number of
handovers. Then the problem is equivalent toan optimization problem
that can be written as
(𝑃1) min (𝑛
∑
𝑖=1
∑
𝑗 ̸= 𝑖
𝑃𝑖,𝑗) (1 ≤ 𝑗 ≤ 𝑛)
s.t. 𝑁𝑖− ∑
𝑗 ̸= 𝑖
𝑃𝑖,𝑗+ ∑
𝑗 ̸= 𝑖
𝑃𝑗,𝑖= 𝑁,
(1 ≤ 𝑖 ≤ 𝑛, 1 ≤ 𝑗 ≤ 𝑛) ,
(3)
where 𝑃𝑖,𝑗
is the number of PRBs occupied by businesswhich switched from
cell 𝑖 to cell 𝑗. It should be noticed
that there may be no solution to the constraint equationof (3)
if 𝑃
𝑖,𝑗are integers, so we assume that 𝑃
𝑖,𝑗are real
numbers in this subsection and round off 𝑃𝑖,𝑗in the novel LB
algorithm subsection. We analyze the optimization problemin the
following cases of Figure 5.
5.1.1. Case 1:Three Cells in a Row. To balance the load of
threecells in a row, we firstly need calculate the average load of
onecell 𝑁. Secondly, we start to balance the load from the cellin
the left side (denoted as cell 1). If the load of cell 1 is
largerthan𝑁, we transfer services which occupy𝑁
1−𝑁 PRBs from
cell 1 to the middle cell (denoted as cell 2). If the load of
cell 1is smaller than𝑁, we transfer services which occupy𝑁−𝑁
1
PRBs from cell 2 to cell 1. At last, we balance the load
betweencell 2 and the cell in the right side (denoted as cell 3).
If theload of cell 1 and cell 2 is larger than 2 ∗ 𝑁, then we
transferservices which occupy𝑁
1+ 𝑁2− 2 ∗ 𝑁 from cell 2 to cell 3.
If the load of cell 1 and cell 2 is smaller than 2 ∗ 𝑁, then
wetransfer services which occupy 2 ∗ 𝑁 − 𝑁
1− 𝑁2from cell 3
to cell 2. At last, the solution of (3) is described as
follows:
𝑃𝑖,𝑗=
{{{{{
{{{{{
{
max((4 − 𝑗)𝑁 −3
∑
𝑥=𝑗
𝑁𝑥, 0) 𝑖 ∈ {1, 2} ; 𝑗 = 𝑖 + 1,
max(𝑗𝑁 −𝑗
∑
𝑥=1
𝑁𝑥, 0) 𝑖 ∈ {2, 3} ; 𝑗 = 𝑖 − 1.
(4)
As a consequence of the objective function in (3), either𝑃𝑖,𝑗or
𝑃𝑗,𝑖is zero and those two parameters are nonnegative,
so we define other parameters 𝑃𝑖,𝑗which can be negative:
𝑃
𝑖,𝑗={
{
{
𝑃𝑖,𝑗
(𝑃𝑖,𝑗> 0) ,
−𝑃𝑗,𝑖
(𝑃𝑖,𝑗= 0) .
(5)
Property (𝑃𝑖,𝑗= −𝑃
𝑗,𝑖). Combining formulas (4) and (5), the
simultaneous equation of LB model is as follows:
𝑁1− 𝑃
1,2= 𝑁, (6)
𝑁2− 𝑃
2,3+ 𝑃
1,2= 𝑁, (7)
𝑁3+ 𝑃
2,3= 𝑁. (8)
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International Journal of Antennas and Propagation 5
Cell A Cell B
Scheme 1
Cell C Cell D
(a)
Scheme 2
(b)
Figure 4: A LB scenario and two corresponding schemes.
Case 1. Three cells in a row
Case 3. n cellsCase 2. n cells in a row
· · · · · ·· · ·
N1 N1
N1
N2 N2
N2
N3
N3 N4 N5
N6Nn
Figure 5: Network layout cases.
Formula (6) means that after transferring some servicefrom cell
1 to cell 2 if 𝑃
1,2≥ 0 (or from cell 2 to cell 1 if
𝑃
1,2< 0), cell 1 has an average load level. Formulas (7)
and
(8) are the same meanings to cell 2 and cell 3. We sum up
(6),(7), and (8) and obtain𝑁
1+𝑁2+𝑁3= 3𝑁which is an identity.
There are two unknown numbers in the above simultaneousequation,
and the number of linearly independent equationsis two; that is,
(6) and (8) are linearly independent. So thesolution (4) is the
optimal solution because of the uniquenessof the solution.
5.1.2. Case 2: 𝑛 Cells in a Row. In this case, using the
samemethod in case 1, we can calculate the solution of (3), whichis
described as
𝑃𝑖,𝑗=
{{{{{{{{{{
{{{{{{{{{{
{
max((𝑛 − 𝑗 + 1)𝑁 −𝑛
∑
𝑥=𝑗
𝑁𝑥, 0)
𝑖 ∈ {1, 2, . . . , 𝑛 − 1} ; 𝑗 = 𝑖 + 1,
max(𝑗𝑁 −𝑗
∑
𝑥=1
𝑁𝑥, 0)
𝑖 ∈ {2, 3, . . . , 𝑛} ; 𝑗 = 𝑖 − 1.
(9)
Similarly to case 1, we can demonstrate the solution (9) isthe
optimal solution.
4
5 1 2
6
3 1
5 4 3
6
2
· · · · · · · · · · · ·
Figure 6: Two methods to mark 𝑛 cells with numbers.
5.1.3. Case 3: 𝑛 Cells. When there are 𝑛 cells, we can markthem
in accordancewith the sequence in Figure 6. If only cellswith
adjacent sequence numbers can switch users, then case3 is equal to
case 2. So (9) is a solution to case 3. But it is notthe optimal
solution. In the remainder of this paper, we usenetwork flow
approach to obtain the optimal solution of theoptimization
problem.
5.2. LB Base on Network Flow Approach. In this section,firstly,
we describe the optimization problem by graph theory.In graph
theory, network flow has been rapidly expandingsince the work of
Ford and Fulkerson [18] on flow in 1962.The broad applicability in
different systems of network flowoptimization has brought great
interest in it. A network flowis a directed graph composed of nodes
and edges. Each edgereceives a flowwhich cannot exceed the edge’s
capacity.Nodesare classified as three types: source, middle, and
sink.
In imbalance traffic distribution scenario, some heavilyloaded
cells have more than 𝑁 PRBs occupied. Therefore,some users need to
switch to adjacent low payload cells. Weterm those heavy payload
cells as the source nodes whilethose low payload cells are termed
as the sink nodes, ingraph theory. The target is to transfer
occupied PRBs in sinknodes exceeding𝑁 to the sink nodes. Handoff
from a cell toanother (𝑖 → 𝑗) is viewed as an arc. The arc is
bidirectional
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6 International Journal of Antennas and Propagation
Cell which has more occupied resources than average
Arc between two cells
Cell which has less occupied resources than average
Figure 7: Seven nodes representing 7 cells.
because handoff between two cells is bidirectional, as shownin
Figure 7.
The number of PRBs occupied by the users switchedbetween two
cells 𝑃
𝑖,𝑗is compared as the amount of flow on
the arc.The number of PRBs occupied by the users which canbe
switched between two cells is the capacity of the arc. Thecapacity
of an arc (𝑖 → 𝑗) is 𝜔 ⋅ 𝑁
𝑖, where 0 < 𝜔 < 1. 𝜔 is
used to indicate that only a part of users at the edge of a
cellcan be switched to adjacent cell. Then the LB is equivalent
tothe following optimization problem:
(𝑃2) min (𝑛
∑
𝑖=1
∑
𝑗 ̸= 𝑖
𝑃𝑖,𝑗) (1 ≤ 𝑗 ≤ 𝑛)
s.t. 𝑁𝑖− ∑
𝑗 ̸= 𝑖
𝑃𝑖,𝑗+ ∑
𝑗 ̸= 𝑖
𝑃𝑗,𝑖= 𝑁,
(1 ≤ 𝑖 ≤ 𝑛, 1 ≤ 𝑗 ≤ 𝑛)
𝑃𝑖,𝑗⩽ 𝜔 ⋅ 𝑁
𝑖.
(10)
Now the optimization problem is a transportation net-work flow
problem including multiple source multiple sinknodes. Each source
node needs to transfer out services whichoccupy 𝑁
𝑘− 𝑁 PRBs and consequently each sink node
needs to take over those services. We need to assign
flowdistribution in each arc of the graph. In the flow
distribution,the difference of the amount of flow from a source
node (i.e.,cell 𝑖) to other nodes and the amount of flow fromother
nodesto the source node is equal to 𝑁
𝑖− 𝑁 so that the source
node will have𝑁 PRBs occupied by users after the
handoverprocess. For a sink node (i.e., cell 𝑗), the difference of
theamount of flow from other nodes to the sink node and theamount
of flow from the sink node to other nodes is equal to𝑁 − 𝑁
𝑗so that the sink node will have𝑁 PRBs occupied by
users after the handover process.Amultiple source nodes and
sinknodes problem is harder
than a single source node and sink node problem. By usinga
virtual source node and a virtual sink node, the problem
The virtual source point
The virtual sink point
Unidirectional arc
Figure 8: Arcs between the virtual source node and source
nodes(sink nodes and the virtual sink node).
is transformed into a single source node and single sinknode
transportation network flow problem. In order to makethe above two
problems equivalent, a unidirectional arc isassumed from the
virtual source node to each source node.The capacity of each
unidirectional arc is the number of PRBsoccupied in each heavily
loaded cell minus 𝑁. Similarly, aunidirectional arc is assumed from
each sink node to thevirtual sink node. The capacity of each
unidirectional arc is𝑁 minus the number of PRBs occupied in each
low payloadcell, as shown in Figure 8. If an arc between the
virtual sourcenode and a source node is saturated, then the source
nodewillhave 𝑁 PRBs occupied by users after the handover
process,because the flow in the arc between the virtual source
nodeand a source node is equal to the amount of flow fromthe source
node to other nodes minus the amount of flowfrom other nodes
(except the virtual source node) to thesource node. Similarly, If
an arc between a sink node and thevirtual sink node is saturated,
then the sink node will have𝑁PRBs occupied by users after the
handover process. Now themultiple source nodes and sink nodes
problem is equal to thesingle source node and single sink node
problem.
If we give a flow distribution, of which the amount of flowout
of the virtual source node is the amount of PRBs occupiedby users
in all source node subtract 𝑙 ⋅ 𝑁 (i.e., arcs betweenthe virtual
source node and all source nodes are saturated),where 𝑙 is the
number of source nodes, then all nodes willhave 𝑁 PRBs occupied
after the handover process and theflow distribution is a solution
to the optimization problem(10). Judging the existence of the
solution to (10) is equal tojudging if there is a flow distribution
where arcs between thevirtual source node and all source nodes are
saturated. Sowe need to calculate the maximum flow between the
virtualsource node and the virtual sink node. If the maximumflow is
equal to the sum of capacities of arcs between thevirtual source
node and all source nodes (i.e., the amount ofPRBs occupied by
users in all source node subtract 𝑙 ⋅ 𝑁),solution to (10) exists.
We can calculate network maximum
-
International Journal of Antennas and Propagation 7
flow from the virtual source node to the virtual sink node
byusing algorithm of Ford and Fulkerson [18], which is to
findaugmented paths by using the idea of finding independentpaths,
and at least one arc will reach saturated state. Thecomputation
complexity of calculating the maximum flow byusing independent
paths method is 𝑂(|𝐸| ∗ 𝑓), where 𝐸 isthe number of edges in the
graph and 𝑓 is the maximum flowin the graph. If aforementioned 𝜔 is
close to 1 (i.e., a largepart of users are located at cell edge and
can be switched toadjacent cell), the maximum flow will be
calculated as equalto the amount of PRBs occupied by users in all
source nodesubtract 𝑙 ⋅ 𝑁 and the solution to (10) will exist. So
we assumethat 𝜔 is close to 1 to ensure the solution to (10) will
existand to keep analysis simple. In future work, we will
analysesome scenario where solution to (10) does not exist.
Aftermaking sure the solution to (10) exists, we need to find a
flowdistribution which needs the least sum of flow between eachtwo
adjacent nodes (i.e., the least sum of handover betweeneach two
adjacent cells). To keep analysis simple, we assumethat the cost
for switching per PRB unit traffic is equal forall cells and users.
Now, finding a flow distribution whichneeds the least sum of flow
between each two adjacent nodesis a minimum cost flow problem.The
optimal solution to theminimumcost flowproblemcan be figured out by
usingOrlinalgorithm [19], and the computation complexity of
Orlinalgorithm is 𝑂(𝑚 log 𝑛(𝑚 + 𝑛 log 𝑛)), where 𝑛 is the numberof
nodes and 𝑚 is the number of arcs. It is not complicatedto
calculate the maximum flow and the minimum cost flowbecause they
all can be solved by polynomial algorithm. Sowe can use the optimal
solution solved by Orlin algorithm toguide load balance.
5.3. A Novel LB Algorithm. In this section, a novel LBalgorithm
is presented based on the optimal solution. Thenovel LB algorithm
is called optimal solution-based LB(OSLB). Firstly, the optimal
solution to the numbers of PRBsoccupied by communication service
transfer between cells forload balancing will be figured out by the
following procedure.
(1) Each cell calculates the PRBs needed by each user inthe cell
through channel measurements and countsthe total PRBs needed, which
is denoted as𝑁
𝑖.
(2) Each cell transmits the 𝑁𝑖to its ambient two layer
cells, so that each cell knows its own 𝑁𝑖and its
ambient two layer cells’𝑁𝑖.Then, by theOrlinmethod
[19], 𝑃𝑖,𝑗can be calculated.
(3) Using (5), 𝑃𝑖,𝑗
can be calculated. Then each celltransmits the 𝑃
𝑖,𝑗to its ambient one layer cells.
(4) All cells average their own 𝑃𝑖,𝑗and the −𝑃
𝑗,𝑖received
from their ambient cells, and the averaged values aredefined as
𝑃
𝑖,𝑗, which are the final amount of PRBs
occupied by the users that should be transferred. Atlast, 𝑃
𝑖,𝑗are rounded down if they are not integers.
Secondly, we pick out cell 𝑖 which has 𝑃𝑖,𝑗
greater thanzero. Then we sequence the users in cell 𝑖 according
tothe size of 𝐷
𝑛= RSRP
𝑛,𝑗− RSRP
𝑛,𝑖. RSRP
𝑛,𝑖is reference
signal received power (RSRP) between cell 𝑖 and user 𝑛.
Thesequence number of user is indicated by 𝑀, and the PRBsoccupied
by user 𝑛 are indicated by PRB
𝑛. PRB𝑛vary among
users because the modulation and coding mode is differentamong
users with the base station.
Lastly, handover for load balancing in the above men-tioned cell
𝑖 will be implemented. According to [20], ahandover event is
initiated when user detects that a neighborcell offers a better
signal quality than its current serving cell.This condition is
referred to as measurement event A3, whichhas been formulated
as
𝑀𝑠+Oc𝑠,𝑡+Hyst < 𝑀
𝑡, (11)
where 𝑀𝑠and 𝑀
𝑡are the signal strength or quality values
for serving cell 𝑠 and target cell 𝑡, and Hyst is
cell-specifichysteresis value. Oc
𝑠,𝑡is the specific offset for RSRP between
cell 𝑠 and cell 𝑡. As can be seen from (11), when Oc𝑠,𝑡is
small,
it is easy for users to migrate to the cell 𝑡 rather than campon
the cell 𝑠. So the coverage of different cells is adjustableby
changing the specific offset Oc among cells. In our LBalgorithm, LB
is performed by automatically adjusting Oc
𝑠,𝑡
based on 𝑃𝑖,𝑗. Oc𝑠,𝑡can not be very large because an
unsuited
value will cause some users to switch to an unsuited cell.Ocmax
is the upper limit of |Oc𝑠,𝑡|. We define that 𝐷
𝑛= 𝐷𝑛−
Hyst.Thehandover for load balancing of cell 𝑖 is implementedby
the procedures in Figure 9, where ∑𝑀
𝑚=1PRB𝑚
is thenumber of PRBs required by𝑀 users who are switched fromthe
heavily loaded cell to the low payload cell.
If the process comes to an end with ∑𝑀𝑚=1
PRB𝑚< 𝑃
𝑖,𝑗
by the reason of −𝐷𝑛< Ocmax, that is to say, there are
not
enough users at the edge of the heavily loaded cell and
thetarget low payload cell, then the load imbalance problem isnot
completely solved. In this case, we search picocells at theedge of
the heavy payload cell and switch those picocells andthe users
served by those picocells to the adjacent low payloadcell to
balance load.
6. Simulation and Performance Analysis
In this section, system-level simulation for the LTE-A
cellularnetwork is carried out to evaluate the performance of
theproposed algorithm. There are 2 reference scenarios: no LBand
the load-based MLB method as presented in [7]. Thesimulation
platform contains 37 regular hexagonal cells, andthe cell radius is
577m. Some detail simulation parametersare presented in Table 2. In
order to avoid boundary effects,wrap-around technique is applied.
For simplicity, only oneeNB is located in the cell center, and no
sectors are divided.In each cell, there are two to four picocells
located randomlyat the cell edge. User numbers of 22 normal cells
are 10. Usernumbers of other 15 busy cells are varying from 10 to
40. Itis assumed that the traffic type of users is constant bit
rate(CBR). The constant target date rate for each user is
1Mbps.Detailed simulation assumptions and parameters are given
inTable 1.
-
8 International Journal of Antennas and Propagation
Start
End
M = 1, Oc = zero
−Dn < Oc
−Dn < Oc
max
OcmaxOc
Mth user ∉ cell iMth user ∈ cell j
Oc = Dn M = M + 1
∑Mm=1
PRBm ≤ Pi,j
=
N
Y
Y
N
N
Y
Figure 9: The load balancing flow chart.
Table 2: Simulation parameters.
Parameters AssumptionsCarrier frequency 1.9GHzBandwidth
40MHzCell radius 577mAntenna type OmnidirectionalMacrocell
transmitter power 46 dBmPicocell transmitter power 3 dBmChannel
model SCMmodel [15]Shadow fading (SF) Log-normalSF correlation
distance 10mNoise Thermal noiseNoise power spectral density −174
dBmNumber of Tx antenna 1Number of Rx antenna 2
Figure 10 shows the load distribution index (LDI), whichis
similar to Jain et al.’s fairness index [21] and is defined
asfollows:
LDI =(∑𝑛
𝑖=1𝑁𝑖)2
|𝑛| ∑𝑛
𝑖=1(𝑁𝑖)2. (12)
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00
Load
dist
ribut
ion
inde
x
The number of users in a heavily loaded cell
NO LB MLB OSLB
5 10 15 20 25 30 35 40 45
Figure 10: The load distribution index versus the number of
usersin a heavily loaded cell.
This index measures the degree of similarity of loadamong
cells.Themore closer the payload values are, the closerthe index is
to 1. When the call arrival rate of busy cells isincreased, the
load among cells is imbalanced. So this valueis decreasing in the
three lines of Figure 11. But the OSLBscheme achieves the highest
load distribution index amongthree scenarios, so OSLB outperforms
references in terms ofLB result. When user numbers of heavy-payload
cells are 10,PRBs needed of cells may vary because PRBs needed by
usersare different (some users in cell edge need more PRBs
thanusers in cell centre). So the LDIs of MLB and NO LB are not1
when all cells have 10 users. The LDI of OSLB is very closeto 1
when all cells have 10 users.
The average resource occupied ratio of heavily loadedcells
versus the user number of a heavily loaded cell is givenin Figure
11.The less resource occupied ratio of heavily loadedcells is
directly proportional to the lower service failure ratioof heavy
payload cells. So this parameter should be as closeas possible to
the line with inverted triangle which means theaverage resource
occupied ratio of all cells. Compared withthe NOLB scenario, busy
cells in OSLB have smaller resourceoccupied ratio. So in OSLB, the
service failure ratio of busycells is less than the NO LB one,
since proper boundary usersare switched to neighboring idle cells
and more resources arereserved to remaining and new coming users.
The resourceoccupied ratio of heavily loaded cell in the MLB
scenario issimilar to the OSLB one, which means that the two
methodshave similar effect on lightening the load of the busy
cell.
As depicted in Figure 12, it is obvious that the proposedscheme
outperforms the compared schemes in terms of theresource occupied
ratio of a particular lowpayload cell, whichaccepts most users
switched from heavily loaded cells andhas the largest PRBs occupied
after handover process amongall old low payload cells. If the
resource occupied ratios ofsome low payload cells after LB are
high, new busy cells are
-
International Journal of Antennas and Propagation 9
30
40
50
60
70
80
90
100
Aver
age r
esou
rce o
ccup
ied
ratio
of
The number of users in a heavily loaded cell
NO LB MLB
OSLB Average resource occupied ratio of all cells
5 10 15 20 25 30 35 40 45
heav
ily lo
aded
cells
(%)
Figure 11: The average resource occupied ratio of heavily
loadedcells versus the number of users in a heavily loaded
cell.
The r
esou
rce o
ccup
ied
ratio
of
a p
artic
ular
low
pay
load
cell
(%)
30
40
50
60
70
80
90
100
The number of users in a heavily loaded cell
NO LB MLB
OSLB Average resource occupied ratio of all cells
5 10 15 20 25 30 35 40 45
Figure 12: The resource occupied ratio of a particular low
payloadcell versus the number of users in a heavily loaded
cell.
brought in. So the ratio in Figure 12 should be low and shouldbe
as close as possible to the line with inverted triangle whichmeans
the average resource occupied ratio of all cells. WhenLB is not
used, this value does not vary and remains near40%. When MLB method
in [7] is used, this value increasesand is larger than average
resource occupied ratio of heavilyloaded cells in the same
scenario, which signifies that newheavily loaded cells are brought
in. When OSLB is used, thisvalue increases but is smaller than
average resource occupiedratio of heavily loaded cells in the same
scenario and is a littlebigger than the average resource occupied
ratio of all cells,
which signifies that new heavily loaded cells are not
broughtin.
7. Conclusion
In this paper, LB is optimized by carefully designing anovel
algorithm named OSLB. Different from the previousliteratures, the
network flow approach is used to derive theoptimal solution, which
plays a large part in OSLB. TheOSLB algorithm is evaluated and
compared by system-levelsimulation. Results show that the load
distribution indexand the resource occupation ratio of cells are
significantlyimproved. In this paper, we assume that each PRB of a
cellcan only be allocated to macrocell users or picousers; thatis,
those two kinds of users can not work on the same
PRBsimultaneously. In the future, we will investigate the
scenariowhere a macrocell user and a picouser can share the
samePRB, which is more realistic and more efficient.
Conflict of Interests
The authors declare that there is no conflict of
interestsregarding the publication of this paper.
Acknowledgments
This work has been partially sponsored by EU FP7
IRSESMobileCloud Project (Grant no. 612212), the 111 Project(no.
B08004), the major project of Ministry of Industryand
Informationization of China (2013ZX03001026), and theFundamental
Research Funds for the Central Universities.
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