Research Article Advanced Load Balancing Based on Network Flow Approach in LTE … · 2019. 5....

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

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

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.


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)


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


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


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.


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


30

40

50

60

70

80

90

100

Aver

age r

esou

rce o

ccup

ied

ratio

of


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


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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