research article advanced load balancing based...

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 jiashucongjsc163com

Received 20 February 2014 Accepted 21 April 2014 Published 20 May 2014

Academic Editor Lin Zhang

Copyright copy 2014 Shucong Jia et al This is an open access article distributed under the Creative Commons Attribution Licensewhich 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 networkcreating 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 proposedTheproposed 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 rapidlyThe 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 networkLong-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 (eg 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 ldquohotspotsrdquo 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 cellshas 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 pageshttpdxdoiorg1011552014934101

2 International Journal of Antennas and Propagation

contract (or expand) the coverage of heavy (or low) payloadcells By controlling beam coverage patterns of ldquocommonsignalsrdquo 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 proposedwhich 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 modelSecondly 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 networkIn 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 cellTheusers 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 119894 isassumed as 120582

119894 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 120582

11 the arrival rate of edge users of cell 1 is 120582

12 and

the arrival rate of picousers of cell 1 is 12058213 Parameters 120582

21

12058222 and 120582

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 119894 is assumedas 120583119894 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 cell119894 can be evaluated by a three-dimensional Markovian modelas shown in Figure 2

The state (119888 119889 119890) denotes that the number of PRBsoccupied by cell center users of cell 119894 is 119888 the number of PRBsoccupied by cell edge users of cell 119894 is 119889 and the number ofPRBs occupied by picousers of cell 119894 is 119890The number of PRBsoccupied by total users of cell 119894 is 119888 + 119889 + 119890 which can notbe larger than the total number of PRBs of each cell that is100 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 119899 PRBs are used by all

International Journal of Antennas and Propagation 3

c d 0

c d e minus 2

0 d e c minus 1 d e c + 1 d ec d e

c 0 e

c d minus 4 e

c d e + 2

c d + 4 e

120582i1 120582i1

120582i2

120582i2

120582i3

120582i3

120583i

120583i

120583i

120583i

120583i

120583i

middot middot middot middot middot middotmiddot middot middot

middot middot middot middot middot middot

middot middot middot

Figure 2 The three-dimensional Markovian model for the PRB occupation of cell 119894

users can be respected by the stationary distribution 119902(119899) in[13] 119902(119899) is determined by the recursive formula as follows

119902 (119899) =

119878

sum

119904=1

119886119904sdot 119887119904

119899sdot 119902 (119899 minus 119887

119904) 119899 = 0 1 119873 (1)

where 119902(119899) = 0 for 119899 lt 0 and sum119873119899=1119902(119899) = 1 119878 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 119886

119904= 120582119904120583119904is the type 119904 offered load 119887

119904is the

number of PRBs required by type 119904119873 is the total number ofPRBs of an LTE cell

The blocking probability 119875119887119904

of type 119904 user can be calcu-lated as

119875119887119904

=

119873

sum

119899=119873minus119887119904+1

119902 (119899) 119904 = 1 2 119878 (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 (1s)

Balanced load distribution scenarioUnbalanced load distribution scenario

10minus6

10minus5

10minus4

10minus3

10minus2

10minus1

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 120582total 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 120582 120583 119887119904

The center user of cell 1 025lowast120582total 02 1

Unbalanced load distribution scenario

The edge user of cell 1 025lowast120582total 02 4The picouser of cell 1 025lowast120582total 02 2

The center user of cell 2 0083lowast120582total 02 1The edge user of cell 2 0083lowast120582total 02 4The picouser of cell 2 0083lowast120582total 02 2

Balanced load distribution scenarioThe center user of cell 1 or 2 0167lowast120582total 02 1The edge user of cell 1 or 2 0167lowast120582total 02 4The picouser of cell 1 or 2 0167lowast120582total 02 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 sectionwe formulate the LB problem as an optimization problem andsolve the problem using network flow approach

51 LB Problem Formulation and Analysis We consider anetwork consisting of 119899 cells and several users Among the 119899cells the number of physical resource blocks (PRBs) neededby a cell 119896 to support the traffic of users in the cell 119896 is denotedby119873119896 Due to traffic distribution imbalance119873

119896varies 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 4In scheme 1 a user in cell B is switched to cell C After the LBthe numbers of users in four cells are 1 2 2 and 3 respectivelyIn 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 119899 cells we need to switch user among cells to make119873119896approaching119873 = (1119899)sum

119899

119896=1119873119896119873 is the average number

of PRBs needed by a cell However switching among cellshas some signaling overhead and the switched userrsquos 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

(1198751) min (

119899

sum

119894=1

sum

119895 = 119894

119875119894119895) (1 le 119895 le 119899)

st 119873119894minus sum

119895 = 119894

119875119894119895+ sum

119895 = 119894

119875119895119894= 119873

(1 le 119894 le 119899 1 le 119895 le 119899)

(3)

where 119875119894119895

is the number of PRBs occupied by businesswhich switched from cell 119894 to cell 119895 It should be noticed

that there may be no solution to the constraint equationof (3) if 119875

119894119895are integers so we assume that 119875

119894119895are real

numbers in this subsection and round off 119875119894119895in the novel LB

algorithm subsection We analyze the optimization problemin the following cases of Figure 5

511 Case 1Three Cells in a Row To balance the load of threecells in a row we firstly need calculate the average load of onecell 119873 Secondly we start to balance the load from the cellin the left side (denoted as cell 1) If the load of cell 1 is largerthan119873 we transfer services which occupy119873

1minus119873 PRBs from

cell 1 to the middle cell (denoted as cell 2) If the load of cell 1is smaller than119873 we transfer services which occupy119873minus119873

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 lowast 119873 then we transferservices which occupy119873

1+ 1198732minus 2 lowast 119873 from cell 2 to cell 3

If the load of cell 1 and cell 2 is smaller than 2 lowast 119873 then wetransfer services which occupy 2 lowast 119873 minus 119873

1minus 1198732from cell 3

to cell 2 At last the solution of (3) is described as follows

119875119894119895=

max((4 minus 119895)119873 minus3

sum

119909=119895

119873119909 0) 119894 isin 1 2 119895 = 119894 + 1

max(119895119873 minus119895

sum

119909=1

119873119909 0) 119894 isin 2 3 119895 = 119894 minus 1

(4)

As a consequence of the objective function in (3) either119875119894119895or 119875119895119894is zero and those two parameters are nonnegative

so we define other parameters 1198751015840119894119895which can be negative

1198751015840

119894119895=

119875119894119895

(119875119894119895gt 0)

minus119875119895119894

(119875119894119895= 0)

(5)

Property (1198751015840119894119895= minus1198751015840

119895119894) Combining formulas (4) and (5) the

simultaneous equation of LB model is as follows

1198731minus 1198751015840

12= 119873 (6)

1198732minus 1198751015840

23+ 1198751015840

12= 119873 (7)

1198733+ 1198751015840

23= 119873 (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


N1N1

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 1198751015840

12ge 0 (or from cell 2 to cell 1 if

1198751015840

12lt 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 obtain119873

1+1198732+1198733= 3119873which 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

512 Case 2 119899 Cells in a Row In this case using the samemethod in case 1 we can calculate the solution of (3) whichis described as

119875119894119895=

max((119899 minus 119895 + 1)119873 minus119899

sum

119909=119895

119873119909 0)

119894 isin 1 2 119899 minus 1 119895 = 119894 + 1

max(119895119873 minus119895

sum

119909=1

119873119909 0)

119894 isin 2 3 119899 119895 = 119894 minus 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

middot middot middot middot middot middot middot middot middot middot middot middot

Figure 6 Two methods to mark 119899 cells with numbers

513 Case 3 119899 Cells When there are 119899 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

52 LB Base on Network Flow Approach In this sectionfirstly we describe the optimization problem by graph theoryIn graph theory network flow has been rapidly expandingsince the work of Ford and Fulkerson [18] on flow in 1962The 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 edgersquos capacityNodesare classified as three types source middle and sink

In imbalance traffic distribution scenario some heavilyloaded cells have more than 119873 PRBs occupied Thereforesome 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 exceeding119873 to the sink nodes Handoff from a cell toanother (119894 rarr 119895) 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 119875

119894119895is compared as the amount of flow on

the arcThe number of PRBs occupied by the users which canbe switched between two cells is the capacity of the arc Thecapacity of an arc (119894 rarr 119895) is 120596 sdot 119873

119894 where 0 lt 120596 lt 1 120596 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

(1198752) min (

119899

sum

119894=1

sum

119895 = 119894

119875119894119895) (1 le 119895 le 119899)


119895 = 119894

119875119894119895+ sum

119895 = 119894

119875119895119894= 119873

(1 le 119894 le 119899 1 le 119895 le 119899)

119875119894119895⩽ 120596 sdot 119873

119894

(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 119873

119896minus 119873 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 distributionthe difference of the amount of flow from a source node (iecell 119894) to other nodes and the amount of flow fromother nodesto the source node is equal to 119873

119894minus 119873 so that the source

node will have119873 PRBs occupied by users after the handoverprocess For a sink node (ie cell 119895) 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 to119873 minus 119873

119895so that the sink node will have119873 PRBs occupied by

users after the handover processAmultiple 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 nodeThe capacity of each unidirectional arc is the number of PRBsoccupied in each heavily loaded cell minus 119873 Similarly aunidirectional arc is assumed from each sink node to thevirtual sink node The capacity of each unidirectional arc is119873 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 119873 PRBs occupied by users after the handover processbecause 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 have119873PRBs 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 119897 sdot 119873 (ie arcs betweenthe virtual source node and all source nodes are saturated)where 119897 is the number of source nodes then all nodes willhave 119873 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 (ie the amount ofPRBs occupied by users in all source node subtract 119897 sdot 119873)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 119874(|119864| lowast 119891) where 119864 isthe number of edges in the graph and 119891 is the maximum flowin the graph If aforementioned 120596 is close to 1 (ie 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 119897 sdot 119873 and the solution to (10) will exist So we assumethat 120596 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 (ie 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 problemThe optimal solution to theminimumcost flowproblemcan be figured out by usingOrlinalgorithm [19] and the computation complexity of Orlinalgorithm is 119874(119898 log 119899(119898 + 119899 log 119899)) where 119899 is the numberof nodes and 119898 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

53 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 as119873

119894

(2) Each cell transmits the 119873119894to its ambient two layer

cells so that each cell knows its own 119873119894and its

ambient two layer cellsrsquo119873119894Then by theOrlinmethod

[19] 119875119894119895can be calculated

(3) Using (5) 1198751015840119894119895

can be calculated Then each celltransmits the 1198751015840

119894119895to its ambient one layer cells

(4) All cells average their own 1198751015840119894119895and the minus1198751015840

119895119894received

from their ambient cells and the averaged values aredefined as 11987510158401015840

119894119895 which are the final amount of PRBs

occupied by the users that should be transferred Atlast 11987510158401015840

119894119895are rounded down if they are not integers

Secondly we pick out cell 119894 which has 11987510158401015840119894119895

greater thanzero Then we sequence the users in cell 119894 according tothe size of 119863

119899= RSRP

119899119895minus RSRP

119899119894 RSRP

119899119894is reference

signal received power (RSRP) between cell 119894 and user 119899 Thesequence number of user is indicated by 119872 and the PRBsoccupied by user 119899 are indicated by PRB

119899 PRB119899vary 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 119894 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 cellThis condition is referred to as measurement event A3 whichhas been formulated as

119872119904+Oc119904119905+Hyst lt 119872

119905 (11)

where 119872119904and 119872

119905are the signal strength or quality values

for serving cell 119904 and target cell 119905 and Hyst is cell-specifichysteresis value Oc

119904119905is the specific offset for RSRP between

cell 119904 and cell 119905 As can be seen from (11) when Oc119904119905is small

it is easy for users to migrate to the cell 119905 rather than campon the cell 119904 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

119904119905

based on 11987510158401015840119894119895 Oc119904119905can not be very large because an unsuited

value will cause some users to switch to an unsuited cellOcmax is the upper limit of |Oc

119904119905| We define that 1198631015840

119899= 119863119899minus

HystThehandover for load balancing of cell 119894 is implementedby the procedures in Figure 9 where sum119872

119898=1PRB119898

is thenumber of PRBs required by119872 users who are switched fromthe heavily loaded cell to the low payload cell

If the process comes to an end with sum119872119898=1

PRB119898lt 11987510158401015840

119894119895

by the reason of minus119863119899lt 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 effectswrap-around technique is applied For simplicity only oneeNB is located in the cell center and no sectors are dividedIn 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 1MbpsDetailed simulation assumptions and parameters are given inTable 1


Start

End

M = 1 Oc = zero

minusDn lt Oc

minusDn lt Oc

max

OcmaxOc

Mth user notin cell i

Mth user isin cell j

Oc = Dn M = M + 1

sumM

m=1PRBm le P998400998400

ij

=

N

Y

Y

N

N

Y

Figure 9 The load balancing flow chart

Table 2 Simulation parameters

Parameters AssumptionsCarrier frequency 19GHzBandwidth 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 minus174 dBmNumber of Tx antenna 1Number of Rx antenna 2

Figure 10 shows the load distribution index (LDI) whichis similar to Jain et alrsquos fairness index [21] and is defined asfollows

LDI =(sum119899

119894=1119873119894)2

|119899| sum119899

119894=1(119873119894)2 (12)

060

065

070

075

080

085

090

095

100

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 cellsThemore 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 10PRBs 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 11The 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


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

References

[1] A P Vasudevan and R Sudhakar ldquoA low complexity near-optimal MIMO antenna subset selection algorithm for capacitymaximisationrdquo International Journal of Antennas and Propaga-tion vol 2013 Article ID 956756 11 pages 2013

[2] 3GPP TR 36 912 v10 0 0 Feasibility study for Further Advance-ments for E-UTRA (LTEAdvanced) 2011

[3] K Zheng F Liu W Xiang and X Xin ldquodynamic downlinkaggregation carrier scheduling scheme for wireless networkscommunicationsrdquo IET vol 8 no 1 pp 114ndash123 2014

[4] M Peng D Liang Y Wei et al ldquoSelf-configuration and self-optimization in LTE-advanced heterogeneous networksrdquo IEEECommunications Magazine vol 51 no 5 pp 36ndash45 2013

[5] S Das H Viswanathan and G Rittenhouse ldquoDynamic loadbalancing through coordinated scheduling in packet data sys-temsrdquo in Proceedings of the 22nd Annual Joint Conference on theIEEEComputer and Communications Societies (INFOCOM rsquo03)pp 786ndash796 San Francisco Calif USA April 2003

[6] H Zhang X S Qiu L M Meng and X D Zhang ldquoAchievingdistributed load balancing in self-organizing LTE radio accessnetwork with autonomic network managementrdquo in Proceedingsof the 25th IEEE GlobecomWorkshops pp 454ndash459 Miami FlaUSA December 2010

[7] R Kwan R Arnott R Paterson R Trivisonno andM KubotaldquoOn mobility load balancing for LTE systemsrdquo in Proceedings ofthe IEEE 72nd Vehicular Technology Conference Fall (VTC-Fallrsquo10) pp 1ndash5 Ottawa Canada September 2010


[8] L Zhang Y Liu M R Zhang S C Jia and X Y DuanldquoA Two-layer mobility load balancing in LTE self-organizationnetworksrdquo in Proceedings of the International Conference onCommunication Technology (ICCT rsquo11) pp 925ndash929 JinanChina September 2011

[9] T Warabino S Kaneko S Nanba and Y Kishi ldquoAdvancedload balancing in LTELTE-A cellular networkrdquo in Proceedingsof the 23rd IEEE International Symposium on Personal Indoorand Mobile Radio Communications (PIMRC rsquo12) pp 530ndash535Sydney Australia September 2012

[10] M Sheng Y Chungang Y Zhang and J Li ldquoZone-based loadbalancing in LTE self-optimizing networks a game theoreticapproachrdquo IEEE Transactions on Vehicular Technology 2013

[11] B Li C Zhang and X Wang ldquoMulti-domain Load resourceoptimization for heterogeneous network in LTE-Ardquo in Proceed-ings of the 23rd IEEE International Symposium on PersonalIndoor andMobile Radio Communications (PIMRC rsquo12) pp 215ndash219 Sydney Australia September 2012

[12] W Bo S Yu Z Lv and J Wang ldquoA novel self-optimizingload balancing method based on ant colony in LTE networkrdquoin Proceedings of the 8th International Conference on WirelessCommunications Networking and Mobile Computing (WiCOMrsquo12) pp 1ndash4 September 2012

[13] J S Kaufman ldquoBlocking in a shared resource environmentrdquoIEEE Transactions on Communications vol 29 no 10 pp 1474ndash1481 1981

[14] K Zheng F Liu L Lei C Lin and Y Jiang ldquoStochasticperformance analysis of a wireless finite-state Markov channelrdquoIEEE Transactions on Wireless Communications vol 12 no 2pp 782ndash793 2013

[15] 3GPP TR 25 996 v6 1 0 Spatial Channel Model for MultipleInput Mutiple Output (MIMO) Simulations 2003

[16] A Damnjanovic J Montojo Y Wei et al ldquoA survey on 3GPPheterogeneous networksrdquo IEEE Wireless Communications vol18 no 3 pp 10ndash21 2011

[17] X Zhang XGuW Li L Zhang J Shen andYWan ldquoThe studyof indoor and field trials on MIMO architecture in TD-LTEnetworkrdquo International Journal of Antennas and Propagationvol 2013 Article ID 181579 9 pages 2013

[18] L R Ford Jr and D R Fulkerson Flows in Networks PrincetonUniversity Press Princeton NJ USA 1962

[19] J B Orlin ldquoA faster strongly polynomial minimum cost flowAlgorithmrdquo in Proceedings of the 20th ACM Symposium on theTheory of Computing pp 377ndash387 1988

[20] 3GPP TS 36 331 v8 4 0 Evolved Universal Terrestrial RadioAccess (E-UTRA) Radio Resource Control (RRC) ProtocolSpecification (Release 8) 2008

[21] R Jain D Chiu and W Hawe ldquoA quantitative measure offairness and discrimination for resource allocation in sharedsystemsrdquo Tech Rep DEC-TR-301 Digital Equipment Corpora-tion 1984

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



contract (or expand) the coverage of heavy (or low) payloadcells By controlling beam coverage patterns of ldquocommonsignalsrdquo 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 proposedwhich 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 modelSecondly 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 networkIn 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 cellTheusers 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 119894 isassumed as 120582

119894 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 120582

11 the arrival rate of edge users of cell 1 is 120582

12 and

the arrival rate of picousers of cell 1 is 12058213 Parameters 120582

21

12058222 and 120582

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 119894 is assumedas 120583119894 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 cell119894 can be evaluated by a three-dimensional Markovian modelas shown in Figure 2

The state (119888 119889 119890) denotes that the number of PRBsoccupied by cell center users of cell 119894 is 119888 the number of PRBsoccupied by cell edge users of cell 119894 is 119889 and the number ofPRBs occupied by picousers of cell 119894 is 119890The number of PRBsoccupied by total users of cell 119894 is 119888 + 119889 + 119890 which can notbe larger than the total number of PRBs of each cell that is100 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 119899 PRBs are used by all


c d 0

c d e minus 2


c 0 e

c d minus 4 e

c d e + 2

c d + 4 e

120582i1 120582i1

120582i2

120582i2

120582i3

120582i3

120583i

120583i

120583i

120583i

120583i

120583i






119902 (119899) =

119878

sum

119904=1

119886119904sdot 119887119904

119899sdot 119902 (119899 minus 119887

119904) 119899 = 0 1 119873 (1)




119904is the




119875119887119904

=

119873

sum

119899=119873minus119887119904+1

119902 (119899) 119904 = 1 2 119878 (2)



0 4 8 12 16 20

Bloc

king

pro

babi

lity



10minus6

10minus5

10minus4

10minus3

10minus2

10minus1

100


















119899



(1198751) min (

119899

sum

119894=1

sum

119895 = 119894

119875119894119895) (1 le 119895 le 119899)


119895 = 119894

119875119894119895+ sum

119895 = 119894

119875119895119894= 119873

(1 le 119894 le 119899 1 le 119895 le 119899)

(3)

where 119875119894119895




119894119895are real






1






119875119894119895=

max((4 minus 119895)119873 minus3

sum

119909=119895

119873119909 0) 119894 isin 1 2 119895 = 119894 + 1

max(119895119873 minus119895

sum

119909=1

119873119909 0) 119894 isin 2 3 119895 = 119894 minus 1

(4)



1198751015840

119894119895=

119875119894119895

(119875119894119895gt 0)

minus119875119895119894

(119875119894119895= 0)

(5)

Property (1198751015840119894119895= minus1198751015840



1198731minus 1198751015840

12= 119873 (6)

1198732minus 1198751015840

23+ 1198751015840

12= 119873 (7)

1198733+ 1198751015840

23= 119873 (8)


Cell A Cell B

Scheme 1

Cell C Cell D

(a)

Scheme 2

(b)





N1N1

N1

N2 N2

N2

N3

N3 N4 N5

N6Nn




1198751015840






119875119894119895=

max((119899 minus 119895 + 1)119873 minus119899

sum

119909=119895

119873119909 0)

119894 isin 1 2 119899 minus 1 119895 = 119894 + 1

max(119895119873 minus119895

sum

119909=1

119873119909 0)

119894 isin 2 3 119899 119895 = 119894 minus 1

(9)


4

5 1 2

6

3 1

5 4 3

6

2















119894 where 0 lt 120596 lt 1 120596 is


(1198752) min (

119899

sum

119894=1

sum

119895 = 119894

119875119894119895) (1 le 119895 le 119899)


119895 = 119894

119875119894119895+ sum

119895 = 119894

119875119895119894= 119873

(1 le 119894 le 119899 1 le 119895 le 119899)

119875119894119895⩽ 120596 sdot 119873

119894

(10)











Unidirectional arc








119894





(3) Using (5) 1198751015840119894119895











119899= RSRP


119899119894 RSRP






119872119904+Oc119904119905+Hyst lt 119872

119905 (11)

where 119872119904and 119872






119904119905



119904119905| We define that 1198631015840

119899= 119863119899minus


119898=1PRB119898



PRB119898lt 11987510158401015840

119894119895






Start

End

M = 1 Oc = zero

minusDn lt Oc

minusDn lt Oc

max

OcmaxOc



Oc = Dn M = M + 1

sumM

m=1PRBm le P998400998400

ij

=

N

Y

Y

N

N

Y





LDI =(sum119899

119894=1119873119894)2

|119899| sum119899

119894=1(119873119894)2 (12)

060

065

070

075

080

085

090

095

100

Load

dist

ribut

ion

inde

x


NO LB MLB OSLB

5 10 15 20 25 30 35 40 45






30

40

50

60

70

80

90

100

Aver

age r

esou

rce o

ccup

ied

ratio

of


NO LB MLB


5 10 15 20 25 30 35 40 45

heav

ily lo

aded

cells

()


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


5 10 15 20 25 30 35 40 45




7 Conclusion




Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










c d 0

c d e minus 2


c 0 e

c d minus 4 e

c d e + 2

c d + 4 e

120582i1 120582i1

120582i2

120582i2

120582i3

120582i3

120583i

120583i

120583i

120583i

120583i

120583i






119902 (119899) =

119878

sum

119904=1

119886119904sdot 119887119904

119899sdot 119902 (119899 minus 119887

119904) 119899 = 0 1 119873 (1)




119904is the




119875119887119904

=

119873

sum

119899=119873minus119887119904+1

119902 (119899) 119904 = 1 2 119878 (2)



0 4 8 12 16 20

Bloc

king

pro

babi

lity



10minus6

10minus5

10minus4

10minus3

10minus2

10minus1

100


















119899



(1198751) min (

119899

sum

119894=1

sum

119895 = 119894

119875119894119895) (1 le 119895 le 119899)


119895 = 119894

119875119894119895+ sum

119895 = 119894

119875119895119894= 119873

(1 le 119894 le 119899 1 le 119895 le 119899)

(3)

where 119875119894119895




119894119895are real






1






119875119894119895=

max((4 minus 119895)119873 minus3

sum

119909=119895

119873119909 0) 119894 isin 1 2 119895 = 119894 + 1

max(119895119873 minus119895

sum

119909=1

119873119909 0) 119894 isin 2 3 119895 = 119894 minus 1

(4)



1198751015840

119894119895=

119875119894119895

(119875119894119895gt 0)

minus119875119895119894

(119875119894119895= 0)

(5)

Property (1198751015840119894119895= minus1198751015840



1198731minus 1198751015840

12= 119873 (6)

1198732minus 1198751015840

23+ 1198751015840

12= 119873 (7)

1198733+ 1198751015840

23= 119873 (8)


Cell A Cell B

Scheme 1

Cell C Cell D

(a)

Scheme 2

(b)





N1N1

N1

N2 N2

N2

N3

N3 N4 N5

N6Nn




1198751015840






119875119894119895=

max((119899 minus 119895 + 1)119873 minus119899

sum

119909=119895

119873119909 0)

119894 isin 1 2 119899 minus 1 119895 = 119894 + 1

max(119895119873 minus119895

sum

119909=1

119873119909 0)

119894 isin 2 3 119899 119895 = 119894 minus 1

(9)


4

5 1 2

6

3 1

5 4 3

6

2















119894 where 0 lt 120596 lt 1 120596 is


(1198752) min (

119899

sum

119894=1

sum

119895 = 119894

119875119894119895) (1 le 119895 le 119899)


119895 = 119894

119875119894119895+ sum

119895 = 119894

119875119895119894= 119873

(1 le 119894 le 119899 1 le 119895 le 119899)

119875119894119895⩽ 120596 sdot 119873

119894

(10)











Unidirectional arc








119894





(3) Using (5) 1198751015840119894119895











119899= RSRP


119899119894 RSRP






119872119904+Oc119904119905+Hyst lt 119872

119905 (11)

where 119872119904and 119872






119904119905



119904119905| We define that 1198631015840

119899= 119863119899minus


119898=1PRB119898



PRB119898lt 11987510158401015840

119894119895






Start

End

M = 1 Oc = zero

minusDn lt Oc

minusDn lt Oc

max

OcmaxOc



Oc = Dn M = M + 1

sumM

m=1PRBm le P998400998400

ij

=

N

Y

Y

N

N

Y





LDI =(sum119899

119894=1119873119894)2

|119899| sum119899

119894=1(119873119894)2 (12)

060

065

070

075

080

085

090

095

100

Load

dist

ribut

ion

inde

x


NO LB MLB OSLB

5 10 15 20 25 30 35 40 45






30

40

50

60

70

80

90

100

Aver

age r

esou

rce o

ccup

ied

ratio

of


NO LB MLB


5 10 15 20 25 30 35 40 45

heav

ily lo

aded

cells

()


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


5 10 15 20 25 30 35 40 45




7 Conclusion




Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation























119899



(1198751) min (

119899

sum

119894=1

sum

119895 = 119894

119875119894119895) (1 le 119895 le 119899)


119895 = 119894

119875119894119895+ sum

119895 = 119894

119875119895119894= 119873

(1 le 119894 le 119899 1 le 119895 le 119899)

(3)

where 119875119894119895




119894119895are real






1






119875119894119895=

max((4 minus 119895)119873 minus3

sum

119909=119895

119873119909 0) 119894 isin 1 2 119895 = 119894 + 1

max(119895119873 minus119895

sum

119909=1

119873119909 0) 119894 isin 2 3 119895 = 119894 minus 1

(4)



1198751015840

119894119895=

119875119894119895

(119875119894119895gt 0)

minus119875119895119894

(119875119894119895= 0)

(5)

Property (1198751015840119894119895= minus1198751015840



1198731minus 1198751015840

12= 119873 (6)

1198732minus 1198751015840

23+ 1198751015840

12= 119873 (7)

1198733+ 1198751015840

23= 119873 (8)


Cell A Cell B

Scheme 1

Cell C Cell D

(a)

Scheme 2

(b)





N1N1

N1

N2 N2

N2

N3

N3 N4 N5

N6Nn




1198751015840






119875119894119895=

max((119899 minus 119895 + 1)119873 minus119899

sum

119909=119895

119873119909 0)

119894 isin 1 2 119899 minus 1 119895 = 119894 + 1

max(119895119873 minus119895

sum

119909=1

119873119909 0)

119894 isin 2 3 119899 119895 = 119894 minus 1

(9)


4

5 1 2

6

3 1

5 4 3

6

2















119894 where 0 lt 120596 lt 1 120596 is


(1198752) min (

119899

sum

119894=1

sum

119895 = 119894

119875119894119895) (1 le 119895 le 119899)


119895 = 119894

119875119894119895+ sum

119895 = 119894

119875119895119894= 119873

(1 le 119894 le 119899 1 le 119895 le 119899)

119875119894119895⩽ 120596 sdot 119873

119894

(10)











Unidirectional arc








119894





(3) Using (5) 1198751015840119894119895











119899= RSRP


119899119894 RSRP






119872119904+Oc119904119905+Hyst lt 119872

119905 (11)

where 119872119904and 119872






119904119905



119904119905| We define that 1198631015840

119899= 119863119899minus


119898=1PRB119898



PRB119898lt 11987510158401015840

119894119895






Start

End

M = 1 Oc = zero

minusDn lt Oc

minusDn lt Oc

max

OcmaxOc



Oc = Dn M = M + 1

sumM

m=1PRBm le P998400998400

ij

=

N

Y

Y

N

N

Y





LDI =(sum119899

119894=1119873119894)2

|119899| sum119899

119894=1(119873119894)2 (12)

060

065

070

075

080

085

090

095

100

Load

dist

ribut

ion

inde

x


NO LB MLB OSLB

5 10 15 20 25 30 35 40 45






30

40

50

60

70

80

90

100

Aver

age r

esou

rce o

ccup

ied

ratio

of


NO LB MLB


5 10 15 20 25 30 35 40 45

heav

ily lo

aded

cells

()


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


5 10 15 20 25 30 35 40 45




7 Conclusion




Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Cell A Cell B

Scheme 1

Cell C Cell D

(a)

Scheme 2

(b)





N1N1

N1

N2 N2

N2

N3

N3 N4 N5

N6Nn




1198751015840






119875119894119895=

max((119899 minus 119895 + 1)119873 minus119899

sum

119909=119895

119873119909 0)

119894 isin 1 2 119899 minus 1 119895 = 119894 + 1

max(119895119873 minus119895

sum

119909=1

119873119909 0)

119894 isin 2 3 119899 119895 = 119894 minus 1

(9)


4

5 1 2

6

3 1

5 4 3

6

2















119894 where 0 lt 120596 lt 1 120596 is


(1198752) min (

119899

sum

119894=1

sum

119895 = 119894

119875119894119895) (1 le 119895 le 119899)


119895 = 119894

119875119894119895+ sum

119895 = 119894

119875119895119894= 119873

(1 le 119894 le 119899 1 le 119895 le 119899)

119875119894119895⩽ 120596 sdot 119873

119894

(10)











Unidirectional arc








119894





(3) Using (5) 1198751015840119894119895











119899= RSRP


119899119894 RSRP






119872119904+Oc119904119905+Hyst lt 119872

119905 (11)

where 119872119904and 119872






119904119905



119904119905| We define that 1198631015840

119899= 119863119899minus


119898=1PRB119898



PRB119898lt 11987510158401015840

119894119895






Start

End

M = 1 Oc = zero

minusDn lt Oc

minusDn lt Oc

max

OcmaxOc



Oc = Dn M = M + 1

sumM

m=1PRBm le P998400998400

ij

=

N

Y

Y

N

N

Y





LDI =(sum119899

119894=1119873119894)2

|119899| sum119899

119894=1(119873119894)2 (12)

060

065

070

075

080

085

090

095

100

Load

dist

ribut

ion

inde

x


NO LB MLB OSLB

5 10 15 20 25 30 35 40 45






30

40

50

60

70

80

90

100

Aver

age r

esou

rce o

ccup

ied

ratio

of


NO LB MLB


5 10 15 20 25 30 35 40 45

heav

ily lo

aded

cells

()


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


5 10 15 20 25 30 35 40 45




7 Conclusion




Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


















119894 where 0 lt 120596 lt 1 120596 is


(1198752) min (

119899

sum

119894=1

sum

119895 = 119894

119875119894119895) (1 le 119895 le 119899)


119895 = 119894

119875119894119895+ sum

119895 = 119894

119875119895119894= 119873

(1 le 119894 le 119899 1 le 119895 le 119899)

119875119894119895⩽ 120596 sdot 119873

119894

(10)











Unidirectional arc








119894





(3) Using (5) 1198751015840119894119895











119899= RSRP


119899119894 RSRP






119872119904+Oc119904119905+Hyst lt 119872

119905 (11)

where 119872119904and 119872






119904119905



119904119905| We define that 1198631015840

119899= 119863119899minus


119898=1PRB119898



PRB119898lt 11987510158401015840

119894119895






Start

End

M = 1 Oc = zero

minusDn lt Oc

minusDn lt Oc

max

OcmaxOc



Oc = Dn M = M + 1

sumM

m=1PRBm le P998400998400

ij

=

N

Y

Y

N

N

Y





LDI =(sum119899

119894=1119873119894)2

|119899| sum119899

119894=1(119873119894)2 (12)

060

065

070

075

080

085

090

095

100

Load

dist

ribut

ion

inde

x


NO LB MLB OSLB

5 10 15 20 25 30 35 40 45






30

40

50

60

70

80

90

100

Aver

age r

esou

rce o

ccup

ied

ratio

of


NO LB MLB


5 10 15 20 25 30 35 40 45

heav

ily lo

aded

cells

()


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


5 10 15 20 25 30 35 40 45




7 Conclusion




Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













119894





(3) Using (5) 1198751015840119894119895











119899= RSRP


119899119894 RSRP






119872119904+Oc119904119905+Hyst lt 119872

119905 (11)

where 119872119904and 119872






119904119905



119904119905| We define that 1198631015840

119899= 119863119899minus


119898=1PRB119898



PRB119898lt 11987510158401015840

119894119895






Start

End

M = 1 Oc = zero

minusDn lt Oc

minusDn lt Oc

max

OcmaxOc



Oc = Dn M = M + 1

sumM

m=1PRBm le P998400998400

ij

=

N

Y

Y

N

N

Y





LDI =(sum119899

119894=1119873119894)2

|119899| sum119899

119894=1(119873119894)2 (12)

060

065

070

075

080

085

090

095

100

Load

dist

ribut

ion

inde

x


NO LB MLB OSLB

5 10 15 20 25 30 35 40 45






30

40

50

60

70

80

90

100

Aver

age r

esou

rce o

ccup

ied

ratio

of


NO LB MLB


5 10 15 20 25 30 35 40 45

heav

ily lo

aded

cells

()


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


5 10 15 20 25 30 35 40 45




7 Conclusion




Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Start

End

M = 1 Oc = zero

minusDn lt Oc

minusDn lt Oc

max

OcmaxOc



Oc = Dn M = M + 1

sumM

m=1PRBm le P998400998400

ij

=

N

Y

Y

N

N

Y





LDI =(sum119899

119894=1119873119894)2

|119899| sum119899

119894=1(119873119894)2 (12)

060

065

070

075

080

085

090

095

100

Load

dist

ribut

ion

inde

x


NO LB MLB OSLB

5 10 15 20 25 30 35 40 45






30

40

50

60

70

80

90

100

Aver

age r

esou

rce o

ccup

ied

ratio

of


NO LB MLB


5 10 15 20 25 30 35 40 45

heav

ily lo

aded

cells

()


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


5 10 15 20 25 30 35 40 45




7 Conclusion




Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










30

40

50

60

70

80

90

100

Aver

age r

esou

rce o

ccup

ied

ratio

of


NO LB MLB


5 10 15 20 25 30 35 40 45

heav

ily lo

aded

cells

()


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


5 10 15 20 25 30 35 40 45




7 Conclusion




Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article advanced load balancing based...

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