Impact of the Connection Admission Process on the Direct Retry Load Balancing Algorithm in Cellular Networks

Impact of the Connection AdmissionProcess on the Direct Retry Load

Balancing Algorithm in Cellular NetworksPrzemyslaw Pawelczak, Member, IEEE, Shaunak Joshi, Member, IEEE, Sateesh Addepalli,

John Villasenor, Senior Member, IEEE, and Danijela �Cabri�c, Member, IEEE

Abstract—We present an analytical framework for modeling a priority-based load balancing scheme in cellular networks based on a

new algorithm called direct retry with truncated offloading channel resource pool (DRK). The model, developed for a baseline case of

two cell network, differs in many respects from previous works on load balancing. Foremost, it incorporates the call admission process,

through random access. In specific, the proposed model implements the Physical Random Access Channel used in 3GPP network

standards. Furthermore, the proposed model allows the differentiation of users based on their priorities. The quantitative results

illustrate that, for example, cellular network operators can control the manner in which traffic is offloaded between neighboring cells by

simply adjusting the length of the random access phase. Our analysis also allows for the quantitative determination of the blocking

probability individual users will experience given a specific length of random access phase. Furthermore, we observe that the

improvement in blocking probability per shared channel for load balanced users using DRK is maximized at an intermediate number of

shared channels, as opposed to the maximum number of these shared resources. This occurs because a balance is achieved between

the number of users requesting connections and those that are already admitted to the network. We also present an extension of our

analytical model to a multicell network (by means of an approximation) and an application of the proposed load balancing scheme in

the context of opportunistic spectrum access.

Index Terms—Cellular networks, load balancing, connection admission, 3GPP, opportunistic spectrum access

Ç

1 INTRODUCTION

GIVEN the rapid current and expected growth in 3G/UMTS and LTE-based networks and in the number of

mobile devices that use such networks to download dataintensive, multimedia-rich content, the need for QoS-enabled connection management is vital. However, thenonuniform distribution of users and consequent imbalancein usage of radio resources leads to an existence of localareas of under- and overutilization of these resources in thenetwork. This phenomenon results in challenging networkmanagement issues. Load balancing is an importanttechnique that attempts to solve such issues, and occurswhen a centralized network controller intelligently dis-tributes connections from highly congested cells to neigh-boring cells which are less occupied. This allows for anincrease in network subscriber satisfaction because moresubscribers meet their QoS requirements. Furthermore, itallows for an increase in overall channel utilization byleveraging the fact that users with access to multiple cellsalso have access to additional resources.

In this work, we aim to quantify the impact of loadbalancing on the overall system as well as user experience(from the separate viewpoints of users that share resourcesand those that use these shared resources) using a detailedanalytical model of a fundamental two cell setup, laterextended by means of approximations to multicell setup.Furthermore, we present an application of our model in thecontext of a cellular system using opportunistic spectrumaccess (OSA), which even further improves the teletrafficproperties of the considered cellular network, to efficientlyutilize system resources.

1.1 Related Work

Load balancing has been explored for many years asdescribed, for example, in earlier works such as [2], [3].More recent works such as [4], [5], [6], [7] have alsoexamined the impacts of various load balancing schemes.

For simplicity, the previous studies of load balancinghave assumed that the connection admission process can beneglected because nonfinite user populations are consid-ered with a particular arrival rate of the number connec-tions. In cellular networks, however, finite user populationexists, where each new connection needs to first send arequest to the serving base station (BS) through somepredefined control channel. In 3GPP standards, this controlchannel is the Physical Random Access Channel (PRACH)[8, Section 2.4.4.4], [9, Section II]. The success of aconnection request by a user is dependent on multiplefactors including the number of requesting users; thepairwise channel quality between the user and the servingBS (measured, for example, in BER or outage probability);

IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 12, NO. 9, SEPTEMBER 2013 1681

. P. Pawelczak is with the Delft University of Technology, Mekelweg 4, 2628CD Delft, The Netherlands. E-mail: [email protected].

. S. Joshi and S. Addepalli are with Cisco Systems, Inc., San Jose, CA 95134.E-mail: {shaunjos, sateeshk}@cisco.com.

. J. Villasenor and D. �Cabri�c are with the Department of ElectricalEngineering, University of California, Los Angeles, 56-125B EngineeringIV Building, Los Angeles, CA 90095-1594.E-mail: {villa, danijela}@ee.ucla.edu.

Manuscript received 14 June 2011; revised 21 Feb. 2012; accepted 27 Apr.2012; published online 31 May 2012.For information on obtaining reprints of this article, please send e-mail to:[email protected], and reference IEEECS Log Number TMC-2011-06-0317.Digital Object Identifier no. 10.1109/TMC.2012.125.

1536-1233/13/$31.00 � 2013 IEEE Published by the IEEE CS, CASS, ComSoc, IES, & SPS

and the actual control channel access technique itself[10], [11], [12].

More recent works, such as [13], use inter- and intracellhandover techniques to alleviate issues of coverage for cell-edge users without specific focus on traffic parameters.Other recent studies propose the use of low-power cellularrelays in the presence of high-power BSs with moreemphasis on a heuristic to determine load balancing andmobile association [14]. It is evident that current literatureon load balancing lacks an analytical model that allows forsubstantial flexibility in terms of finite user populationconsideration and the use of various traffic parameters.

1.2 Our Contribution

Until now the exact impact of random access overhead onload balancing performance is not well understood. Morespecifically, the quantitative relationship between therandom access phase length, the user blocking probability,and system channel utilization in a load balancing-enabledcellular system is unknown. To the best of our knowledgean analytical model to quantify system wide and userexperience metrics in this respect has not been previouslyprovided. Our work:

1. Through development of an analytical model for abaseline (fundamental) two-cell network, demon-strates the benefits of load balancing, from ateletraffic point of view, using realistic trafficscenarios, various network configurations and para-meters, and simplified physical layer model forchannel quality.

2. Provides a detailed connection admission process todetermine the effects of a finite user population onthe efficiency of load balancing performance metrics.

3. Allows extension to more complex network setups.More specifically, we present an approximation to amulticell case and also provide an application of themodel in the context of cellular OSA.

Our model can be used in:

1. Demonstrating that the random access phase lengthis an important tool that can be used to control bothsystem wide and user experience performancemetrics, for example, quantifying the tradeoffsbetween random access channel (RACH) collisionprobability and blocking probability for load-balanced users as a function of random accessphase length.

2. Determining the impact of channel quality to improvethe accuracy of reported load balancing efficiency; forexample, quantifying the loss in accuracy due toperfect channel condition assumptions.

3. Exploring the effects of varying shared channelaccess on system-wide performance and user ex-perience, for example, determining the marginalgain of adding more channels for shared accessbetween cells.

The rest of the paper is organized as follows: The systemmodel is introduced in Section 2, while the analytical modelis introduced in Section 3. The numerical results arepresented in Section 4. Lastly, the paper is concluded inSection 5.

2 SYSTEM MODEL

In the following sections, we will describe the system modelin detail. We start with a description of the channelstructure in Section 2.1, followed by the description of nodeplacement in Section 2.2. Section 2.3 describes the signaltransmission model and Section 2.4 prioritization policies inload balancing. Then, in Section 2.5, introduces a randomaccess process in the context of cellular networks, followedby the introduction of a data transfer model in Section 2.6.Finally, the whole load balancing process is introduced inSection 2.7.

2.1 Channel Structure

We consider a cellular system, where two BSs arepositioned such that they create a region of overlap incoverage. Naturally, while cellular systems typically havefar more than two BSs, a reduction to a two-BS system foranalytical reasons enables a tractable analytical frameworkwhile still allowing exploration of a large number ofmicroscopic parameters to use in optimizing networkperformance. Furthermore, two-cells provide a fundamen-tal functional pair for the purposes of studying loadbalancing from the context of off-loading connections froma highly congested cell to a less congested one. We stronglyemphasize that consideration of load balancing in thecontext of a two-BS system has been used extensively andsuccessfully in previous treatments, e.g., [4], [7], [15], [16].

Cell 1 has M1 available basic bandwidth units, asreferred to in [17] or more commonly referred to aschannels, and cell 2 has M2 available channels. Note thatchannels can also represent WCDMA codes in the context ofUMTS. The throughput of every channel in each cell is thesame and equal to R bits/second. We assume that channelsare mutually orthogonal and that there is no interference inthe set of channels belonging to cells 1 and 2. Each BS emitsa signal using omnidirectional antennas and we assume acircular contour signal coverage model, in which full signalstrength is received within a certain radius of the BS, and nosignal is available beyond that radius, as used in, e.g., [2],[4], [13], [18].

2.2 Node Placement

Each mobile terminal, referred to as user equipment (UE),remains at fixed positions following an initial UE placementprocess, with each UE located in one of three separateregions. N1 UEs are in group 1 and have access only to oneBS, N2 UEs are in group 2 and have access only to thesecond BS, and N3 UEs are in group 3 and can potentiallyaccess either BS. Such nonhomogenous UE placement hasbeen considered, for example, in [16], which allows for atractable analysis of the considered system and includes allimportant groups participating in the load balancingprocess. The nonhomogenous case of UE distribution isthe most widespread because UEs are generally distributednonuniformly over a cellular area. UEs in group 3 are in theregion of overlap in coverage between the two cells, alsoknown as the Traffic Transferable Region (TTR) [4]. Sinceonly one UE can occupy a channel at a time,1 a maximum of

1682 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 12, NO. 9, SEPTEMBER 2013

1. For other, more involved channel assignment procedures including,for example, channel bonding the reader is referred to, e.g., [19], wheremultiple channel assignment problem is studied in an ad hoc scenario.

M1 þM2 UEs can be connected to both cells in the system atany given time. We assume that UEs from groups 1 and 3are initially registered to cell 1 (serving as the overloadedcell), while UEs in group 2 are initially registered to cell 2.

2.3 Signal Transmission Model

Time is slotted and the minimum time unit is a frame lengthof � seconds. Connections and channel conditions areassumed to remain constant for the duration of a frame,though they will in general vary from frame to frame. Weassume that Adaptive Modulation and Coding (AMC) isnot used in this framework because it does not aid inevaluating load balancing performance. Please note thatAMC is not considered in similar previous works such as[2], [4], [18]. For simplicity, we also do not consideradvanced error control methods such as Hybrid AutomaticRepeat Request.2 On the other hand, we do assume that theconnection and termination processes for UEs are directlydependent on the channel states experienced between eachgroup of UEs and the BSs they are connected to. We alsoassume that channel states are binary and independentfrom slot to slot, much as occurs in [22], and that all of theUEs in each group experience the same channel quality to agiven BS. Therefore, in any given time slot a UE is eitherexperiencing a good state with probability wðiÞx;y, (x denotesthe particular pair-wise connection between group x of UEsand associated BS y, and i 2 fd; ug denotes the downlinkand uplink, respectively), or a bad state, with probability1� wðiÞx;y. The value of wðiÞx;y is dependent on the distancebetween UEs in group x and BS y, which is denoted as dx;y.In our analysis, we use the distance as an input to acombined path loss and shadowing propagation model.This serves as an average channel quality consideration forthe model instead of the use of channel quality indicators onthe uplink per transmitted packet.

2.4 Prioritization

Because of the strict boundaries between groups of UEs, weassign priorities on a per group basis. A single, higherpriority is given to all UEs in groups 1 and 2 because thereis no flexibility to reassign them to a different BS; group 3UEs can potentially be reassigned and thus given a lowerpriority. Priorities for UEs are determined on a per time slotbasis. A very similar priority model has been used in othertreatments of load balancing. For example, in [15], [23],newly arriving connections in the non-TTR are given firstpriority to acquire channels from their serving BSs, whilethe connections from the TTR are assigned to the remainingchannels. Our model allows for the implementation of awide range of scenarios that require such traffic prioritiza-tion. One potential application is for the modeling ofnetworks, where load balancing traffic originating fromUEs in the TTR has lower priority than nonbalancedconnections due to several factors including a loweraverage channel quality [24], [25], QoS requirements [26],nonuniform spatial distribution of traffic classes [16], or celldwell time. Furthermore, it allows for modeling integratedhybrid cellular/WLAN/Ad Hoc networks as discussed in

[6], [27], where noncellular terminals in the TTR have alower priority than cellular UEs, and hierarchical cellularsystems [28], where members of different tiers haveindependent priorities. Finally, it enables the modeling offemtocell traffic prioritization, where UEs in groups 1 and 3are those in the Closed Subscriber Group (CSG) [29], whileUEs in the TTR are neighboring UEs outside of the CSG.

2.5 Random Access

In the connection process, a UE first attempts to connect tothe BS it is initially registered to by requesting aconnection through a RACH. We assume a frequencydivision duplex transmission mode, where control anddata traffic are transmitted and received simultaneously. Inaddition, time division duplexing is considered during thetransmission of control packets. Specifically, each UEgenerates a connection request with probability px. Aconnection is requested randomly in one of Lx � �nonoverlapping, time slotted control resources, unique togroup x 2 f1; 2; 3g of UEs. In other words, each group hasa unique set of sub slots within a frame during which UEsmay, but are not required to, request a connection. Therandom access phase length is equal to slot length � .Collisions between connection requests from UEs in thesame group are possible.

The random access procedure considered in this workshares features of the 3GPP-based cellular network stan-dards, which use the PRACH, mapped on a one-to-onebasis to the logical RACH. RACH uses the S-ALOHAprotocol and, in relation to the priorities assumed in thispaper, allows the prioritization of connection requestsbased on Active Service Classes (ASC) [10] that are uniqueto each UE, and can be adapted by the 3GPP-MAC layeronce the UE is in connected mode [8, Section 2.4.2.6]. The BSadvertises itself to the UEs within range through thebroadcast channel using signatures (3GPP release 99, e.g.,UMTS), subcarriers (3GPP release 8, e.g., LTE), or time slots,which each ASC can in-turn use for connection requests onRACH. The adaptation of the ASC is performed in the timeintervals predefined by the operator. For the purpose of ourpaper, we assume that the BSs collectively, through theRadio Network Controller, map the received signal fromevery registered UE to an associated ASC.

We assume a zero-persistence protocol, i.e., a collisionduring a connection request implies that connections arelost, and also UEs do not retry to generate anotherdependent connection. Due to this assumption, a powerramping process, i.e., feedback from the UE to the BS on anunsuccessful connection request [10, Section II-B], isredundant. To isolate the impact of each group of UEs oncollision rates, we assume mutually exclusive RACHresources assigned to each ASC [11, Fig. 4]. Analysis ofPRACH performance in isolation can be found in [9], [11].

2.6 Data Transfer

A connection request is granted during the connectionarrangement process if a good channel state occurs betweenthe UE and its associated BS at the moment of the request,and if no collisions occur between multiple requests fromdifferent UEs. Once a connection is established, the BSrandomly selects a channel and assigns the connected UE toit. The UE then begins to receive downlink data. UEs

PAWELCZAK ET AL.: IMPACT OF CONNECTION ADMISSION PROCESS ON THE DIRECT RETRY LOAD BALANCING ALGORITHM IN... 1683

2. Recent papers [20], [21] are a good source of information on theperformance of Hybrid Automatic Repeat Request.

occupy a time slot with probability q, where 1=q ¼ rp=ðR�Þis the average connection transfer size and rp is the averagepacket size given in bits. We assume that the transfer size isat least one time slot long. A connection terminates eitherwhen a transmission completes, or when the channel is in abad state during transmission.

2.7 Load Balancing Process

In the case of a UE in group 3, if a connection request issuccessful and there are no resources available in cell 1, weassume that the radio network controller performs loadbalancing by transferring the call from cell 1 to cell 2.3 Toavoid overloading cell 2 and protecting UEs that are alreadyregistered to it, UEs in group 3 can access a maximum of Kchannels from cell 2, where 0 � K �M2. UEs in group 3have access to an additional K shared channels; therefore,they have access to a total of M1 þK channels.

Using the nomenclature of [4, Sections 2 and 3], this loadbalancing scheme belongs to a class of direct load balancingschemes. It is closest in operation to direct retry [2]. Sincewe allow at most K available channels to offload trafficfrom cell 1 to cell 2 (as in simple borrowing scheme [4,Section 2]) we denote our scheme as direct retry withtruncated offloading channel resource pool (abbreviated asDRK). With K ¼M2 our scheme reduces to classical directretry, while for K ¼ 0 it reduces to a system in which noload balancing takes place.

In our model, we do not use a take-back process, i.e.,bidirectional load balancing is not considered. That is, onceconnections from group 3 are offloaded onto cell 2, theyremain connected to cell 2 during the transmission despitewhether or not resources have been freed in cell 1. In [5], theauthors remark that the take-back process, although morefair to cell 2 because it minimizes blocking at cell 2, is notalways advantageous to the network due to the highsignaling load that accompanies it. Additionally, as in [4],[18], we do not use queuing, so there is no consideration ofa call give-up process [5]. Moreover, we do not allowpreemption of connections from the TTR by connectionsthat have access to channels only from their respective BSs.

Note that all variables introduced in this section, as wellas all other variables used in this paper, are summarizedin Table 1 presented in Appendix A, which can be foundon the Computer Society Digital Library at http://doi.ieeecomputersociety.org/10.1109/TMC.2012.125.

3 ANALYTICAL MODEL

Let fA; Y ð1Þ; Y ð2Þ; Cg denote a state of a Markov system,where A denotes the number of resources used by group 1UEs, Y ð1Þ and Y ð2Þ denote the number of resources used bygroup 3 UEs associated with cell 1 and 2, respectively, andC denotes the number of resources used by group 2 UEs.

Then, the steady state probabilities can be denoted as�a;b;c;d ¼4 PrðA ¼ a; Y ð1Þ ¼ b; Y ð2Þ ¼ c; C ¼ dÞ. Note that

aþ bþ cþ d � minfN1 þN2 þN3;M1 þM2g;aþ b � minfN1 þN3;M1g;cþ d � minfN2 þN3;M2g; and

bþ c � minfN3;M1 þKg:

These conditions govern what states are possible in thetransition probability matrix.

We define the state transition probability as

rðat;bt;ct;dtÞat�1;bt�1;ct�1;dt�1

¼4 Pr�At ¼ at; Y ð1Þt ¼ bt; Y

ð2Þt ¼ ct;

Ct ¼ dtjAt�1 ¼ at�1; Yð1Þt�1 ¼ bt�1;

Yð2Þt�1 ¼ ct�1; Ct�1 ¼ dt�1

�;

ð1Þ

where subscripts t and t� 1 denote the current and the

previous time slots, respectively. This allows for computa-

tion of the transition probability matrix required to obtain

�a;b;c;d, which is in-turn used to compute the performance

metrics of the load balancing-enabled cellular system. In the

subsequent sections, we describe the process of deriving the

transition probability rðat;bt;ct;dtÞat�1;bt�1;ct�1;dt�1

. We begin by explaining

the computation process for the channel quality, and then

focus on the derivation of the functions that support (1).

3.1 Derivation of Channel Quality

In the downlink, the probability of a UE belonging to groupx 2 f1; 2; 3g and receiving a good signal from BS y 2 f1; 2g,is defined as

wðdÞx;y ¼4

1� Pr�J ðdÞx;y � �ðdÞq

�¼ 1�

Z �ðdÞq

0

pSðdÞx;yð�; dx;yÞd�; ð2Þ

where �ðdÞq is the signal reception threshold for the down-link, expressed as the minimum required received power ofthe received signal JðdÞx;y, and p

SðdÞx;yð�; dx;yÞ is the distribution

of the signal � received at group x, which is at a distance ofdx;y from BS y. As an example, we consider an environmentwith path loss and shadowing, where wðdÞx;y is expressed in[30, (2.52)] as

wðdÞx;y ¼ Q�ðdÞq � P

ðdÞt � 10 log10 W

ðdÞ þ 10� log10dx;y

dðdÞ0;x;y

��

0BBB@

1CCCA; ð3Þ

where W ðdÞ is a unit-less constant dependent on both theantenna characteristics and an average channel attenuation,and for W ðdÞ < 1 approximating empirical measurementsand assuming omnidirectional antennas is given as [30,(2.41)],

W ðdÞdB ¼ 20 log10

�

4�dðdÞ0;x;y

; ð4Þ

where � is the wavelength of the carrier frequency; PðdÞt is

the BS transmitted power (which is assumed to be the samefor both BSs, dx;y is the distance of the UE in group x locatedfarthest from BS y; d

ðdÞ0;x;y is the reference distance for the BS


3. The network controller maximizes the utilization of resources persingle cell to minimize the degradation of performance metrics for itsneighboring cells caused by load balancing. As users in group 3 areregistered to cell 1 (which is their primary cell), see Section 2.2, and users ingroup 2 are initially registered to cell 2, load balancing for group 3 userstakes place only when all resources in cell 1 are occupied. In the oppositecase (when users from group 3 will randomly select a cell for every newconnection), the probability of blocking for users in group 2 can potentiallyincrease, causing unnecessary disruption to their quality of service.

antenna far field; �� is the log-normal shadowing variance

given in dB; � is the path loss exponent; and the Q function

is defined in the usual manner as

QðzÞ ¼4Z 1z

1ffiffiffiffiffiffi2�p e�u

2=2du: ð5Þ

In the uplink, the probability that a good signal is received

by BS y from a UE in group x is wðuÞx;y, and is expressed in the

same manner as (2) and (3), by replacing all variables

having superscript ðdÞ with ðuÞ, where PðuÞt denotes the UE

transmission power; W ðuÞ denotes the constant for the UE

antenna (which again can be calculated in the same manner

as W ðdÞ using (4)); dðuÞ0;x;y is the reference distance for the UE

antenna far-field; and �ðuÞq is the signal reception threshold

for the uplink. The downlink and uplink channel quality

information governs the success rate of the connection

admission process, as well as the duration of a downlink

transmission.

3.2 Derivation of Connection ArrangementProbability

An important feature of the model is the consideration of

connection admission in the load-balancing process. This

process is a function of the total number of UEs, the number

of UEs receiving data from their respective serving BSs, the

pairwise channel quality between the UEs and its serving

BSs, and the underlying random access algorithm. The

probability that j new connections have successfully

requested downlink data given it�1 2 fat�1; bt�1; ct�1; dt�1gcurrently active connections from group x, with a RACH

consisting of Lx time slots is

SðjÞit�1¼4

�ðitÞit�1;x;y

; j > 0;

1� wðuÞx;y þ �ð1Þit�1;x;y

; j ¼ 0;0; otherwise;

8><>: ð6Þ

where

�ðjÞit�1;x;y

¼4XNx�it�1

k¼j

Nx � it�1

k

� �pkxð1� pxÞ

Nx�it�1�kðjÞk w

ðuÞx;y; ð7Þ

px is the probability of a connection request by an

individual UE in group x; and ðjÞk is the probability that

among k UEs requesting a connection, j were successful in

obtaining a resource. Note that the reference to x; y in SðjÞit�1

is

omitted due to space constraints, keeping in mind that for

at; at�1x ¼ 1, y ¼ 1, for bt; bt�1x ¼ 3, y ¼ 1, for ct; ct�1x ¼ 3,

y ¼ 2, and for dt; dt�1x ¼ 2, y ¼ 2.For consistency with cellular networks such as 3GPP, we

consider a PRACH-like control channel, for which ðjÞk can

be described in the manner of [31, (3)]

ðjÞk ¼

Xminðk;LxÞ

m¼j

ð�1ÞmþjðLx �mÞk�mk!

ðm� jÞ!ðLx �mÞ!ðk�mÞ!n!: ð8Þ

Note that depending on the assumption of how collisions

are resolved, different definitions of ðjÞk in (8) can be

applied when calculating the connection arrangement

probability according to (6).

3.3 Derivation of Connection TerminationProbability

Once a UE successfully requests a connection from theserving BS, a downlink transmission is started providedthat at least one free channel is available for the UE. Theconnection terminates when the BS finishes transmittingdata to the UE or when the downlink signal received by theUE is in outage. The probability that j connections from it�1

active connections at group x terminate is

TðjÞit�1¼4 it�1

j

� �ljx;yð1� lx;yÞ

it�1�j; ð9Þ

where lx;y ¼ 1� wðdÞx;y þ wðdÞx;yq is the inverse of the averagepacket length, accounting for truncation of some packetsdue to a bad channel quality. Again, the indices x; y havebeen omitted for notational simplicity in the symbol T

ðjÞit�1

,assuming that the same relationship between x; y and j; it�1

as given in Section 3.2 holds.

3.4 Derivation of the State Transition Probability

Using the definitions of the arrangement and terminationprobabilities, expressed in (6) and (9), respectively, we canfinally introduce the state transition probabilities for thecomplete model. The transition probability is constructedusing the termination and arrangement probability defini-tions and the respective relationship between the variablesof these two definitions (which are dependent on the startand end states of the transition). Due to the complexity ofthe derivation we begin with a highly simplified example.

3.4.1 State Transition Probabilities for a Single UE

Group

To facilitate understanding the derivation of the completestate transition probabilities, we first consider a network inwhich no load balancing occurs and all of the UEs are ingroup 1, such that N1 > 0 and N2 ¼ N3 ¼ 0. The state of theMarkov chain then simplifies to fA; 0; 0; 0g and thetransition probability becomes r

ðat;0;0;0Þat�1;0;0;0

, where

rðat;0;0;0Þat�1;0;0;0

¼

Xati¼0

T ðiþat�1�atÞat�1

SðiÞat�1; at�1 � at;

at < M1;Xati¼0

T ðiÞat�1Sðiþat�at�1Þat�1

; at�1 < at;

at < M1;Xati¼0

T ðiÞat�1Sðiþat�at�1Þat�1

þXati¼0

T ðiÞat�1

�XN1

j¼M1

Sðiþj�at�1Þat�1

; at�1 � at;

at ¼M1:

8>>>>>>>>>>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>>>>>>>>>>:

ð10Þ

In (10), the case at�1 � at, at < M1 denotes the transitionfrom a higher to a lower channel occupancy, subject to theconstraint that the number of channels occupied in the endstate must be less than the total BS capacity. The number ofterminating UEs is set to compensate for the UEs thatgenerate successful connections. The case at�1 < at, at < M1

denotes the transition from a lower to a higher channel


occupancy (given, again, that the number of occupiedchannels is less than the total BS capacity). In this case, UEsfrom group 1 need to generate exactly as many connectionsas given by the end state, not forgetting to generateconnections to compensate for the total number ofterminations. Lastly, for the case of at�1 � at, at ¼M1 theend state equals the total channel capacity. The first term inthe definition of this transition probability includes exactlythe number of connections needed to reach the end state,once again compensating for terminations. The second termaccounts for all successful connections generated thatexceed those needed to reach the end state, which willnot be admitted.

3.4.2 General Solution for the State Transition

Probabilities

Due to the complexity of the general solution, the mainanalytical equations describing the construction of the four-dimensional transitional probability matrix are presented inthe Appendix B, available in the online supplementalmaterial.

3.5 Performance Metrics

Given the complete description of the system, we are able toderive important metrics that would describe the efficiencyof the load balancing process involving connection admis-sion. While there are many performance metrics that can beextracted given the above framework, we focus on threeprimary metrics: 1) the blocking probability, which de-scribes the probability that at least one UE which requests aconnection from a particular group will be denied access toa channel; 2) the channel utilization, which expresses thefraction of the available channels are being used; and 3) thecollision probability on a control channel, which providesthe probability that at least one requesting connection willbe lost due to a collision with another UE.

3.5.1 Blocking Probability

As used here, blocking occurs when at least one UErequests a new connection, but cannot be admitted to anyBS due to lack of available channels. Since each group hasaccess to a different number of channels and can follow adifferent connection strategy, it is necessary to defineseparate blocking probability metrics for UEs in groups 1and 2, as contrasted with UEs in group 3. For groups 1 and2, the blocking probability is defined according to

BðzÞ ¼Xa;b;c;d

Xxi¼0

XNz

j¼Mv�x�yþ1

Xyk¼0

�a;b;c;dTðiÞx T ðkÞy SðiþjþkÞx ; ð11Þ

where for z ¼ 1x ¼ a, y ¼ b, v ¼ 1 and for z ¼ 2x ¼ d, y ¼ c,v ¼ 2. For group 3 UEs, the blocking probability is given as

Bð3Þ ¼Xa;b;c;d

Xaia¼0

XN1

ja¼0

Xdid¼0

XN3

jd¼0

Xbi¼0

Xcj¼0

XN2

k¼�a;b;c;dT

ðiaÞa SðjaÞa

� T ðjdÞd SðjdÞd T

ðiÞb T ðjÞc S

ðiþjþkÞbþc ;

ð12Þ

where is defined separately for K < M2 and K ¼M2. ForK ¼M2 ¼M1 þM2 � a� b� c� d� ga � gd þ ia þ id þ 1,where

ga ¼M1 � aþ ia � bþ i; ja > M1 � aþ ia � bþ i;ja; otherwise;

�ð13Þ

and gd is defined as (13) replacing M1 with M2, a with c, iawith id, b with d and i with j. For K < M2 ¼M1 � ga �b� ja þ ia þ iþ gc þ 1, where ga is defined as (13) and

gc ¼maxf0; geg; ge < K;K � cþ j; c� j < K and ge � K;0; otherwise;

8<: ð14Þ

where ge ¼M2 � c� dþ id þ j� jd.We briefly explain the above equations. The derivation of

the blocking probability for group 3 UEs is more compli-cated than for those UEs in groups 1 and 2 because thisgroup can access channels from both cells. Therefore, thenumber of generations for group 3 UEs that leads toblocking has to account for the terminations within thesame group, and also for the possible changes in thenumber of connections of UEs in groups 1 and 2.

The blocking for group 3 UEs can be analyzed in twoseparate cases. The first case accounts for the number ofgenerations needed to occupy all the channels in cell 1(K ¼M2), while the second case accounts for the number ofgenerations needed to occupy all available channels in cell 2(K < M2). The first case is simpler to analyze because group3 UEs need only generate as many connections as there areavailable resources on cell 1.

When K < M2, group 3 UEs can only access a maximumof K channels on cell 2. Therefore, extra conditions areadded for the situation in which group 3 UEs are blockedwhen exceeding K connections in cell 2. If there are lessthan K available free channels after terminations of group 3UEs connected to cell 2, the function maxf0; geg representsthe number of connections to cause blocking by generatingthe exact number of connections to occupy all availablechannels. The maxf0; geg function is used to lower boundthe necessary number of connections for blocking. This isbecause the number of connections on cell 2, in general, isnot restricted to K and can thus have more than K currentoccupancies resulting in a possibly negative value for ge. Onthe other hand, if there are more than K available channelsafter terminations, exactly K channels are used by group 3UEs to cause blocking.

3.5.2 Channel Utilization and Total System Throughput

The overall channel utilization is

U ¼ 1

M1 þM2

Xa;b;c;d

ðaþ bþ cþ dÞ�a;b;c;d; ð15Þ

which refers to the fraction of the collective capacity thathas been used by all UEs in all groups. The average totalsystem throughput is obtained by multiplying (15) by R.

3.5.3 Collision Probability

Because the model uses a RACH for connection requests, itis necessary to compute the collision probability of thesystem. The collision probability for UEs in group x is:

DðxÞ ¼Xa;b;c;d

XNx�a

k¼0

XKj¼0

ðjÞk I

ð1Þk�j�a;b;c;d

Nx � �k

� �

� pkð1� pÞNx��kwðuÞx;y;

ð16Þ


where IðjÞi ¼ 1 when i � j and I

ðjÞi ¼ 0, otherwise, � ¼

fa; dg for group x ¼ f1; 2g, respectively, and � ¼ bþ c forgroup x ¼ 3.

3.6 A Special Case: Load Balancing with OSA

In this section, we illustrate the use of the proposed systemto analyze other, more complex, cellular setups. As anexample, we present a case where the connections can beoffloaded to a neighboring cell belonging to a separatenetwork (such as that of another provider when there isneither shared signaling between cells nor a centralcontroller to coordinate the distribution of connectionsfrom one system to another). In the proposed system, usersregistered to one cell must detect the availability of freechannels in the neighboring cell by means of passivechannel observations, i.e., spectrum sensing. Such a systemcan be referred to as OSA-enabled load balancing [32].

We note that very little work has been done to considerthe system-level performance of OSA-enabled cellularnetworks. A group of papers, e.g., [33], [34], analyzessharing mechanisms of radio resources based on OSA,focusing on the physical characteristics, while abstractinghigher layers. These papers provide insights on how OSAcan be beneficial in a cellular system, but do not addressthe specific system performance and tradeoffs involved—specifically, the traffic characteristics of primary andsecondary cells and the connection admission processduring the random access phase. While many papers haveanalyzed the performance of OSA networks, e.g., [35], [36],the connection between OSA and its use in cellular loadbalancing has not been deeply addressed.

3.6.1 Extensions to the System Model

The following changes need to be made to the system model.Spectrum sensing. First, due to spectrum sensing assump-

tion, each user in cell 1 is equipped with a spectrum sensorto detect whether any of the channels on cell 2 is occupied.It is assumed that �s < � seconds are needed for spectrumsensing within each time slot. Channel availability detectionis assumed to be imperfect. We denote �f as the probabilityof false alarm, i.e., that users in cell 1 will declare that achannel is occupied in cell 2 when in fact it is not. If usersfrom group 3 attempt to access a channel detected asoccupied by users from cell 2, the users in group 3 areblocked from connecting to that channel. The probability ofmisdetecting the presence of a vacant channel in cell 2 isdenoted as �m. If a misdetection occurs, it is assumed thatthe users from group 3 will occupy the channel at cell 2 andsuccessfully be able to receive downlink data despite thepresence of the licensed users in cell 2. We assume that aslong as the users in cell 1 fulfills the minimum requirementon detection probability, 1� �m, it does not violate QoSrequirements of the users in cell 2. We also assume that thecoding scheme of the users in cell 1 can be designed tocompensate for the increased level of interference in theevent of a misdetection. An existing connection of any userfrom cell 1 is preempted by users in cell 2 that accesses thesame channel on cell 2. Once user from group 3 ispreempted its connection is dropped.

Connection termination. Cell 2 users receive downlink datafrom the BS using channels assigned to cell 2 until the

earlier of: 1) the termination of the connection aftersuccessful transmission of all data, or 2) preemption byusers in cell 2 (if cell 2 users occupy the same channel). Forthe sake of brevity, we assume that perfect channelconditions are experienced in the system, i.e., wðiÞx;y; i 2fu; dg. Due to spectrum sensing phase, the average packetlength is now 1=q ¼ rp=ðRð� � �sÞÞ.

Load balancing scheme. The same load balancing process isused, DRK ; however, we assume K ¼M2 throughout theanalysis of OSA system, as control over access to channelsused for load balancing is governed by the spectrumsensing quality, not by size of the channel pool accessible tocell 1. For the sake of brevity, we assume that there are nousers in the group 1 and 2. Instead, we assume that users incell 2 occupy any channel on cell 2, with a geometricallydistributed average slot occupancy probability of qp. Ascell 2 does not take part in load balancing process thischoice is well motivated.

3.6.2 Analytical Model

As in case of the general load balancing system, we construct

a Markov chain to derive performance metrics. We reuse the

notation from the general load balancing system. Let a state

of a Markov system be given as fY ð1Þ; Y ð2Þ; Cg, where Y ð1Þ

denotes the number of users from group 3 connected to cell 1,

Y ð2Þ denotes the number of users from group 3 connected to

cell 2, and C denotes the number of users of cell 2 connected

to cell 2. We denote the steady-state probabilities as

�b;c;d ¼4 PrðY ð1Þ ¼ b; Y ð2Þ ¼ c; C ¼ dÞ. We also define the state

transition probability rðbt;ct;dtÞbt�1;ct�1;dt�1

¼ PrðY ð1Þt ¼ bt; Y ð2Þt ct; C ¼dtjY ð1Þt�1 ¼ bt�1; Y

ð2Þt�1 ¼ ct�1; Ct�1 ¼ dt�1Þ, where subscripts t

and t� 1 denote the current and the previous time slots,respectively. The transition probabilities allow for the

computation of the transition probability matrix, which is

subsequently used to compute the steady-state distribution,

which is denoted by �ðb; c; dÞ.The transition probabilities are governed by arrange-

ment probability, defined as (6), termination probability,defined as (9), and preemption probability defined as [35,Section IV-C1]

P ðiÞx;y ¼xþ ii

� �M2 � x� i

y� i

� �qyp 1� qp� �M2�y; ð17Þ

where x is the current number of group 3 users connectionson cell 2, y is the current number of connections occupied byusers of cell 2, and i is the number of incoming group 3users connection generations.

Having these three equations, we can derive the set ofequations that describe the transition probability matrix forthe general solution. They are presented in the Appendix C,available in the online supplemental material.

3.6.3 Performance Metrics

We can define two important performance metrics for themodel.

Group 3 Users Throughput. The Group 3 users throughputis defined as

Z ¼ � � �s�

RXb;c;d

bþ cð Þ� b; c; dð Þ: ð18Þ


Collision probability between Cell 1 and cell 2 users. Acollision occurs when users in group 3 occupy the samechannel as users in cell 2 after misdetecting their presencewithin a time slot. The probability that there is a mis-detected channel is given by xq ¼ qp�m. The probability thatthere are y collisions in a time slot is denoted as y and isdescribed as follows: If y � b

y ¼Xa;b;c

� a; b; cð ÞXM2

m¼y

M2

m

� �xmq 1� xq� �M2�m

�Xak¼0

Xbl¼0

XM2�m

r¼0

Tka TlbSðy�bþrþkþM1�aþlÞaþb

m

y

� �M2�m

r

� �M2

yþ r

� �0BBB@

þ ð0ÞIðmÞy

Xak¼0

Xbl¼0

XN2

r¼M2�bþM1�aþ1

Tka TlbSðkþlþrÞaþb

!:

ð19Þ

If the number of collisions is greater than or equal to thecurrent number of occupancies of group 3 users on cell 2,the number of group 3 users connection generations oncell 2 are increased to meet the number of collisions. Whenthe number of group 3 users connection generations oncell 2 exceeds the desired number of collisions, a hypergeo-metric term is used to calculate the exact probability ofhaving y collisions. When y ¼ m an excess term is neededfor additional group 3 users connection generations thatcannot be accommodated. On the other hand, if y < b

y¼Xa;b;c

� a; b; cð ÞXM2

m¼y

M2

m

� �xmq 1� xq� �M2�m Xa

k¼0

Xbl¼0

�XM2�bþl

r¼max y�bþl;0ð ÞTka T

lbSðrþM1�aþkÞaþb

m

y

� �M2 �m

bþ r� k� y

� �M2

bþ r� k

� �

þ ð0ÞIðmÞy

Xak¼0

Xbl¼0

XN2

r¼M2�bþM1�aþ1

Tka TlbSðkþlþrÞaþb

!:

ð20Þ

If the number of collisions is strictly less than the number ofoccupancies on cell 2, then additional group 3 usersconnection generations are unnecessary. However, if addi-tional group 3 users terminations occur, group 3 usersgenerations are needed to ensure at least an equal numberof collisions. In turn, the average number of collisions isdefined as a ¼

PM2

y¼0 y y.

4 RESULTS

Since our model incorporates a very large number ofparameters, in the interest of clarity and brevity we focusour study on certain scenarios that are the most importantin the context of our model. First, we present results thatdemonstrate the impact of a varying channel quality on theload balancing efficiency. Second, we examine the influenceof the random access phase on load balancing efficiency.Third, we provide insight on the optimal channel sharingpolicy between BS 1 and BS 2. Fourth, we present results onload balancing in the OSA context in Section 4.4. Finally, in

Section 4.5, we present insight on how to extend ouranalytical model to a multicell scenario.

To confirm the correctness of the analytical model, wecreated a simulation environment in Matlab for verifyingthe analytical results. The results in Sections 4.1, 4.2, 4.4,and 4.5 obtained using both the analytical and simulationapproaches to confirm correctness, while those in Section 4.3are obtained using simulation. Finally, all code used togenerate numerical and simulation results in this paper isavailable upon request or via http://arxiv.org/abs/1004.0534.

Note, that our model is related to [2], [7], [18]. However,the exact comparison of our model with [2], [7], [18] isimpossible, due to the following differences: 1) our modeland those of [2], [7], [18] consider a system, where users areuniquely identified and treated as a single group, respec-tively; 2) our model, in contrary to [2], [7], [18] considers amore involved connection allocation process where, inaddition to channel allocation (considered in [2], [7], [18]only), connection admission through a RACH is analyzed;3) model of [7], [18] considers queuing, while our modeldoes not (for tractability reasons).

4.1 Impact of Channel Quality on Load BalancingProcess

In this simulation, we model, among others, the call

admission, termination, and load balancing processes exactly

as described in our system model. As an example, we

consider a scenario in which two identical cells are positioned

such that they form a small TTR. For simplicity, we assume

that Nx ¼ Lx, where x 2 f1; 2; 3g and M1 ¼ M2 ¼ K. This

particular analysis represents the effect of an increasing wðiÞ3;1

on the overall system-wide channel utilization, while setting

wðiÞ1;1 ¼ w

ðiÞ3;2 ¼ w

ðiÞ2;2 ¼ 0:806 for all i 2fu; dg, assuming recipro-

cal uplink and downlink conditions. This is equivalent to

varying d3;1 from a location that is out of range to being right

next to BS 1, and setting d1;1 ¼ d3;2 ¼ d2;2 ¼ 30 m. We use the

pathloss model with the following parameters: �ðiÞq ¼ �85

dBm,PðiÞt ¼ 30 dBm,W ðiÞ ¼ 7:01ð10Þ�4, �� ¼ 3:65 dB, d

ðiÞ0;x;y ¼

1 m and lastly � ¼ 4:76. Furthermore, we assume an average

channel capacity of R ¼ 250 kbps per channel with an

average packet size rp ¼ 1 kB and � ¼ 8 ms slot length. This

yields an average packet length of 31.25 time slots, or

equivalently 32 ms and probability of time slot occupancy

of q ¼ 0:25. The channel throughput represents a typical

value used in radio access network planning calculations [37,

Table 8.17]. The packet size represents a realistic packet

length sent over the Internet [38], where packets are

distributed between a minimum value of 40 B (Transport

Control Protocol acknowledgement packet) and a Maximum

Transmission Unit, which for IPv6 equals 1.268 kB, for IEEE

802.3 equals 1.492 kB, for Ethernet II equals 1.5 kB, and for

IEEE 802.11 equals 2.272 kB.To determine the best performance of the load-balan-

cing scheme, represented by the proposed DRK algorithm(in the context of the considered system mode and chosenparameter values), for a varying channel quality wedetermine the level of traffic intensity, which results inmaximum channel utilization. Fig. 1a expresses the channel


utilization as a function of increasing traffic intensity p1 ¼p2 ¼ p3 ¼ p for two extreme K values, i.e., K ¼ 0 (when noload balancing is used) and K ¼M2 (all of cell 2’s channelsmay be used for load balancing) considering two networksetups: setup 1 with Lx ¼ Nx ¼ 6, M1 ¼M2 ¼ 3, andsetup 2 with Lx ¼ Nx ¼ 12, M1 ¼M2 ¼ 6. As expected,the channel utilization increases with more traffic intensitybecause an increase in p results in more frequentconnection requests from UEs in all groups leading to ahigher probability of successful connections. Moreover, thelarger the number of channels and users in both cells, thelarger the channel utilization—for both cases consideringK ¼ 0 and K ¼M2. The increase in channel utilization tailsoff as the system reaches saturation, i.e., close to100 percent channel utilization. Similarly, an increase inK results in a higher channel utilization as more UEs fromgroup 3, that are blocked from cell 1, are offloaded ontocell 2, where they have access to an additional K channels.We observe that there is a decreasing rate of gain inchannel utilization with an increase in the number ofshared channels K. As Fig. 1a shows a traffic intensity ofp ¼ 0:4 is the point at which the system begins to operatein saturation, i.e., the relative difference between channelutilizations for K ¼M2 and K ¼ 0 remains relativelyconstant thereafter for both network setups. With theknowledge of decreasing gains in channel utilization withincreasing K, there may exist an intermediate value of Kthat not only leads to an improvement in total channelutilization, but also maximizes improvement with respectto the overall UE experience. This value of K is explored inSection 4.3. In the current section, we continue ourinvestigation using p ¼ 0:4 and explore the impacts ofchannel quality on performance.

Fig. 1b illustrates an increase in channel utilization withan increase in w

ðiÞ3;1 for two extreme values of K. Increasing

wðiÞ3;1 results in group 3 UEs having more successful requests

for receiving downlink transmissions because the averagechannel quality, in which requests are granted for group 3UEs, improves. Therefore, ignoring the channel effects byassuming perfect channel conditions (also done by settingwðiÞ3;1 ¼ 1 in our model) in the analysis of load-balancing

schemes, even for one particular group of UEs, produces anontrivial difference in the channel utilization and leads toan exaggerated improvement in performance due to loadbalancing. By selecting a reasonable scheme to determinethe channel quality, as presented in Section 3.1, we are ableto provide a more realistic evaluation of the improvementsof load balancing. Note that the average channel utilizationsignificantly increases as more channels can be borrowedfrom BS 2. When w

ðiÞ3;1 increases, the difference in channel

utilization between cases K ¼ 0 and K ¼ 3 becomes moreprofound. This proves that with low-channel qualitysystem-wide improvement from load balancing might notbe as significant as in the case of perfect channel conditions.

In Fig. 2, we examine Bð3Þ, Dð3Þ, Bð1Þ, and Bð2Þ, as afunction of w

ðiÞ3;1 for all possible shared channels, i.e.,

K ¼ f0; 1; 2; 3g. The scenario used in this result is identicalto the one used previously. By comparing an increasingvalue of K in Figs. 2a, 2b, 2c, and 2d, we observe theimpact of an increasing number of shared channels on theconsidered performance benchmarks. The first interestingobservation is that irrespective of the value of K theblocking probability for group 1 UEs, Bð1Þ, is relativelyconstant. This means that the quality of service require-ments for UEs not involved in load balancing will be met,even with load balancing enabled. Second, as K increases,blocking probability for group 3 UEs, Bð3Þ, significantlydecreases, which proves the effectiveness of load balancingin this context. Furthermore, the collision probability forUEs in group 3, Dð3Þ, also reduces because with moreshared channels there are fewer unconnected UEs torequest connections. Note, however, that the difference incollision probability for an increasing K is not assignificant as observed for the blocking probability becauseincreasing the number of shared channels has a minimaleffect on the performance of the random access phase.Finally, increasing K only slightly increases blockingprobability Bð2Þ because these UEs have priority inconnecting to any of cell 2’s free channels.

Focusing on Fig. 2d only, where load balancing isenabled, we note that as w3;1 increases, all curves experiencean increase. This can be explained as follows: With an


Fig. 1. Impact of K on channel utilization: (a) The channel utilization as a function of traffic intensity p. Two extremes of shared channels, i.e., K ¼ 0

(no load balancing) and K ¼M2 (all of cell 2’s channels used in load balancing) are shown. Furthermore, two network setups are considered

(a) Setup 1: Lx ¼ Nx ¼ 6, M1 ¼M2 ¼ 3, and (b) Setup 2: Lx ¼ Nx ¼ 12, M1 ¼M2 ¼ 6, where x 2 f1; 2; 3g; the other parameters of the network are

common for both cases and described in Section 4.1. The figure shows good agreement between the results from the analytical model and from

simulation; (b) The channel utilization, represented as a percentage on the vertical axis, as a function of the channel quality between group 3 UEs

and BS 1, wðiÞ3;1 for two extreme values of K. As w

ðiÞ3;1 improves, more group 3 UEs generate successful connections to cell 1 resulting in more UEs that

connect to BS 1 and consequently are offloaded onto cell 2, resulting in an overall increase in channel utilization.

increase in wðiÞ3;1, more group 3 UEs are able to generate

successful connections to BS 1 resulting in an increase in the

contention for sub slots during admission control, and hence

an increase inDð3Þ. Also, there is an accompanied increase in

Bð3Þ because as more UEs generate successful connections,

an increasing number of UEs contend for free channels on

both cell 1 (where load balancing does not occur) and cell 2

(where load balancing occurs). Consequently, this also

results in an increase in Bð1Þ and Bð2Þ. Although these trends

are obvious, the exact degradation in UE experience for each

group is not. For example, in this specific scenario, Fig. 2

illustrates that Bð3Þ is always the primary factor in the

degradation of the group 3 UE experience as compared to

Dð3Þ. This knowledge is significant as the network operator

can determine whether an increase in K, or an increase L3

will be more beneficial to group 3 UEs. Observe that Figs. 1b

and 2 show an extremely good match between the analytical

result and simulation.

4.2 Impact of Random Access Phase on LoadBalancing Process

In this section, we present results on the effect of random

access phase on the performance of load balancing. The

results are presented in Fig. 3. All network parameters are


Fig. 3. Impact of random access phase on load balancing process: (a) total network-wide blocking probability as a function of access probability p;(b) impact of random access phase length Lx on the performance metrics of the considered system. We observe that the blocking probability is not amonotonous function of p and there is an extremum beyond which blocking starts to drop-off. As a result, the network metrics can be easily adaptedby the network operator by dynamically selecting number of random access slots.

Fig. 2. Illustration of the relationship of the blocking probability for group 3 UEs, Bð3Þ, the collision probability for group 3 UEs, Dð3Þ, the blockingprobability for group 1 UEs, Bð1Þ, and the blocking probability for group 2 UEs, Bð2Þ, as a function of the channel quality between group 3 UEsand BS 1, w

ðiÞ3;1 and four all possible shared channels, i.e., (a) K ¼ 0, (b) K ¼ 1, (c) K ¼ 2, (d) K ¼ 3. We observe that the primary factor in the

degradation of performance for group 3 UEs in this particular scenario is Bð3Þ as compared to Dð3Þ and this difference increases as wðiÞ3;1

improves. Once again, this figure shows good agreement between the results from the analytical model and from simulation.

set identically to the network considered in Section 4.1,except for Lx ¼ 3, where x 2 f1; 2g.

We begin by investigating the impact of different UEdistributions on the performance of load balancing. Weperform three experiments and denote each experiment as aspecific case. In the first case, we set the number of UEs,such that more UEs are distributed in groups 1 and 2, thanin group 3, i.e., N1 ¼ N2 ¼ 6, N3 ¼ 4. In the second case, weset the number of UEs equal in each group, i.e., N1 ¼ N2 ¼N3 ¼ 6. And finally, in the third case, we set the number ofUEs in group 3 larger than in the other two groups, i.e.,N1 ¼ N2 ¼ 6, N3 ¼ 8. The metric that is studied in the threecases described above is the total network-wide blockingprobability, calculated as 1

3

P3i¼1 B

ðiÞ, as a function ofchannel access probability pi ¼ p for i 2 f1; 2; 3g. Thismetric is used to give a simple overall indication of theblocking suffered by UEs in all groups. Results arepresented in Fig. 3a.

The most interesting observation from Fig. 3a is that withan increase in the number of UEs in the TTR, the totalblocking probability becomes smaller for moderate valuesof p. Surprisingly, the blocking probability starts to dropsharply as the value of p continues to increase. Thisphenomenon occurs because as p increases, so do collisionson the RACH, which in-turn limits the blocking probabilitybecause fewer UEs successfully access available channels.The result is easier to understand when one observes thatthe blocking probability is the probability of not finding afree data channel for a connection that has successfullyconnected to the BS via a control channel. It has to be kept inmind that for each case presented in Fig. 3a the length of therandom access phase remains the same. What is importantto note is that for moderate values of p, the differencebetween blocking probabilities for each case is small, i.e.,less than 5 percent (please compare values of blockingprobability for each case in the range of p 2 ð0; 0:6Þ).However, as p becomes very large, the curves with a highernumber of group 3 UEs drop-off faster because theyexperience a substantial increase in the number of colli-sions. Therefore, a certain value of p can maximize thechannel utilization achieved through load balancing andalso maintain the blocking probability at approximately thesame level (given negligible changes in UE distribution).

We now move our focus to the impact of random accessphase length Lx on the performance of load balancing. Theresults are presented in Fig. 3b. The set of parametersremain the same as in the earlier experiment in this section,however px ¼ p ¼ 0:4. As an example, three networkmetrics are evaluated as a function of number of slots inthe random access phase, Lx: 1) total channel utilizationin both cells, U ; 2) collision probability at group 3, Dð3Þ; and3) blocking probability at group 3, Bð3Þ. For simplicity, thenumber of slots is set equal among each group of UEs.

Obviously, as the number of random access slots increasethe collision probability decreases for group 3 UEs, and theoverall channel utilization increases. However, as thecollision probability decreases the blocking probability,within the same group of UEs, becomes larger. This is inline with the results presented in Fig. 3a. Recall, that asmore UEs gain access to the BS, the probability thatchannels become unavailable increases. The results shown

in Fig. 3b further demonstrate the fundamental tradeoffbetween the delay caused by random access and overallnetwork utilization. With an increase in traffic intensity p,we expect that the graphs shown in Fig. 3b to shift upwardsproportional to the increase in p because we expect that ahigher traffic intensity would result in more collisions andblocking for users in group 3. We demonstrate that thenetwork operator has a powerful tool, i.e., random accessphase length, through which network metrics can be easilyregulated. It is obvious that the operator has no control overthe channel access probability, p, of individual UEs.However, the operator is able to set a higher value of Lxto the ASC of interest to maintain an expected access delayfor each UE against a required blocking probability.

4.3 Impact of Varying Shared Channel Pool KK onLoad Balancing Efficiency of DDRK

We consider a macrocell scenario in which the distributionof UEs in groups 1, 2, and 3 follow the relationship given byN1 ¼ N2 < N3 and Lx ¼ Nx, where x 2 f1; 2; 3g. Let N1 ¼N2 ¼ L1 ¼ L2 ¼ 25 and N3 ¼ L3 ¼ 40. We consider a sym-metric system, where each cell has 10 channels, i.e.,M1 ¼M2 ¼ 10, and the distances between each group ofUEs and their respective serving BSs are identical, i.e., d1;1 ¼d3;1 ¼ d3;2 ¼ d2;2 ¼ 220 m. Once again, we assume an averagechannel capacity of R ¼ 250 kbps per channel with anaverage packet size rp ¼ 1 kB. A frame duration of � ¼ 1 msis used. We assume a simplified path loss model withidentical parameters as in Section 4.1 except with � ¼ 3,which is more appropriate for outdoor channel conditions.

In Fig. 4a, we explore the system-wide improvement inchannel utilization (represented as a percentage on thevertical axis) as a function of the number of shared channelsK (represented on the horizontal axis). Note that for theremainder of our study we fix traffic intensity for all groupsto p ¼ 0:2 to determine the maximum gain in channelutilization for every value of K at traffic intensities that arevery near saturation. The line with circle markers representsthe total percentage improvement experienced as a functionof K, while the line with triangle markers represents theimprovement experienced in channel utilization per sharedchannel. As K increases, there is a decreasing improvementin channel utilization per additional channel, which in-dicates that the extra cost of sharing more channels for loadbalancing may outweigh the added benefit of serving agreater number of UEs.

Although there is an overall improvement in the system-wide channel utilization, the exact effect of the load-balancing scheme on the UE experience is unknown.Obviously, Bð3Þ decreases with an increase in K becausegroup 3 has access to more channels. In contrast, Bð2Þ

increases because more UEs in group 3 access channelsbelonging to cell 2, which are of course also accessible to UEsin group 2. Although these general trends are obvious, theexact relationship between the amount of decrease in Bð3Þ

versus the amount of increase in Bð2Þ is unknown. In Fig. 4b,we examine this relationship in more detail, where thedecrease in Bð3Þ (solid line with triangle markers) is plottedwith the consequent increase in Bð2Þ (solid line with circles)as a percentage on the vertical axis with increasing K on thehorizontal axis. We observe that in this particular scenario,


the total decrease in Bð3Þ is always more than the totalincrease in Bð2Þ, suggesting that the overall UE experienceimproves with the proposed load-balancing scheme. Thisreaffirms the increase in channel utilization with an increasein K for DRK , which is previously observed in Fig. 4a.

The total improvement in overall UE blocking prob-ability demonstrates the effectiveness of the load balancingscheme. However, from a network operator viewpoint,knowledge of the changes in UE experience per additionalshared channel is also very important. Fig. 4b examines theeffect of an increase in K on both the decrease in Bð3Þ=K(dashed line with triangles), and the consequent increase inBð2Þ=K (dashed line with circles). We observe, that for thisparticular scenario, a decrease in Bð3Þ=K is always morethan the increase in Bð2Þ=K, which suggests that the UEs ingroup 3 experience more of an improvement in perfor-mance than the performance degradation experienced byUEs in group 2 per additional shared channel. This allowsdirect evaluation of the effectiveness of the load-balancingscheme on the overall UE experience per additional sharedchannel. In Fig. 4b, we note that Bð3Þ=K reaches a maximumat an intermediate value of K, i.e., K ¼ 3, because thesystem reaches a balance between the number of UEsrequesting connections and those that are already con-nected through load balancing. Our model allows for thedirect observation of this system state because of thecombined modeling of a finite number of UEs togetherwith a detailed call admission process. With the use ofFig. 4b, we are able to determine the best K to improve theoverall UE experience on a per shared channel basis, andthen find the corresponding improvement in the overallchannel utilization using Fig. 4a. For this particularscenario, the maximum difference between the increase inBð3Þ=K and decrease in Bð2Þ=K occurs at K ¼ 6 andcorresponds to an overall improvement in channel utiliza-tion of 12.6 percent.

In summary, we can construct the following optimiza-tion function. Given fundamental descriptors of the net-work considered in Section 3, i.e., Ni, Mi, Lx, pi, w

ðiÞx;y, rp, and

� , the network operator should find

arg maxK

U=K subject to 8iBðiÞ � mðiÞ; DðiÞ � oðiÞ; ð21Þ

where mðiÞ and oðiÞ are the required maximum blocking andcollision probabilities, respectively, for group i. The devel-oped analytical model provided in Section 3 allows solvingthe optimization function (21), since each metric, U , BðiÞ andDðiÞ is given in closed form. The optimization formulaallows obtaining the value of K to obtain the maximumutilization per shared channel, such that all consideredquality of service metrics required by the operator, mi andoi, are met. Note that finding the optimal solution to (21) isbeyond the scope of this paper. On the other hand, note thatbecause the complexity of the optimization problem (21)increases linearly with K, it can be solved efficiently via,e.g., exhaustive search, provided the existence of quickcomputation of �a;b;c;d. Then, the complexity of calculating�a;b;c;d increases nearly exponentially with increasing Mi.Note, however, that calculating �a;b;c;d even for large valuesof state space (e.g., for K ¼ 3, M1 ¼M2 ¼ 12 and Nx ¼ 24size of �a;b;c;d is 16,744 elements), can be handled efficientlywith any standard personal computer with optimizedimplementation of the transition probability matrix devel-oped in this paper.

4.4 Load Balancing with OSA Results

We consider an energy detection technique to detect thepresence of cell 2 users and an AWGN channel for which �fand �m is given as [39, Section III]. The sensing bandwidthis 200 kHz, with cell 2 users detected SNR of �5 dB and thedetection threshold of �109:4 dBm is set to the noise floor.

4.4.1 Impact of Varying M2 on Throughput for Group 3

Users Z

To illustrate an application of the model, we consider thefollowing parameters: The number of channels on cell1 M1 ¼ 7, the number of subscribers in the region of overlapN3 ¼ 40, connection request probability p ¼ 0:1, randomaccess phase length L ¼ N3=2 ¼ 20. Furthermore, we con-sider an average packet size of rp ¼ 1 kB, channel through-put R ¼ 250 kbps, and a transmission time of � � �s ¼ 9 ms,where �s ¼ 1 ms. This results in an inverse of the packetlength q ¼ 0:2813, false-alarm probability �f ¼ 0:1398, andmisdetection probability �m ¼ 0:0861.


Fig. 4. Impact of K on load balancing efficiency: (a) The percentage improvement of channel utilization (left vertical axis) and the percentageimprovement of channel utilization per shared channel (right vertical axis) as a function of shared channels, K. As K increases, there is an obviousimprovement in channel utilization; however, there are decreasing gains experienced per additional K; (b) The total change in blocking probability,BðxÞ, and blocking probability per shared channel, BðxÞ=K, where x 2 f2; 3g. In this scenario, we observe that the decrease in Bð3Þ is always greaterthan the corresponding increase in Bð2Þ for all K, suggesting that there is an overall improvement in the UE experience. Furthermore, it is seen thatat K ¼ 6 we have the greatest difference between the decrease in Bð2Þ=K and the corresponding increase in Bð2Þ=K suggesting that this is theoptimal number of shared channels to use to gain the best UE experience per K.

Results associated with the above parameters arepresented in Fig. 5a. For comparison, we also plot thethroughput using a random cell 1/cell 2 channel selectionalgorithm for new group 3 user connections, which wasanalyzed in [36]. As expected, in both cases group 3 userthroughput decreases with an increase in cell 2 useractivity. This decrease in throughput is attributed to moregroup 3 user preemptions and blocked connections.Furthermore, group 3 user throughput increases with anincrease in M2. More interestingly, as M2 increases theOSA-enabled cellular network experiences less marginalgain in throughput for each additional group 3 useraccessible channel on cell 2. Moreover, the greatest gainin throughput for additional M2 channels is seen at lowvalues of qp, e.g., qp < 0:2. With such knowledge operatorshave insight on the marginal gains in throughput withadditional M2 and the specific role qp plays in limiting thesegains. The solution in the present paper based on firstassigning channels from cell 1 results in a significantimprovements over the random assignment approach. Forexample, for M2 ¼ 7 at qp ¼ 0:7 our algorithm providesmore than one and a half times improvement.

4.4.2 Impact of Sensing Time �s on Cell 1/Cell 2 Users

Collision Probability aThe impact of �s on the collision probability of cell 1/cell 2users is shown in Fig. 5b. All parameters remain the same asin Section 4.4.1, except that the sensing threshold equals�109:7 dBm, rp ¼ 800 kB, and M1 ¼ 1, M2 ¼ 6 for thepurpose of better illustrating the impact of �s. More collisionswith an increase in qp are experienced because moremisdetections of cell 2 occur. Furthermore, an increase in �sresults in an accompanying decrease in �m, thus, reducing adue to lower levels of perceived cell 2 user activity. Inaddition, increasing �s to reduce the number cell 1/cell 2 users collisions is more effective at high qp. At high qp,the system is highly sensitive to �m, i.e., a small reduction in�m results in large improvements. Therefore, networkoperators need to account for relative levels of qp to determineif increasing �s will result in a considerable improvement forcell 2 users. At low qp, network operators can determine the

optimal �s to maximize Z while measuring the exact

improvement in a.

4.5 Extension of the Model to a Multicell Scenario

Due to the complexity of deriving performance metricsbased on an analytical model for a multicell network, wepresent a numerical approximation and simulation resultsto provide insight into the behavior of such a system. Weconsider a general, non-OSA, scenario in which a centralcell overlaps with X neighboring cells. UEs are divided intogroups, in the same fashion as in the system modelpresented earlier. Specifically, there are three groups:1) UEs in the central cell (referred to as group 1); 2) UEsin the neighboring cell (referred to as group 2); and 3) UEsin the overlap region between the central and neighboringcells (referred to as group 3). It is assumed that UEs in thecentral cell and in each of the overlapping regions areregistered to the central cell. To avoid ambiguity, weassume that there are no overlaps between cells neighbor-ing the center cell, so that the UEs in the overlap regionobserve signals only from two cells. This assumption makesevaluation of the multicell extension relatively easier.

Each of the groups considered consists of N UEs, while

every cell has M available channels. Therefore, a particular

UE belonging to any group in the overlap region has access

to 2M possibly unoccupied channels, i.e., M from the

central cell and an additional M from the neighboring cell,

while the UEs from the remaining groups have access to

only M channels. Each channel is assumed to be error free

(in other words channel conditions are not considered).

Note that the decision on which users are granted

connections to the central cell in the presence of load

balancing is left solely to the radio network controller (as in

the case of base two-cell case, refer to Section 2.7 for details).

In the case of our analysis, we apply a simple decision

strategy, where users are selected randomly from each cell

when load balancing needs to occur. In practical scenarios,

the radio network controller can apply user selection

strategies based on, e.g., 1) user/cell priority; 2) fairness;

and/or 3) channel quality. We present the results on two


Fig. 5. Performance of OSA load balancing system: (a) Group 3 users throughput, Z, as a function of cell 2 user activity, qp, for varying number ofchannels accessible to group 3 users on cell 2, M2. The labels (An. S1) and (Sim. S1) represent the analytical and simulation results, respectively,for the DRK load balancing scheme. (Sim. S2) represents the results from a random cell 1/cell 2 channel selection algorithm as analyzed in [36]. Weobserve a decreasing marginal gain in throughput as M2 increases with significant gains experienced at relatively low values of qp. Note the perfectmatch between analysis and simulations of system S1; (b) Average cell 1/cell 2 users collision probability, a, as a function of the sensing time, �s, forvarying levels of cell 2 users activity, qp. An increase in �s to reduce a is more effective at high levels of qp, where the system is highly sensitive tochanges in the probability of mis-detection, �m. Note that just as in Fig. 5a there is a perfect match between analysis and simulations.

essential metrics: 1) the overall channel utilization; and2) the overall blocking probability.

We utilize a simple numerical approximation for overallchannel utilization. We represent the two-cell system, as aspecial case of a multicell system, which has one central celland X neighboring cells. For simplicity, in this particularcase, we assume that only group 3 UEs are present in themulticell system. Furthermore, cell one of the two-cellsystem represents the central cell of the multicell system,while cell two represents a linear combination of the Xneighboring cells in the multicell system. The number ofUEs in the group residing in the region of overlap of thetwo-cell system is now XN , the number of channels in eachcell is bðXMÞ=2c, and the number of assigned randomaccess slots is XL. In this manner, we keep the ratio of thenumber of UEs per channel approximately the same forboth the two-cell and multicell systems. We present theresults for three network scenarios: 1) a large-scale net-work; with M ¼ 15 and N ¼ 30; 2) a medium-scale net-work, with M ¼ 8, N ¼ 16; and 3) a small-scale networkwith M ¼ 3, N ¼ 6. For each scenario, we assume a channelaccess probability p ¼ 0:4, average channel capacity of R ¼250 kbps per channel with an average packet size rp ¼ 0:833kB, and � ¼ 8 ms slot length (the same parameters as inSection 4.1), which translates to a slot occupancy prob-ability of q ¼ 0:3. Since the traffic generated by users ineach cell neighboring the central cell is the same, we keepK ¼M for every cell. Note the an unequal pool of sharedchannels would penalize some cells during the loadbalancing process and defeat the goal of maintaining anequal level of throughput for each cell.

In Fig. 6a, we observe that as the number of neighboringcells increases, so does the channel utilization. Interestingly,the channel utilization does not change considerably with anincrease in UE population and channel pool. Observe thatthe channel utilization is well represented by our approx-imation, i.e., the difference between the exact model and theapproximation does not exceed 10 percent for all networksetups. Note that the approximation is looser for the small-scale network, in Fig. 6a for X ¼ f3; 5g, i.e., when the ratio ofUEs to channels is not an integer. This is simply due to therounding down of the number of the channels by the floorfunction. Recall that the code used to generate the results for

numerical approximation (and to test the accuracy ofapproximation for other parameter sets) is available uponrequest or via http://arxiv.org/abs/1004.0534.

In Fig. 6b, we present simulation results on the blockingprobability as a function of the number of the neighboringcells X. We assume the same UE distribution as that of themedium-scale network, i.e., M ¼ 8, N ¼ 16, with p ¼ 0:3with rp ¼ 0:625 kB, R ¼ 250 kB, � ¼ 8 ms (the same valuesas considered earlier), which translates to q ¼ 0:4. Weobserve the average blocking probability for each consid-ered group in the scenario using three different values forthe random access phase length L ¼ f4; 8; 16g. The blockingprobability for UEs in group 3 is more than that of the othergroups with an increase in X. This is attributed to theincrease in the number of UEs in the overlap region with anincrease in the number of neighboring cells. The blockingprobability for UEs in groups 1 and 2 stays relativelyconstant with changes in X because UEs in group 1 havepriority over UEs in group 3, while the UEs in group 2 docompete for cell resources with the UEs in the overlapregion. Also, the relative difference between blocking forUEs in groups 1 and 2 for each value of L is small becausethe ratio of accessible channels per UE remains the sameregardless of X. As the number of random access slotsincrease, so does the blocking probability, which is fullyconsistent with the earlier observation expressed analyti-cally and presented in Fig. 3b. This supports a conclusionthat the analysis of the two-cell system is highly relevant tothe behavior of the multicell network.

5 CONCLUSIONS

We have presented a new analytical model to assess theperformance of the load balancing process in a two-cellsystem, later extended via approximations to a multicellsystem. The model differs in many respects from previouswork on load balancing analysis in several important ways.First, it aids in determining the impact of channel quality toimprove the accuracy of reported load balancing efficiency.Second, it demonstrates that the random access phaselength can be used as an important network regulatory toolto control both system-wide and user experience perfor-mance metrics. Lastly, it facilitates the exploration of theeffects of varying shared channel access on system-wide


Fig. 6. Results for the multicell system: (a) channel utilization (Ex.: exact; Ap.: approximation; S: small; M: medium; L: large) and (b) simulationresults for blocking probability (Gr.: Group). The parameter setup and explanation of the naming convention is presented in Section 4.5. We alsonote that the channel utilization in the multicell system does not drastically differ as the number of UEs and channels change. Also, the blockingprobability for each group increases with an increase in the number of neighboring cells. The blocking probability experiences the most increase forUEs in the overlap region (group 3).

performance and user experience. In addition, we havepresented a new application of our model, which allows forthe consideration of new load balancing techniques. Inspecific, we have considered OSA as an additional featurein the load balancing process. We have shown that OSAbrings a large benefit to the cellular network, especially inthe absence of central coordination. We have presented avariety of results derived from this framework, and inparticular explored the tradeoffs in terms of channelutilization, blocking probability, and collision probabilitywhen traffic is transferred from a highly congested cell to aless-loaded neighboring cell.

ACKNOWLEDGMENTS

Part of this work was published in the Proceedings of IEEEGlobeCom, 6-10 Dec. 2010, Miami, Florida [1].

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Przemyslaw Pawelczak received the MScdegree from Wroclaw University of Technology,Poland, in 2004 and the PhD degree from DelftUniversity of Technology, The Netherlands, in2009. During Fall 2007, he was a visitingscholar at the Connectivity Lab, University ofCalifornia, Berkeley. From 2009 to 2011, hewas a postdoctoral researcher at the CognitiveReconfigurable Embedded Systems Lab, Uni-versity of California, Los Angeles. Between

2011 and 2012, he has been a research staff member at FraunhoferInstitute for Telecommunications, Heinrich Hertz Institute, Berlin,Germany. Currently he is a (tenure track) assistant professor withthe faculty of Electrical Engineering, Mathematics and ComputerScience at the Delft University of Technology. His research interestsinclude cross-layer analysis of opportunistic spectrum access networks.He received the NWO Veni grant in 2012. He was nominated for the2011 UCLA Chancellor Award for Postdoctoral Research and receivedthe annual Telecom Prize for Best PhD Student in Telecommunicationsin The Netherlands in 2008 awarded by the Dutch Royal Institute ofEngineers. He is a member of the IEEE.

Shaunak Joshi received the BSc degree inelectrical engineering from North Carolina StateUniversity in 2007 and the MSc and PhDdegrees, both in electrical engineering, fromthe University of California, Los Angeles, in 2008and 2012, respectively. He has served as aprofessional referee for many IEEE journals andconferences. He was also a board member ofthe Technical Entrepreneurship Club at theUniversity of California, Los Angeles, in 2010.

Since 2011, he has been with the Wireless Network Business Unit atCisco Systems, Inc., San Jose, California, where he develops spectrumsensing capabilities for enterprise WiFi products. His research interestsinclude next generation cellular and WiFi systems, channel bonding inwireless networks, network modeling, cognitive radio systems, and loadbalancing strategies. He is a member of the IEEE.

Sateesh Addepalli is currently the director ofthe Advanced Architecture, Research, andInnovation Group of Cisco Systems, Inc., SanJose, California. He has been responsible forlaunching and driving various successful initia-tives related to mobile and wireless, sensors andsensor networks, cloud and ubiquitous/perva-sive computing, data mining and analytics,internet of things, machine-to-machine, human-to-machine, health and wellness, and smart and

connected communities. He currently serves on the advisory boards ofthe Center for Advanced Technology in Telecommunications, New YorkUniversity, and Quality of Life Lab, University of Texas, Dallas,respectively. In addition, He serves on the editorial board for the Journalof Cyber Security and Mobility.

John Villasenor received the BSc degreefrom the University of Virginia, and the MScand PhD degrees from Stanford University. Heis a professor of electrical engineering at theUniversity of California, Los Angeles, and anonresident senior fellow at the BrookingsInstitution. His work addresses the technologiesand policy issues associated with digital infor-mation. He is a senior member of the IEEE.

Danijela �Cabri�c received the Dipl Ing degreefrom the University of Belgrade, Serbia, in 1998,the MSc degree in electrical engineering fromthe University of California, Los Angeles, in2001, and the PhD degree in electrical engineer-ing from University of California, Berkeley, in2007, where she was a member of the BerkeleyWireless Research Center. In 2008, she joinedthe faculty of Electrical Engineering of Universityof California, Los Angeles, as an assistant

professor. Her key contributions involve the novel radio architecture,signal processing, and networking techniques to implement spectrumsensing functionality in cognitive radios. He has written three bookchapters and more than 25 major journal and conference papers in thefields of wireless communications and circuits and embedded systems.She was awarded the Samueli Fellowship in 2008, an OkawaFoundation research grant in 2009, and the National Science Founda-tion CAREER award in 2012. She is a member of the IEEE.

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