Call Admission Control for Reducing Dropped Calls in Code DivisionMultiple Access (CDMA) Cellular Systems

Yue MaGlobal Software Division

Motorola Inc.1303 E. Algonquin Rd.,

IL01/Anx 2Schaumburg, IL 60196-1065

Yue.Ma@motorola.com

James J. HanGlobal Software Division

Motorola Inc.1303 E. Algonquin Rd.,

IL01/Anx 2Schaumburg, IL 60196-1065James Han@email.mot.com

Kishor S. TrivediDepartment of Electrical and

Computer Engineering1112 Hudson Hall

Duke University, Box 90291Durham, NC 27708-0291

kst@ee.duke.edu

Abstract— Call admission control algorithms that reducedropped calls in CDMA cellular systems are discussed in thispaper. The capacity of a CDMA system is confined by inter-ference of users from both inside and outside of the targetcell. Earlier algorithms for call admission control is basedon the effective traffic load for the target cell if one call isaccepted. These algorithms ignore the interference effect ofthe to-be-accepted call on the neighboring cells. In our algo-rithms, the call admission decision is based on the effectivetraffic loads for both the target cell and the neighboring cells.In addition, to prioritize handoff calls, we also introduce theidea of soft guard channel, which reserves some traffic loadexclusively for handoff calls. Stochastic reward net (SRN)models are constructed to compare the performance of thealgorithms. The numerical results show that our algorithmscan significantly reduce the dropped calls with a price of in-creasing the blocked calls. To show the potential gain dueto our algorithms, we introduce two new metrics: the in-creased blocking ratio for our algorithms and the increaseddropping ratio for the conventional algorithms. From the nu-merical results, it is shown that our algorithms can reducethe dropped calls significantly while the blocked calls are in-creased at a relatively small rate under both homogeneousand hot spot traffic loads.

Keywords— call admission control, CDMA, interference,soft guard channel, Markov reward models, stochastic re-ward net (SRN).

I. INTRODUCTION

Since the early 1990’s, personal communications services(PCS) have been growing at an explosive rate. To meet the con-tinuing growth of the customer demand, the limited spectrumneeds to be used as efficiently as possible. Spread spectrumcode-division multiple access (CDMA) scheme provides highspectrum efficiency [23]. In a CDMA system, all the users sharethe same radio frequency at the same time, the system capacity isstrictly interference limited. Unlike a frequency-division multi-ple access (FDMA)/time-division multiple access (TDMA) sys-tem where capacity is fixed due to the frequency/time allocation,the capacity of a CDMA system is soft. As the number of userssharing the same radio frequency is increased, the signal-to-interference ratio (SIR) generally degrades. Therefore, to some

extent, the capacity of a CDMA cellular system depends on howsensitive the subscriber is to the background noise.

Call admission control (CAC) algorithms for reducingdropped calls in CDMA systems are discussed in this paper. Thecapacity of a CDMA system is confined by interference of usersfrom both inside and outside of the target cell. The earlier CACalgorithms [9], [12], [18] are based on the effective traffic loadfor the target cell if the call is accepted. However, these methodsignore the interference effect of the to-be-accepted calls fromthe neighboring cells. The following example shows the poten-tial negative effect of this ignorance.

Suppose that cell A and cell B are in a common neighbor-hood. The traffic load in cell B has already reached its max-imum, while the traffic load in cell A is quite light. All thenew call arrivals in cell B will be denied because it has alreadyreached its saturation point. According to the earlier method(we refer to it as the SD algorithm), any new call arrivals will beaccepted in cell A because it has not reached its maximum loadyet. Since cell B has already reached its maximum load, accept-ing a new call in cell A could possibly deteriorate the quality ofthe traffic channels in cell B beyond tolerance and consequentlycausing dropped calls or outage. Hence, to maintain the overallQoS for the whole system, it is necessary to consider the inter-ference impact on the neighboring cells when accepting a call ina cell.

In this paper, we propose a method (called the LA algorithm)for call admission control in CDMA systems. In this method,the call admission decision is based on the effective traffic loadsfor both the target cell and the neighboring cells. From the nu-merical results, it is shown that the LA algorithm can signifi-cantly reduce the probability for dropped calls. However, wedo need to pay a price: an increased blocking probability. Thisis well justified because when the system is heavily loaded, theacceptance of a new call (NC) in one cell would cause possi-ble dropping or outage in adjacent cells. To analyze the tradeoffbetween the decreased dropping probabilities and the increasedblocking probabilities, we introduce two new metrics, namely,the decreased dropping ratio and the increased blocking ratio.From the numerical results, we can see that the gain for thedecreased dropping probabilities is worthwhile. From the nu-merical results, it is shown that our algorithms can reduce thedropped calls significantly while the blocked calls are increased

at a relatively small rate, under both the homogeneous and non-homogeneous traffic.

Another contribution of this paper is that we introduce theidea of soft guard channel to prioritize soft handoff calls (SHC).In FDMA/TDMA systems, physical hard guard channels informs of frequencies/time slots are reserved exclusively forhandoff calls. In CDMA cellular systems, the capacity is inter-ference limited. There are no physical resources which can beused as guard channels. Instead, a certain amount (either inte-gral or fractional) of traffic load, denoted as soft guard channels,is reserved exclusively for soft handoff calls.

This paper is organized as follows. In Section II, some ofthe related features of a CDMA cellular system are described.In Section III, we present our CAC algorithms for reducingdropped calls. To obtain numerical results for the CAC algo-rithms, stochastic reward nets (SRNs) are developed in Sec-tion IV. A brief introduction of SRN is first given at the be-ginning of that section. In Section V, the performance of the LAand the SD algorithms are compared. Finally, conclusions aremade in Section VI.

II. SYSTEM DESCRIPTION

A. Soft Handoff

In cellular networks, different multiple access schemes areused to provide resources (channels) for setting up/maintainingcalls. In FDMA, each channel can be regarded as a different fre-quency. In TDMA, the calls are served with different time slots.In CDMA, the calls are served with different pseudonoise (PN)sequences. When a mobile station (MS) travels across the cellboundaries, the channel in the old serving cell is released, andan idle channel is required in the target cell, which would be thenew serving cell. This process is called handoff. In a conven-tional cellular network, the MS breaks the communication linkwith the old base station (BS) before establishing a new com-munication link with the new BS. This kind of handoff process(break before make) is generally experienced with a brief in-terception of communication and is commonly referred as hardhandoff.

In an IS-95 [19] CDMA system, a so called soft handoffmechanism is utilized. Each MS measures the signal strengthfrom its surrounding BSs. The PN offsets of the BSs serve asthe identification numbers for the BSs. When an adjacent basestation’s pilot strength is strong enough to establish a communi-cation link, the base station’s PN offset is stored in the mobilestation’s Active Set. With lower signal thresholds, the MS alsomaintains a Candidate Set and a Neighborhood Set. When anMS is undergoing a soft handoff, more than one pilot is storedin the Active Set. The MS communicates with two or more BSsuntil the communication link between the mobile and one basestation is firmly established. The “Ping-Pong” effect (constanthanding back and forth between base stations at the border),a common phenomena in hard handoff, is avoided under this“make before break” strategy. Thus, the signal quality and ser-vice reliability is substantially improved through soft handoff.

B. CDMA Cellular System Model

Assume that a target cell in a wireless network can be par-titioned into two zones: core zone (CZ) and the soft handoffzone (SHZ). With respect to the base station in the target cell,the area immediately adjacent to the SHZ is called the neigh-borhood zone (NZ). Fig. 1 shows a concentric geometry usedfor the purpose of illustrating the relationship among the threezones. In [11], similar concentric geometry approaches are usedfor analyzing the performance of cellular networks.

Soft Handoff Zone (SHZ)

Core Zone (CZ)

Neighborhood Zone (NZ)

Target Cell

Fig. 1. A concentric geometry for a target cell and its neighbor-hood area.

When an MS is in soft handoff phase, we assume that at mosttwo base stations are in diversity reception. New call interar-rival times are assumed to be independent and exponentiallydistributed [10], with rate

���. A new call may arrive in either a

core zone or a soft handoff zone.Assume that new calls are uniformly distributed in the target

cell, the new call arrival rates for the two zones are:

�������� ������ ������������� ��

where� ��

or� �

is respectively the new call arrival rate in CZ orSHZ and

����������� �"!$#&%(')�+*��,��� � �-!$#/.0���21��3.546�37,7,�. Suppose

that the mean target cell dwelling time is 859 , then the averagetime that an MS spends in CZ and SHZ is respectively

� 8:9 and�0�;�<��� 8 9 . For reasons of tractability [7], [8], the call holdingtimes are assumed to be exponentially distributed.

III. CALL ADMISSION CONTROL (CAC) ALGORITHMS

THROUGH Looking Around

When a NC/SHC arrives, one method for call admission isbased on local information without ‘consulting’ the neighbor-hood. We refer to this as the SD algorithm because the call ad-mission is based on self-decision. We enhance the SD algorithmby considering the possible interference from the neighborhoodcells. The enhanced algorithm is denoted as the LA algorithmbecause the call admission is made after ‘looking around’ at theneighborhood cells.

37

Y

Blockthe call

MELA<

Threshold ?

Blockthe call

Calculate the effective loadfor the target cell (ELT)

Y

Calculate the effective loadfor the other cell whichcovers the SHZ (ELS2)

Get the maximumeffective load for the

adjacent cells (MELA)

N

Proceed to setup the new call

Y

Check whether the NC is inCZ or SHZ and update the

related parameters

Is the NC in theSHZ? N

ELS2<

Threshold ?

NELT

<Threshold ?

New Call (NC) Arrival

N

Y

Fig. 2. CAC algorithm for the new call arrivals in the target cell.

A. CAC Algorithm for New Calls

Fig. 2 shows the CAC algorithm for the new calls. When anew call arrives, the base station at the target cell first checks ifit is in the CZ or SHZ. This can be achieved through two ways.One way is to obtain the information by the signal strength. Theother is to check the number of pilots in the Active Set of thenew call. The effective load for the target cell (ELT) is thencalculated through the following equation:

����� ��� ��� �� � �� � � � �

where� � (� ) is the number of calls in the CZ (SHZ) before a

possible admission of an NC;� �

is the number of calls in theNZ; and

�are the weights. If the target cell is already

saturated, the new call is blocked. Otherwise, if the NC is in theSHZ, the effective load for the other cell (ELS2) that covers theSHZ is also calculated. Again, the threshold is compared withELS2, if no saturation point is reached for the other cell, thealgorithm continues with the final check for the neighborhood

38

N

Y

Calculate the maximumeffective load for the

adjacent cells (MELA)

NY

Deny soft handoffcall attempt

MELS<

Threshold ?

Soft Handoff Call (SHC) Arrival

Get the maximum of the effective loads(MELS) for the cells that would beadded to the Active Set of the call

Is the queuefull?

N

Y

Time out?

N

Wait in queue

Soft handoff call acceptance

Y

MELA<

Threshold ?

Drop the softhandoff call

Fig. 3. CAC algorithm for soft handoff calls in the target cell.

cells. The call is accepted if the maximum effective load for theadjacent cells (MELA) is below the threshold.

Notice that in [18], if a new call is denied in the SHZ of onecell, it is allowed to be set up through another cell whose SHZalso covers the call. This algorithm would have the risk of drop-ping some ongoing calls in the already saturated cell.

B. CAC Algorithm for Soft Handoff Calls

The CAC algorithm for soft handoff calls is shown throughFig. 3. When a soft handoff call is required, the effective loadsfor the cells that cover the SHZ are calculated. The largest valuefrom these (denoted as MELS) is compared with the predeter-mined threshold. If there is still room for the cells, the algorithmcontinues with calculating the maximum effective load for theadjacent cells. If again the MELA is under the threshold, thesoft handoff call is accepted and diversity combination is ap-plied for receiving the call. If either MELS or MELA is abovethe threshold, the SHC requirement would be put in a queue ifthe queue is not full. Otherwise, the SHC is denied. While wait-ing in the queue, the SHCs are periodically checked on whetherthe time out event has occurred or not. If a time out event hasoccurred before the SHC can obtain access to the target cell, itis dropped.

C. Soft Guard Channel

The dropping of a handoff call (which is an ongoing call) isconsidered more disturbing than the blocking of a new call. Pri-oritizing handoff calls [20], [22] is an important way to reduce

handoff failures. In our CAC algorithm, we introduce the ideaof soft guard channel to prioritize handoff calls. In addition,queuing [17] is also used to enhance the handoff success prob-ability. Unlike FDMA or TDMA systems, which use frequencyor time slot as resources for ‘hard’ guard channels, the resourcesin CDMA cellular systems are interference limited. There are nophysical resources in CDMA systems that can be used for guardchannels. To prioritize SHCs, a certain amount of traffic capac-ity is reserved exclusively for SHCs. In the remainder of thispaper, we refer to the reserved traffic capacity as the soft guardchannels (SGC). Assume that the threshold in Fig. 2 is denotedas���

and the threshold in Fig. 3 is denoted as���

. Using softguard channels to prioritize SHC,

���is always greater than or

equal to���

. Denoting the numerical value of SGC as1

, wehave

1 � ��� � ���. The value of

1can be either integral or

fractional depending on the traffic volume of the environment.

IV. SRN MODELS FOR THE CAC ALGORITHMS

A. Introduction to SRN

Stochastic reward net (SRN) [4] is an extension of Petri net(PN) [16], which is a high level description language for for-mally specifying complex systems. A PN is a bipartite directedgraph with two types of nodes: places and transitions. Eachplace may contain an arbitrary (natural) number of tokens. For agraphical presentation, places are depicted as circles, transitionsare represented by bars and tokens are represented by dots orintegers in the places. Each transition may have zero or moreinput arcs, coming from its input places; and zero or more out-put arcs, going to its output places. A transition is enabled if allof its input places have at least as many tokens as required by themultiplicities of the corresponding input arcs. When enabled, atransition can fire and will remove from each input place andadd to each output place the number of tokens correspondingto the multiplicities of the input/output arcs. A marking depictsthe state of a PN which is characterized by the assignment oftokens in all the places. With respect to a given initial mark-ing, the reachability set is defined as the set of all markingsreachable through any possible firing sequences of transitions,starting from the initial marking.

Generalized stochastic Petri nets (GSPNs) [1] extend the PNsby assigning a firing time to each transition. Transitions with ex-ponentially distributed firing times are called timed transitionswhile the transitions with zero firing times are called immedi-ate transitions. A marking in a GSPN is called vanishing if atleast one immediate transition is enabled; otherwise it is calleda tangible marking. For a given GSPN, an extended reachabilitygraph ( ����� ) is generated with the markings of the reachabil-ity set as the nodes and some stochastic information attached tothe arcs, thus connecting the markings to each other. Under thecondition that only a finite number of transitions can fire in fi-nite time with non-zero probability, it can be shown that a given����� can be reduced to a homogeneous continuous time Markovchain (CTMC) [1].

In order to make more compact models of complex systems,several extensions are made to GSPN, leading to the SRN. Oneof the most important features of SRN is its ability to allow ex-tensive marking dependency. In an SRN, each tangible marking

34

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

Fig. 4. A cluster of cells for analytical study.

can be assigned with one or more reward rate(s). Parameterssuch as the firing rate of the timed transitions, the multiplici-ties of input/output arcs and the reward rate in a marking can bespecified as functions of the number of tokens in any place inthe SRN. Another important characteristic of SRN is the abilityto express complex enabling/disabling conditions through guardfunctions. This can greatly simplify the graphical representa-tions of complex systems. For an SRN, all the output measuresare expressed in terms of the expected values of the reward ratefunctions. To get the performance and reliability/availabilitymeasures of a system, appropriate reward rates are assigned toits SRN. As SRN is automatically transformed into a Markov re-ward model (MRM) [4], [21], steady state and/or transient anal-ysis of the MRM produces the required measures of the originalSRN. In this paper, we use the tool SPNP [3], [6] to specify andsolve the SRN models.

B. Model Description

In this section, we construct SRN models in accordance withthe CAC algorithms described in Section III. Because of theinteraction among the cells, an SRN model for even a clusterof cells (Fig. 4) would instigate a huge state space for the un-derlying Markov reward process. Depending on the nature ofthe system to be modeled, different approaches can be appliedto reduce the underlying state space for SRN models. Exam-ples for these approaches are: state truncation [15]; hierarchicalapproach [13] and decomposition approach [5]. In this paper,our SRN models are based on a decomposition approach. Fig. 4shows a cluster of seven cells (in solid lines) together with theiroutside neighborhood cells shown with dashed lines. We willconcentrate on the center cell,

%. The LA algorithm for call ad-

mission control in a generic cell can be represented by an SRNmodel shown in Fig. 5.

In Fig. 5, places CZ and SHZ respectively represent the corezone and the soft handoff zone for a generic cell. New call ar-rivals for the CZ and SHZ are represented by the transitions

. ��and

. �, respectively. Whether the current load of the target cell

is under the threshold or not is determined by the enabling func-tions for transitions

. ��and

. �. If the adjacent cells are not over-

36

dsλ

Q1

c

SHZ#

acλ

act

dst

#dsλ

#

dcλ

dct

tct

CZ

#

tλ

c

#

4t

#

eλ

# 1qt

#

#

1et eλ

eλ

2t

3t Q3

Q

1 qλhλht

1t

2et

3et

Q2

Q4

#

2qtdsλ

3qtdsλ

c

c

5t

c6t

T1

1-c 7t

cnλc

ntsnλs

nt

T2

c

1-c9t

8t

Fig. 5. An SRN model for a generic cell in a CDMA cellularnetwork with LA algorithms for CAC.

loaded, the new calls are accepted through immediate transitions���and

���, with probability � . Otherwise, the calls are blocked

through immediate transitions���

and���

, with probability ��� .Transition

��� represents the normal termination of a call while

it is in the CZ. A user can move from the CZ to the SHZ andvice versa while talking. These are depicted through transitions���

and���

. With regard to the other cell which covers the SHZ,transition

� � also represents a handoff arrival for that cell; while

transition� �

represents a handoff departure.While a user is in SHZ, three possibilities exist:� The user moves to the CZ of the cell being modeled; this is

represented by transition� �

.� The user moves to an ‘outside’ adjacent cell, with rate � �� .� The call is normally terminated, with rate � � . In Fig. 5, theselast two transitions are combined into one transition

� ��, with� ���� � ���� � � .

For a handoff arrival, represented by transition� �

, the call canbe accepted immediately through transition

���if the cell and its

neighborhood are not overloaded. If the effective load is overthe threshold and the queue is not full, the SHC can wait inthe queue. While waiting in the queue, a call will be droppedif a time out event occurs. The dashed rectangle in Fig. 5 de-scribes a queue with time out. The time out event is modeled bya three stage Erlang distribution [2], [24]. Transition

����, where�! #" �%$�&(' , represents a time delay in the queue. Before a user

reaches place )�* , the user can be accepted (from transitions�+�

to� * ) to SHZ whenever the effective load is under the threshold.In addition, the user may go to another cell or undergo a nor-mal call termination via transitions

� �, through��-, . Once the user

enters place ).* , the final step in checking the time out eventis carried out. If at that moment, the threshold conditions aresatisfied, the call is accepted to place SHZ from the immediatetransition

� * . Otherwise, the call is dropped through the imme-diate transition

��/. The loading effects of the adjacent cells are

reflected through probability � , which is associated with transi-tions

���through

� * . Because of the nature of the soft handoffcall, a denied SHC does not necessarily mean that it is dropped.We will discuss a dropped SHC in a later section.

Transitions���

,� �

,� �

,� ��

,����

, and���, have marking dependent

firing rates; that is, the actual firing rates for these transitions

35

dsλ

#

cnλc

ntsnλs

nt

SHZ

#

acλ

act

tct

dcλCZ

#

tλdst

#dsλ

dct

#

4t

#

eλ

# 1qt

#

#

1et eλ

eλ

2t

3t Q3

qλhλht

1t

2et

3et

Q2

Q4

#

2qtdsλ

3qtdsλ

5t

Q1

Fig. 6. An SRN model for a generic cell in a CDMA cellularnetwork with SD algorithms for CAC.

are proportional to the number of tokens in the respective inputplaces. In SRN, the marking dependent firing rate is representedby the sharp sign, #.

For comparison purposes, an SRN model of the SD algorithmis developed as well. It is shown in Fig. 6. The main differ-ence between the LA and the SD algorithms is that SD algo-rithm does not ‘look around’ to the neighbors before acceptingan NC/SHC. Therefore, compared with Fig. 5, immediate tran-sitions

� �through

���and the places 0 � and 021 are removed from

Fig. 6. In addition, because the CAC decision in the SD algo-rithm is based purely on the local information, the probability �is not associated with the immediate transitions

�3�through

� * .C. Fixed-point iteration

With different NC arrival rates, the following parameters varyaccordingly:4 5 : the total number of MSs in the CZ and the SHZ.� : the probability that the effective load (EL) of a cell is lessthan the threshold.� � : handoff arrival rate.

To capture this dynamic behavior, a fixed-point iterationscheme [14] is applied to determine the above parameters. Thevalues of these parameters are calculated as following:4 5 � 67�8:9<;>= " ?A@ 7 ' � = " BDCE@ 7 'GFIH3J 7 ;

4 5 $��($�� � F+$ (1)

� � 67�8:9LK 7 HMJ 7 ;4 5 $��($�� � F�$ (2)

� � � ;ON �� � N�, � N 1 , � N - , F<HP� ��� � � � �� � N � $ (3)

where Q is the set of tangible markings in the SRN models andJ 7 is the steady state probability of marking R . We use N todenote the throughput of a transition. For example, N �� is thethroughput of transition

� ��. In (2), the reward rate assignment

K 7 is of the following form:

� � � � � �if

����� %('�� � � ��� � '�� � � � � � ��� � � 1,

otherwise.(4)

In (4),�

represents the number of tokens in a place,�

rep-resents the maximum effective load allowed in a cell, and

1is

the number of soft guard channels. Fig. 7 shows the fixed-pointiteration algorithm we use for solving the SRN in Fig. 5 underhomogeneous traffic. According to Theorem 2 in [14], a fixedpoint will exist if :� The iteration function is a weighted sum of state probabilitiesand the weights are constants;� The CTMCs underlying the SRNs are irreducible with morethan one state.

It is easy to verify that the SRN models developed in thispaper satisfy the above two conditions. Therefore, fixed-pointsexist for (1), (2) and (3). The proofs for the uniqueness of thesolutions are under investigation.

/* initialization,��� ��� ,

4 � �� , � � ��� are initial values. */1.

� ��� ���� � � �����2.

4 ��� � � 4 � �� ;3.

� ��� �� � � � ��� ;

4. repeat5. solve the SRN in Fig. 5;

6. compute��������� ��

,4 ������� � and

� ������� ��according to (1), (2) and (3), respectively;

7. � �"! �������#� �� � �$��� ��%! * �$��� ��;

8. '& �"! 4 �����#� � � 4 ��� � ! *$4 ��� � ;9. '( �"! � ������� �� � � ��� �� ! * � ��� �� ;

10. � max( � , )& , ( );11. until +*-, ;

Fig. 7. A fixed-point iteration algorithm for the SRN in Fig. 5under homogeneous traffic.

D. Homogeneous traffic

In this section, we assume that all the cells are statisticallyidentical and behave independently. We also assume that thecellular system is undergoing homogeneous traffic. The charac-teristics of the overall system can be captured by focusing on asingle cell.

D.1 Enabling function

The NC and SHC arrivals are accepted only if the CAC con-ditions are satisfied. In SRN, this is achieved through enablingfunctions and the probabilities associated with the transitions.At transition

. ��, a new call is accepted under the following con-

ditions:�/.10 23547698;:=<>.10 ?A@93B47698�C#<ED)CGFIHKJL8�:M<ONBJGP . This condition isassociated with the enabling function of

. ��for both the LA and

the SD algorithms.� Maximum effective load in the adjacent (MELA) cells is lessthan the threshold. This condition is only required in the LA

algorithm. It is carried out through the probability4, which is

associated with transitions.7Q

,.SR

, and. � through

.UT.

The enabling functions for the LA algorithm are summarizedin Table I. The First-Come-First-Served (FCFS) policy is as-sumed for the queue. The queue length is denoted as

7��in the

table.

Transition Enabling FunctionVXWC .Y0 2354)6I8 : <7.10 ?A@93B4)6I8 C <ZD C FH[J\8;:�<SNJ[PV :C .Y0 2354)6I8;:;<7.10 ?A@93B4)6I8;CY<ZD)CKFH[J\8 : <^]�N_6�P7`V�a .Y0 2354)6I8 : <7.10 ?A@93B4)6I8 C <ZD C FH[J\8;:�bb�.Y]Xced�`Affhg5bb.L]Xci^`Affhg5bbj.Y]�ck^`AffhgV d .Y0 2354)6I8;:;<7.10 ?A@93B4)6I8;CY<ZD)CKFH[J\8;:�bb�.Y]Xci^`Affhg5bb.L]Xck^`AffhgV i .Y0 2354)6I8;:;<7.10 ?A@93B4)6I8;CY<ZD)CKFH[J\8 : bb�.Y]Xc k `AffhgV k .Y0 2354)6I8 : <7.10 ?A@93B4)6I8 C <ZD C FH[J\8;:VEl .L]Xc a `m6�.L]Xced�`m6�.L]Xci^`�n�o�pTABLE I

ENABLING FUNCTIONS FOR THE LA ALGORITHMS

D.2 Dropping probability

Under homogeneous traffic, we denote the dropping proba-bility for the LA and the SD algorithms as q �9�r and q �9 , respec-tively. They are obtained through the following equations:

q �9�r � ������4 � q T � �'s (ts � �qKuv � � 9� *xw�Ay

�� 9�

(5)

q �9 � ����� q T � �zs (ts � �qKuv � � 9� *xw� y � � 9� � �0��� 46� � q � (6)

where {}| f-~ WC 6 ~ :C 6 ~ l J[]EP;J{_� `}< ~ i� J ~ a� J ~ d� J ~ i�~ W C 6 ~ :C 6 ~ l �

In the above equations, q T is the probability that the enablingfunction for transition

. Tis enabled, qKuv is the probability that

the queue is full. There are two possibilities that a call can bedropped in the LA algorithm:1. The call is dropped after time out, represented by the firstterm of (5).2. The queue is full, and a SHC ‘insists’ on going to the targetcell. This is represented by the second term of (5).

For the SD algorithm, in addition to the above two factorsthat might cause a call to drop, a call might be dropped if thecell it resides in is full and one of its immediate neighboringcells accepts a call without ‘consulting’ this target cell. This isrepresented by the third term of (6).

D.3 Blocking probability

Under homogeneous traffic, the blocking probability for theLA and the SD algorithms is denoted as q �� r and q �� , respec-tively. They are calculated according to the following formulas:

q �� r � �0��� ��� � q � � �� � � q � � ��� �0��� 46� � s �� � s �� �� � � � (7)

q �� � �0��� ��� � q � � � q � � �� � � q � � � (8)

where q � � � and q � � respectively represents the probability thatthe new call is blocked at the CZ or SHZ , if the target cell isoverloaded. In the LA algorithm, an NC can still be blocked ifthe target cell is not overloaded but one of its adjacent cells hasreached its loading threshold. This is represented by the thirdterm of (7). In the SD algorithm, if the NC is blocked at one cellwhich covers the SHZ, it still has a second chance in another cellthat covers the SHZ. This is the reason why q � � is used twicein (8).

E. Hot spot (non-homogeneous) traffic

In this section, we assume that the traffic load is non-homogeneous. Specifically, we assume that Cell

in Fig. 4 is

a hot spot. The traffic load for that cell is always higher thanthat of its adjacent cells. We apply a decomposition approach tomodel the system behavior under non-homogeneous traffic. Thecluster of cells as shown in Fig. 4 is decomposed into two SRNs,%

and% � . SRN

% describes the behaviors of the MSs in Cell

. SRN% � describes the behaviors of the MSs in cells

�tow.

We also assume that the traffic loads in the boundary cells�

to���are similar to those in cells

�tow.

E.1 Dropping probability

For non-homogeneous traffic, the dropping probabilities forthe LA and the SD algorithms in

% and

% � are denoted andcalculated as following:

q � �9�r � ��� � 4 � � q T � �zs (ts � �

qKuv � � 9� *xw�Ay�

� 9�

q � �9 � ��� � q�� � �)s (ts � �

qKuv � � 9� * w� y � � 9� � ��� ��4 � � q �X� q � �9�r � � ��� � 4 � � � q T � �)s (ts � �

qKuv � � 9� * w�My�

� 9�

q � �9 � � ��� � q�� � �)s (ts � �

qKuv � � 9� * w� y � � 9�� ������4 � � � � q ��� ��� * w � q � � � * w ��

The probabilities that Cell

and the adjacent cells are not over-loaded are respectively represented by

4 and

4 � . The parame-ters q ��� and q � are calculated in the same way as q � in the pre-vious section. Their numerical values are calculated from theSRN

% � and SRN%

, respectively. The weighted probability4 � � is calculated through4 � � � 4 * w �� � 4 � * w .

E.2 Blocking probability

The blocking probabilities for the LA and the SD algorithmsin

% and

% � are respectively denoted and calculated as follow-

ing:

q � �� r � �0� � ��� � q � � � � � q � � � � �0��� 4 � � � s �� � s �� �� � � �

q � �� � �0� � ��� � q � � � q � � � � � q � � � q � �� r � � �0� � ��� � q � � � � � q � � � � �0��� 4 � � � � s �� � s �� �� � � �

q � �� � � �0� � ��� � q � � � q � � � � � q � � � �E.3 Average dropping/blocking probability

To get an overall picture of the performance for a cluster ofseven cells (cells

tow

in Fig. 4), an average dropping/blockingprobability for the LA algorithm is calculated as following:q � �

9�r ��� q � �9�r � w � q � �

9�r � �+* � q � �� r � � q � �� r � w � q � �� r � �+* � �An average dropping/blocking probability for the SD algo-

rithm can be obtained in a similar manner.

V. NUMERICAL RESULTS AND DISCUSSION

For the purpose of discussion, we make the following as-sumptions. The load threshold for a single cell is set to be � � .According to [23], � �

and � � � � � . We set the queue

length to be � and the number of soft guard channels (1

) is setequal to

�. The ratio of the CZ area over the SHZ area is

�.

The average inter-call time is assumed to be � minutes. The celldwelling time is assumed to be exponentially distributed and itsmean is set to be � minutes. The time out period is set to be�

minute. Table II shows the state space for the SRN modelspresented in this paper.

Models No. of No. ofAlgorithm Traffic Tangible Nonzero

Markings Transitions

LAHomogeneous 1281 7240

Non-homogeneous 3332 18960

SDHomogeneous 1230 6944

Non-homogeneous 3332 18960

TABLE II

STATE SPACE FOR THE SRN MODELS

Because it considers the traffic loads in both the target celland the neighboring cells, the LA algorithm would block somenew calls which would otherwise be accepted in the SD algo-rithm. As a result, compared with the SD algorithm, the LAalgorithm reduces the dropped calls at the expense of increasingthe blocked calls. To evaluate the tradeoff between the droppedand blocked calls, we introduce two metrics, increased droppingratio (

� 9 ) and increased blocking ratio (� � ), which are defined

as following:

� 9 � q ���9 � q����9q ���9 � � � q����� � q ����q ����where q����9 and q����9 are dropping probabilities for the SD andthe LA algorithms, respectively; q����� and q ���� represent theblocking probability for the SD and the LA algorithms, respec-tively.

20 22 24 26 28 30 320

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Dro

ppin

g pr

obab

ility

Traffic load (Erlangs/cell)

LA algorithmSD algorithm

Fig. 8. Dropping probability under homogeneous traffic.

20 22 24 26 28 30 320

0.05

0.1

0.15

0.2

0.25

Blo

ckin

g pr

obab

ility

Traffic load (Erlangs/cell)

LA algorithmSD algorithm

Fig. 9. Blocking probability under homogeneous traffic.

A. Homogeneous scenario

In Fig. 8, the dropping probabilities for different NC arrivalloads under homogeneous traffic are shown. Compared withthe SD algorithm, the LA algorithm can nearly eliminate thedropped calls. However, we do need to pay a price: an increasedblocking probability for the LA algorithm as shown in Fig. 9.

Traffic Load in ErlangsRatio 20 22 24 26 28 30 32

��� ( � PZg d ) 2.4 1.9 1.7 1.7 1.7 1.6 1.6��� 1.2 1.2 1.2 1.2 1.0 0.9 0.8

TABLE III

INCREASED DROPPING/BLOCKING RATIOS UNDER HOMOGENEOUS TRAFFIC

B. Hot spot (non-homogeneous) scenario

Next we assume that the traffic loads in Cell

(a hot spot) is� �� percent higher than that of its adjacent cells. Figs. 10 and11 show that the LA algorithm nearly eliminates the droppedcalls in both the hot spot and its adjacent cells.

Figs. 12 and 13 show that the LA algorithm increases

21 24 27 30 33 36 390

0.05

0.1

0.15

Dro

ppin

g pr

obab

ility

in th

e ho

t spo

t

Traffic load (Erlangs/cell)

LA algorithmSD algorithm

Fig. 10. Dropping probability in the hot spot.

14 16 18 20 22 24 260

0.005

0.01

0.015

0.02

0.025

0.03

Dro

ppin

g pr

obab

ility

in th

e no

n−ho

t spo

t

Traffic load (Erlangs/cell)

LA algorithmSD algorithm

Fig. 11. Dropping probability in the non-hot spot.

21 24 27 30 33 36 390

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Blo

ckin

g pr

obab

ility

in th

e ho

t spo

t

Traffic load (Erlangs/cell)

LA algorithmSD algorithm

Fig. 12. Blocking probability in the hot spot.

14 16 18 20 22 24 260

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1B

lock

ing

prob

abili

ty in

the

non−

hot s

pot

Traffic load (Erlangs/cell)

LA algorithmSD algorithm

Fig. 13. Blocking probability in the non-hot spot.

21/14 24/16 27/18 30/20 33/22 36/24 39/260

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

Ave

rage

dro

ppin

g pr

obab

ility

Traffic load (hot spot/non−hot spot, Erlangs per. cell)

LA algorithmSD algorithm

Fig. 14. Average dropping probability under non-homogeneoustraffic.

21/14 24/16 27/18 30/20 33/22 36/24 39/260

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Ave

rage

blo

ckin

g pr

obab

ility

Traffic load (hot spot/non−hot spot, Erlangs per. cell)

LA algorithmSD algorithm

Fig. 15. Average blocking probability under non-homogeneoustraffic.

Traffic Load in ErlangsRatio 21 24 27 30 33 36 39

��� ( � PZg d ) 3.4 4.1 2.4 2.1 1.8 1.7 1.6��� 1.0 0.9 0.9 0.8 0.7 0.6 0.5

TABLE IV

INCREASED DROPPING/BLOCKING RATIOS FOR THE HOT-SPOT UNDER

NON-HOMOGENEOUS TRAFFIC

Traffic Load in ErlangsRatio 14 16 18 20 22 24 26

� � ( � PZg d ) 8.3 15.3 1.9 1.1 1.8 1.9 1.6� � 82 17 8.5 3.0 2.5 1.6 1.4

TABLE V

INCREASED DROPPING/BLOCKING RATIOS FOR THE NON-HOT SPOT UNDER

NON-HOMOGENEOUS TRAFFIC

the blocking probability vs. the SD algorithm under non-homogeneous traffic. For the average dropping/blocking prob-abilities, which are shown in Figs. 14 and 15, we get the sameconclusion as above.

Under homogeneous and non-homogeneous traffics, the in-creased dropping ratio (

� 9 ) for the SD algorithm and the in-creased blocking ratio (

� � ) for the LA algorithm are shown inTables III to V. From the data shown in Tables III and IV, weobserve that the LA algorithm can decrease the dropping prob-ability significantly while increasing the blocking probability ata relatively slow rate for homogeneous traffic and the hot-spotunder non-homogeneous traffic. For the non-hot spots undernon-homogeneous traffic (as shown in Table V), when the trafficis low (below

�zwErlangs), the LA algorithm reduces the drop-

ping probability and increases the blocking probability at nearlythe same pace. For these traffic loads, since the traffic is light,the QoS can be guaranteed by using either the LA or the SDalgorithm. When the traffic load is over

�zwErlangs, the LA al-

gorithm can reduce the dropping probability significantly whileincreasing the blocking probability at a fairly small rate for thenon-hot spots under non-homogeneous traffic.

VI. CONCLUSION

In this paper, call admission control algorithms (the LA algo-rithms) with emphasis in reducing dropped calls are proposed.To give priority to soft handoff calls, we introduce the idea of‘soft guard channels’. SRN models are developed to analyze theperformance of our algorithms.

The numerical results show that the LA algorithm can reducethe dropped calls to nearly zero. This is achieved by denyingsome of the new call arrivals. Consequently, the blocking prob-ability in the LA algorithm is increased. Because of the capacityof the CDMA system is interference limited, when a new call iscoming, we should base our admission decision on the loads ofboth the local and the adjacent cells. The conventional CACmethods only consider the local effect. Therefore their blockingprobabilities are lower than the ones obtained from our algo-rithm. The drawback of the conventional methods is that they

might cause dropped calls (or outage) in its adjacent cells whenthey have reached their saturate points.

Generally, there is a tradeoff between blocking probabilityand dropping probability. Our algorithm might be a good can-didate for a system that requires a low dropping probability. Tojustify the gain we obtain through using the LA algorithm, twonew metrics (increased dropping ratio and increased blockingratio) are introduced. By using the LA algorithm, it is possibleto reduce the dropped calls significantly by paying the price ofincreasing the blocking probability slowly.

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