admission control for wireless multimedia networks with hard call level quality of service bounds

Ž .Computer Networks 31 1999 125–140

Admission control for wireless multimedia networks with hardcall level quality of service bounds

Jelena Misic ), Samuel T. Chanson 1, Frederick S. Lai 2ˇ ´Department of Computer Science, Hong Kong UniÕersity of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, PR China

Abstract

In this paper, a new adaptive admission control scheme for wireless cellular network supporting mixed narrowband andwideband traffic is proposed. The scheme is event-based and provides hard constraints on hand-off dropping probability

Ž .requirements. The role of the quality of service QoS regulation parameter P in the call admission process is analyzed andoÕ

presented. The analytic results are validated by simulation. We also show that the analytic model is extensible to more thantwo types of traffic. q 1999 Elsevier Science B.V. All rights reserved.

Keywords: Wireless cellular networks; Call admission control; Quality-of-service

1. Introduction

Cellular wireless networks are widely used today to carry voice and text information. More and more, usersare demanding to transmit images, videos and other multimedia data simultaneously. Therefore, there is a need

Ž .to provide quality of service QoS that satisfies the requirements of different types of traffic in cellular wirelessnetworks. In this paper, we present a new admission control scheme with QoS guarantees for both wideband andnarrowband traffic. The performance characteristics of the scheme are studied using analytic models which areverified by simulation results.

The call level QoS of cellular wireless networks are often measured in terms of the new call blockingprobability and the hand-off dropping probability 3. The former is the probability that a new call cannot getthrough due to lack of bandwidth. That latter is the probability that when a caller crosses cell boundary the newcell does not have sufficient bandwidth to allow the call to continue.

ŽDifferent types of traffic with different call characteristics including bandwidth requirements, distributions.of call duration and dwell time, and the directional properties of the mobile user will impose different QoS

) Corresponding author. E-mail: [email protected] E-mail: [email protected] E-mail: [email protected] Some writers use forced call termination probability instead of hand-off dropping probability which is the probability of call termination

w xdue to an unsuccessful hand-off during its life-time 1,4,5 .

1389-1286r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved.Ž .PII: S0169-7552 98 00235-9

( )J. Misic et al.rComputer Networks 31 1999 125–140ˇ ´126

requirements within the network. Regulation techniques which will provide reliable QoS guarantees for alltraffic types are needed to ensure user satisfaction.

Admission control prevents congestion by limiting the admission of new calls in order to provide the QoSŽrequired by the existing connections. The objective is to maintain the sum of loads in a cell due to both new

.calls and hand-off calls to below some predetermined congestion level. Some aspects of admission control andŽ .QoS in wireless networks with Fixed Channel Allocation FCA have been studied in the literature. Admission

Ž .control for real-time connections having the same homogeneous bandwidth requirements which does not adaptw x w xto changes in hand-off and new input traffic has been studied in 13 for single cell environments and in 1,2 for

cell cluster environments. Adaptive admission control polices for homogeneous calls based on short-termw xestimation of hand-off load are discussed in 3,4,10 .

w xNon-adaptive resource allocation for mixed wideband and narrowband calls is considered in 6 . However, tothe best of our knowledge, no work has been reported on QoS management of heterogeneous calls in adaptiveadmission control schemes. One of the reasons for the lack of results for heterogeneous traffic is that exactmathematical modeling requires multidimensional Markov chains. Computing the bounds for the hand-offdropping probabilities and tuning them to give satisfactory QoS for narrowband and wideband calls in a giventraffic mix is a challenging task.

w xRecently, we have proposed an adaptive admission control with event-based hand-off load estimation 12 .The events which trigger the calculation of resources are hand-off, origination, and termination of calls in theneighborhood of the target cell instead of short regular time periods. The event based updating scheme requiresless computation overhead while producing comparable QoS performance than schemes that do regular periodicestimation of hand-off resources.

Under this scheme, the admission control algorithm is executed by the base station in the originating cell aswell as by the base stations in a group of surrounding cells in a distributed fashion. To admit a new call theremust be enough bandwidth in the originating cell and enough bandwidth must be reserved in the surroundingcells to meet the predicted future bandwidth requirements of the call. The amount of reserved bandwidth is

Ž .determined using the ‘‘spatial activity factor’’ SAF of the call, which is the probability that the mobile willvisit the target cell during the call’s lifetime.

In this paper we propose an approximate technique which allows quick derivation of the QoS controlparameter for heterogeneous calls in an event-based adaptive admission strategy. Moreover, the properties of theQoS regulation are discussed. This allows the network administrator to choose the appropriate value of theregulation parameter for a particular narrowbandrwideband traffic mix to optimize performance.

The rest of the paper is organized as follows. In Section 2 the expression for overload probability is derivedand an admission algorithm is proposed. Performance analysis for wideband traffic is discussed in Section 3.Section 4 presents the simulation results, and Section 5 concludes the paper. The derivation of spatial activityfactors is given in the Appendix.

2. Admission control strategy based on SAFs

Consider a wireless cellular system with J types of traffic and that the call duration and dwell time of the jthtraffic type are exponentially distributed with parameters m and h respectively. Assume that cells are arrangedj j

as shown in Fig. 1.Ž .Let the joint probability P i,k to be the probability that a mobile call of type j will visit a cell in the ithjŽ Ž . .ring after its ky1 hand-offs a detailed treatment of P i,k can be found in Appendix A . Define then thej

K Ž .lifetime ‘‘spatial activity factor’’ for ring i to be b sÝ P i,k which is the probability for a call of type ji, j ks1 jŽ .to visit ring i in its lifetime K being the number of hops included in the SAF calculation . The lifetime spatial

Ž . Ž .activity factor for a particular cell in ring i is a sb rmax 1,6 i . The partial spatial activity factor PSAF fori, j i, j

traffic type j, bÕ , denotes the probability of visiting ring i after Õ cells have already been visited, ori, jÕ K Ž . Õ Õ Ž .b sÝ P i,k . The PSAF for a cell in ring i is a sb rmax 1,6 i .i, j ksÕq1 j i, j i, j

( )J. Misic et al.rComputer Networks 31 1999 125–140ˇ ´ 127

Fig. 1. Representation of hexagonal cellular network.

Let traffic type j consume a portion of the total bandwidth equal to a . The value of a can be determined asj jy1 Žk rN where k is an integer and N is the normalized bandwidth for narrowband channels in the cell itj j

w x.corresponds to the Basic Bandwidth Unit in 6 . In packet switched wireless networks, a can also bejw xdetermined using the concept of equiÕalent bandwidth 8,9 applied to packet level QoS requirements such as

w xdownstream packet delay 11 .

2.1. PGF for the load in a cell

Ž .In this section we shall briefly describe the modeling of the load in cell 0,0 using the load information fromŽ w x.cells in the I surrounding rings a more detailed analysis can be found in 12 . Using SAF as an estimate for

predicting future hand-off load the A connections of traffic type j established in the cells from ring i willi, jŽ .generate the binomial predicted hand-off traffic load distribution in cell 0,0 with probability generating

Ž .function PGF :A i , ja jh x s a x q 1ya ,Ž . Ž .Ž .i , j i , j i , j

Ž .where a is the probability that a type j call established in ring i will visit cell 0,0 during its lifetime. Fori, jw xlarge A and small a , the predicted hand-off load distribution converges to a Poisson distribution 7 . Byi, j i, j

convolving the predicted hand-off loads over the I surrounding rings, and for J traffic types, the PGF of thepredicted hand-off load becomes:

JJ a jÝ n Ž x y1.js 1 jh x s h x se ,Ž . Ž .Ł j

js1

where n sÝI A a denotes the reserved average rate of hand-off events for type j traffic.j is0 i, j i, jŽ . Ž . Ý js 1

J A0, j a jThe active load in cell 0,0 has a PGF equal to l x sx , where A denotes the number of type j0, jŽ .connections which are currently active in cell 0,0 .

The probability distribution for the total load in the cell is the convolution of the probability distributions forthe active load and reserved hand-off load. The PGF for the total load in the cell is therefore:

` ` q q q1 j Jn . . . n . . . nJ a J J J1 j JjÝ A a Ý n Ž x y1. yÝ n Ý A a qÝ q aj 0 , j j js1 j js1 j js1 0 , j j js1 j jL x sx e se . . . Px . 1Ž . Ž .Ý Ýq ! . . . q ! . . . q !1 j Jq s0 q s01 J

Since the normalized cell capacity is 1, the cell is overloaded when the cell load is greater than 1, i.e.,ÝJ A a qÝJ q a )1. The overload probability is given by:js1 0, j j js1 j j

Ž .2


2.2. Admission algorithm based on Po Õ

The overload probability depends on the portion of target cell capacity occupied by the current activeŽ J .connections Ý A a and on the predicted hand-off load given by the predicted hand-off rate for trafficjs1 0, j j

Ž . Ž .type j n and its bandwidth requirements a . The predicted hand-off rate for a particular traffic type isj j

calculated as a sum of products of the number of connections within each surrounding cell and thecorresponding SAF. Calls with high ratio of call duration time to dwell time will have large SAFs and larger

Ž .portions of bandwidth should be reserved for their hand-offs. Wideband calls e.g. image transfer have shorterŽ .durations i.e. small SAF-s , but they may require non-negligible reserved bandwidth in the neighboring cells.

The region of influence of the connection to the neighboring cells used for calculating n can be set tojŽ .Ss1,2,3, . . . , Iy1 rings. We shall illustrate the algorithm using cell 0,0 . Note that due to symmetry of the

Ž .hexagonal network Fig. 1 any other cell can be considered. The main steps of this algorithm are:Ž1. Variables A and n are initialized to zero. The values of a are known for a given traffic type with0, j j i, j

.known m and h .Ž . Ž .2. When a new type j call arrives, the overload probability has to be calculated using Eq. 2 in cell 0,0 and in

the surrounding cells.Ž . Ž .P checking in cell 0,0 : A is incremented by one and the overload probability P 0,0 is recalculatedo Õ 0, j o Õ

with the new value of A . If the updated value is larger than the predetermined limit, the new call is0, j

blocked.Ž . Ž . Ž .P checking in surrounding cells: In each cell i,l , 0- iFS , 0- l-6 iy1 , the value of local n iso Õ j

incremented by a and the overload probability is recalculated. If the overload probability bound in anyi, j

surrounding cell within S rings is violated, the new call must be blocked.Ž .3. The calls which are admitted in cell 0,0 can freely hand-off to neighboring cells without invoking the call

admission algorithm again. The hand-off call is dropped only when there is insufficient bandwidth forŽ . Ž .serving the call. However, the values of SAFs PSAFs must be updated decreased after each hand-off in

order to accurately reflect the call’s bandwidth demand. In particular, when a type j call hands-off from cellŽ . Ž .0,0 to a neighbor cell 1,l in ring 1 and given that there is available bandwidth in the cell for the call, thefollowing actions must be performed:

Ž . Ž .Update load in cell 1,l : A 1,l is incremented by one, n is decremented by the value of activity factor0, j j

a .1, jŽ . Ž .Update load in neighborhood of cells 0,0 and 1,l :

Ž .3.1. The new values of PSAFs are distributed to the S rings surrounding cell 1,l to which the hand-offoccurred and the corresponding values of n are updated.j

Ž . Ž .3.2. The cells within the S rings of cell 0,0 which was hosting the call before the hand-off but which donot belong to the S-ring neighborhood of the cell currently hosting the call should delete their SAF-sŽ . 4PSAF-s using the time-out mechanism .

4. When a call terminates, all corresponding PSAFs in the neighboring cells are deleted and A in the hosting0, j

cell is decremented by one.

3. Performance analysis for multiple types of traffic

In this section we shall derive performance bounds for two types of traffic, narrowband and wideband in acomplete capacity sharing environment. The extension to more traffic types is straightforward. Narrowband

4 The time-out value T can be calculated from the condition that the probability of residence time larger than T is smaller than a giveno o

bound e . For example, for exponentially distributed residence time, the probability that the call has executed hand-off after T s3rh iso

95%.


Ž . Ž .traffic type 1 is characterized by parameters l ,h ,m ,a s1rN, B while wideband traffic type 2 is1 1 1 1 1

characterized by parameters l ,h ,m ,a skrN, B . In the text that follows, when deriving performance2 2 2 2 2

parameters which are common to both traffic types we shall use the appropriate symbols without indices.The purpose of the following performance analysis is to illustrate the regulatory property of the overload

Ž .probability parameter P . Since the initial statistical bandwidth reservation for hand-off events with P s0o Õ o Õ

is done based on lifetime call properties, the reserved bandwidth is adequate and leads to very low hand-offw xdropping probability. However, by tuning P in the range 0,1 , the reserved bandwidth can be decreased to ao Õ

level which just satisfies the required hand-off dropping probability while keeping the cell utilization at thehighest possible level.

3.1. ReserÕation rate n

Ž .In order to estimate the parameter n we shall concentrate on the S rings surrounding cell 0,0 . Every cellhas rN active connections, or, the utilization of any cell is r. When a mobile terminal enters a cell spatial

Ž .activity factors are distributed to the S surrounding rings. When a the terminal leaves the cell, these P SAFs areŽ .clearedrreplaced by new ones which reflect the new position of the mobile and the new status stage of the

Ž .connection. A call or connection is in stage 0 if it is new, in stage 1 if it has executed one hand-off and so on.If we assume equal traffic intensity in all cells, then all cells will have the same number n of connections ink

Ž . ` S kstage k. Therefore, the central cell 0,0 will receive the sum of nsÝ n Ý b activity factors whichks0 k ds1 dqk

constitute the reservation rate. However, for the reasons of uniform traffic and symmetry, connections from theŽ .central cell 0,0 will send out the same sum of activity factors. By dividing this sum by the number of

connections within the cell, we get` Sn

kBs s Ps b , 3Ž .Ý Ýk dqkNr ks0 ds1

Ž . Ž .Ž Ž ..kwhere Ps sn r Nr smr mqh hr mqh denotes the probability that a randomly picked connection isk kŽ .in stage k of its lifetime. Therefore B denotes the average sum of SAF-s or PSAF-s which will be received per

Ž . Ž .connection in cell 0,0 , or which will be distributed by an active connection in cell 0,0 to cells in the Ssurrounding rings.

3.2. P tuning for single type of traffico Õ

The overload probability is defined in Section 2 as the probability that the sum of channels occupied by theactive calls and the reserved channels exceeds the capacity of a cell. In practice when an overload event occurs,the new call will start to ‘‘borrow’’ bandwidth reserved for future hand-off calls. Thus, the overload probabilitycan be viewed as the probability that the reserved channels are being borrowed by new calls. Therefore,considering the PGF of the reserved load only, P can be expressed by:o Õ

` qnn 1

yn yx NŽ1yr .P se s e x d x . 4Ž .Ý Ho Õ q! G N 1yrŽ .Ž . 0u Ž .vqs N 1yr

Let l be the new call arrival rate and L be the total admitted arrival rate in the cell. Furthermore, let P beB

the new call blocking probability and P be the hand-off dropping probability. The cell capacity is N channels.hd

Then,h

Lsl 1yP qL 1yP , andŽ . Ž .B hdhqm

Lrs . 5Ž .

N mqhŽ .Ž . Ž .The value of nsrNB can therefore be written as nsl 1yP PBr mqhP .B hd


Ž .Fig. 2. Markov chain for single type of traffic where dshqm .

Since we are considering practical systems where the hand-off dropping probability for narrowband trafficcannot exceed 10y3, the product hP is very small compared to realistic values of m and n can be simplifiedhd

Ž . Ž .to nfl 1yP Brm. Therefore, for a given value of P , the value of n can be found from Eq. 4 and theB o Õ

channel utilization can be determined as:n

rs . 6Ž .NB

Ž .The clipping utilization of the system for a particular input rate l is r sn r NB .max max

3.3. MarkoÕian analysis of a single cell

The Markov chain that represents our system for a single type of traffic is given in Fig. 2. The states in thechain refer to the number of ongoing calls in the target cell, while the surrounding cells are assumed to operateat the average utilization of the given load. The value Msr N is the maximum number of utilized channelsmax

allowed for all input rate l under our admission control policy for a given P threshold. This r can beo Õ maxŽ .found from Eq. 6 by using the P threshold determined by the network administrator. Note that M is also theo Õ

state where the system is operating at the P threshold and no more new calls are admitted. l is the hand-offo Õ h

call arrival rate before the admission algorithm starts to stop new calls from joining the system and is equal tol Ž .the average utilization multiplied by the hand-off rate, 1yP h. Beyond state M, only hand-off calls areBm

accepted. The probabilities of blocking and dropping for this system are therefore given by:

M iyMNlql 1 lh hÝž / ž /mqh i! mqhisMP l,m ,h , M , N s , 7Ž . Ž .B i M iyMM N1 lql lql 1 lh h hqÝ Ýž / ž / ž /i! mqh mqh i! mqhis0 isMq1

M Nym1 lql lh hž / ž /N ! mqh mqhP l,m ,h , M , N s . 8Ž . Ž .hd i M iyMM N1 lql lql 1 lh h h

qÝ Ýž / ž / ž /i! mqh mqh i! mqhis0 isMq1

lŽ . Ž Ž . .Notice that as l in the right-hand side of Eq. 7 is a function of P l s 1yP h , iterative solving ish B h Bm

Ž .required for the solution of P . The solution of P follows immediately from the solution of P and Eq. 8 .B hd B

3.4. Performance tuning property of P under multiple types of traffico Õ

Instead of using a two-dimensional Markov chain, we shall use approximate analysis to compute theapproximate QoS bounds and the related P value quickly.o Õ


Ž .The total admission rates i.e., traffic admitted and the corresponding cell utilizations for narrowband andwideband traffic are given by the following set of expressions:

h1L sl 1yP qL 1yP ,Ž . Ž .1 1 B1 1 hd1h qm1 1

h2L sl 1yP qL 1yP ,Ž . Ž .2 2 B 2 2 hd2h qm2 2

L k L1 1r s , r s . 9Ž .1 2N h qm N h qmŽ . Ž .1 1 2 2

Therefore, the reservation rates n and n are given by:1 2

B B1 2n sl 1yP , and n sl 1yP , 10Ž . Ž . Ž .1 1 B1 2 2 B 2

m qh P m qh P1 1 hd1 2 2 hd2

and the number of utilized channels is:

r Ns r qr Nsn rB qkn rB . 11Ž . Ž .t o t 1 2 1 1 2 2

By considering the number of reserved channels as done in Section 3.2, the cell capacity overload probabilitycan be written as

? @ q Žqyk q .qrk` 2 2n n2 1yŽn qn .1 2P se . 12Ž .Ý Ýo Õ q ! qykq !Ž .2 2u Ž .v q s0qs N 1yr 2t o t

Furthermore, if the ratio of the two input traffic rates is denoted as ksl rl , and the ratio of the new call1 2Ž . Ž .admission probabilities is given by hs 1yP r 1yP , the ratio n rn can be determined as:B1 B 2 1 2

m qh P BŽ .2 2 hd2 1K sn rn skh . 13Ž .r 1 2

m qh P BŽ .1 1 hd1 2

The most important problem in performance evaluation for two traffic types is to determine the values of n 1

and n , i.e., the calculation of the maximum utilizations r Nsn rB and r Nsn krB for each traffic type2 1 1 1 2 2 2Ž . Ž .for a given input load. This is difficult to do since there are two unknowns n and n in Eq. 12 . When the1 2

values of n and n are known, approximate QoS parameters can be easily determined.1 2

Fortunately, qualitative analysis of the system behavior is possible even without explicitly calculating n and1

n . Let us examine the changes in overload probability when the ratio K varies. Again, we consider a system2 r

with hard constraints on the hand-off dropping probabilities for both types of traffic, e.g., 10y3 for narrowbandtraffic and 10y2 for wideband traffic. Therefore, the impact of the hand-off dropping probability for wideband

Ž .traffic cannot be neglected and we use the approximate formula P fE r Nrk, Nrk .hd2 t o tŽ .Assuming k is constant, the major parameter in Eq. 13 which changes with increase in input load

Ž . Ž . Ž .utilization is hs 1yP r 1yP . For small input loads, hf1. However as the input load grows,B1 B 2

wideband traffic will experience higher blocking probability than the narrowband traffic and h will increase.ŽFor a given cell capacity and wideband traffic bandwidth requirement k we shall assume ks5 in our

.calculations , the overload probability depends on the ratio h and also on the current number of utilizedŽ .channels in the cell i.e. on the load as shown in Fig. 3.

We note that a constant value of P cannot give the exact limit on cell utilization like in the case of singleo ÕŽtype of traffic. This limit changes with increase in the offered load. Knowing that for constant k , hs 1y

. Ž .P r 1yP grows with increase in input load, we see that for a given P threshold, the operating pointB1 B 2 o Õw xr N,h moves across the curves according to the value of h. Therefore a single threshold value P offers at o t o Õ


Fig. 3. Overload probability as function of the number of utilized channels in the cell, i.e. r Nsn rB q kn rB , with ks5,t o t 1 1 2 2Ž .h s h s0.01, m s0.002, m s0.005 and Ns50. The dotted line is P curve for system with narrowband traffic only.1 2 1 2 o Õ

range of utilization values corresponding to different values of the input load. In order to choose a single valueof maximum utilization for a given P , we shall use the overload probability curve for h™`, i.e., the case foro Õ

Ž .narrowband traffic only. Then, for a given value of P we can determine n P , N, B and the maximumo Õ o Õ 1Ž .utilization for narrowband traffic Msn P , N, B rB . Knowing the value M and the input traffic intensities,o Õ 1 1

we can determine the actual utilizations for both traffic types as will be shown in the next subsection.Ž . ŽNote also that for small threshold values P -0.5 , the impact of hand-off dropping is small see also theo Õ

.simulation results from Section 4 and the number of utilized channels is mainly determined by the new callblocking probability. In this case, as the offered load increases, the ratio h increases and so does and maximum

Ž .utilization at the threshold value of P . For large threshold values P )0.5 the rate of increase of theo Õ o Õ

maximum utilization slows down due to hand-off dropping.

3.5. Blocking, hand-off dropping probabilities and utilization

In a system with narrowband traffic only, the chosen P threshold value limits the maximum number ofo Õ

utilized channels in a cell to Msr N dependent of the input rate l. Now, for a system with two types ofmax

traffic, in which the ratio of the input rates ksl rl is fixed, we shall assume the maximum number of1 2Ž .utilized channels by narrowband and wideband traffic under the same k and P threshold to be M sr No Õ 1 1,max

and M sr N respectively, where r and r are maximum utilization of the two traffic types given2 2,max 1,max 2,max

by the algorithm.Ž .Let msrN be the average number of utilized channels in a cell for a system with narrowband calls only

and m sr N and m sr N be the average number of utilized channels by narrowband and wideband traffic1 1 2 2Ž .for particular input rates l and l in the 2-traffic environment respectively. Note that for a particular P1 2 o Õ

threshold and a fixed k , the maximum values for m, m and m are M, M and M respectively.1 2 1 2

Complete performance analysis of the 2-traffic system could be done using a 2-D Markov chain with aboutŽ .250 balance equations for a cell with 50 channels and for ks5 . For more types of traffic, the corresponding

Markov analysis will become very tedious and time consuming. Therefore, we use an approximate analysiswhich decouples the system into different subsystems where different traffic types are analyzed separately. Inparticular, the narrowband and wideband traffic could be analyzed separately using the Markov chains depictedin Figs. 4 and 5. Again the states in the chains represent the number of calls in the two subsystems modeling thenarrowband and the wideband traffic respectively.


Fig. 4. Markov chain for narrowband traffic.

Note that the two states in the two chains in which P regulation starts to occur are Mym ando Õ 2?Ž . @Mym rk respectively. l and l are the hand-off call arrival rates of the system and are simply the1 h1 h2

Ž . Ž .average utilization multiplied by the hand-off rate, l 1yP h rm and l 1yP h rm , respectively. We1 B1 1 1 2 B 2 2 2Ž .shall assume that hand-off calls from the two traffic types will have exclusive use of all the NyM channels

Ž .reserved for the hand-off events Figs. 4 and 5 . One should note that the capacities left for hand-off calls forboth types of traffic when the P threshold is reached are in fact coupled and both types of traffic can competeo Õ

for any of these channels. However, since the hand-off dropping probabilities are very small due to theadmission control mechanism, the chances of reaching a state in any of the chains where there is no more roomfor a hand-off call will be small and hence the coupling of the chains is ignored.

3.5.1. Hand-off dropping probabilitiesŽ .Following our solution of the Markov chain for one type of traffic Eq. 8 , the hand-off dropping

probabilities for the two traffic types can be represented with the following expressions:

P sP l ,m ,h , Mym , Nym , andŽ .hd1 hd 1 1 1 2 2

Mym Nym1 1P sP l ,m ,h , , . 14Ž .hd2 hd 2 2 2ž /k k

Note that m and m for a particular input l must be known in order for P and P to be solved from the1 2 hd1 hd2

above equation. The way to obtain them are given in the next subsection.

3.5.2. Blocking probabilities and utilizationŽ . Ž .Blocking probabilities of the two types of traffic or the two chains can be computed using Eq. 7 . In this

section, we shall present a simpler method in which the utilizations and blocking probabilities of the system canbe solved at the same time.

Fig. 5. Markov chain for wideband traffic.


According to the hexagonal cell geometry and the properties of the admission algorithm, the blockingprobabilities for the two traffic types are given by:

S6 iP s1y 1yP 1yP P , andŽ . Ž .ŁB1 B1,h B1, i B 2, i

is1

S6 iP s1y 1yP 1yP P , 15Ž . Ž . Ž .ŁB 2 B 2,h B 2, i B1, i

is1

Ž . Ž Ž Ž .. Ž . .where P sE l rm , Mym and P sE l r k m qh P , Mym rk denote the probabilitiesB1,h 1 1 2 B 2,h 1 2 2 hd2 1Ž . Ž Ž .that a new narrowband wideband call will be blocked in the hosting cell note that E m,n s

Ž n . n i . Ž . Ž Žm rn! rÝ m ri! is the Erlang’s loss formula . Similarly, P sE m , Mym and P sE m rk, Mis0 B1, i 1 2 B 2, i 2. .ym rk denote the probabilities that new calls will be blocked because one of the surrounding cells is already1

operating at the maximum utilization for a given traffic type already.Then, assuming equal traffic intensities in all the cells, the relationship between the average number of

utilized channels of the two traffic, m and m , is given by:1 2

Sl1 6 im s 1yP 1yP P , andŽ . Ž .Ł1 B1,h B1, i B 2, im qh P is11 2 hd1

Sl k1 6 im s 1yP 1yP P . 16Ž . Ž . Ž .Ł2 B 2,h B 2, i B1, ik m qh PŽ . is12 2 hd2

Again, since the system is intended to satisfy hard hand-off dropping probability constraints, the value ofP will be very small and can be neglected in the computation of m and m . Then, the relation between mhd1 1 2 1

and m is given by the following equations:2

6 iSl l m Mym1 1 2 1m s 1yE , Mym 1yE m , Mym E , , andŽ .Ł1 2 1 2 ž /ž /ž /ž /m m k kis11 1

l k l Mym1 1 1m s 1yE ,2 ž /ž /k m qh P k m qh P kŽ . Ž .2 2 hd2 2 2 hd2

=

6 iS m Mym2 11yE , E m , Mym . 17Ž . Ž .Ł 1 2ž /ž /k kis1

This system of equations can be numerically solved for given values of l , k and k and the blocking1Ž .probabilities follow immediately from Eq. 17 :

6 iSl m Mym1 2 1P s1y 1yE , Mym 1yE m , Mym E , , andŽ .ŁB1 2 1 2 ž /ž /ž /ž /m k kis11

6 iSl Mym m Mym1 1 2 1P s1y 1yE , 1yE , E m , Mym . 18Ž . Ž .ŁB 2 1 2ž /ž /ž /ž /k m qh P k k kŽ . is12 2 hd2

Fig. 6 shows the calculated number of utilized channels m , m for overload probability values P s0.05,1 2 o Õ

0.2 and 0.8. From the graph, it is shown that the total number of utilized channels for narrowband and widebandtraffic is smaller than the number of utilized channels for the case of narrowband traffic only, i.e. m qm FM1 2 1

qM -M. This agrees with the discussion in the previous subsection. For example if P s0.2, ks9 and2 o Õ

Ns50, the difference between M and M qM under high loads is 3 narrowband channels.1 2


Ž .Fig. 6. Maximum utilizations for different input loads. k s9, ks5, h s h s0.01, m s0.002, m s0.005 and Ns50 .1 2 1 2

Ž .Note that adding more traffic types will increase the number of equations in the system Eq. 17 . However,Žnumerical equation solvers nowadays can cope successfully with systems of more than two equations obtaining

.the graph in Fig. 6 with 9 points for one P value takes less than a minute on a 300MHz PC .o Õ

4. Numerical results and discussion

We have performed simulations of the SAF based algorithm in a cellular environment with two types oftraffic: narrowband and wideband. In particular, results are obtained with the following assumptions 5:Ø New call arrivals of different traffic types in the cell are modeled using Poisson processes.Ø Call duration and dwell times of narrowband traffic are exponentially distributed with average values 500 s

and 100 s respectively and those for wideband are 200 s and 100 s respectively.Ø The ratios of the input traffic rates are ksl rl s9 and 6.1 2

Ø The number of channels per cell is 50.Ø The number of steps in PSAF calculation is Ks7.Ø The number of rings in SAF distribution is Ss1.

Ž .Ø The environment consists of 8 rings 169 cells and statistics are drawn from the center cell.Ø The admission threshold values used in the experiments are P s 0.05, 0.2 and 0.8.o Õ

Figs. 7–9 show the blocking, hand-off dropping probabilities and the channel utilization for both narrowbandand wideband traffic with different P settings for ksl rlambda s9. The relative results for ks6 areo Õ 1 2

shown in Figs. 10–12.With ks9 and Ns50 and with the hard constraints for hand-off dropping probabilities for narrowband and

wideband traffic equal 10y3 and 10y2 respectively, we can see from Fig. 8 that a P value of 0.2 will giveo ÕŽ Ž . .good performance under nominal load when lr mN s1 . From Fig. 9, we see that under high load, a

5 Naming convention of system parameters follows that in Section 3.


Fig. 7. Blocking probabilities with two types of traffic and k s9.

Fig. 8. Hand-off dropping probabilities with two types of traffic and k s9.

Fig. 9. Channel utilization with two types of traffic and k s9.


Fig. 10. Blocking probabilities with two types of traffic and k s6.

Fig. 11. Hand-off dropping probabilities with two types of traffic and k s6.

Fig. 12. Channel utilization with two types of traffic and k s6.


utilization of narrowband traffic around 60% together with a 10% utilization of wideband traffic for a totalchannel utilization of 70% is obtained.

Notice that high values of P , for example P s0.8, will give low new call blocking probabilities and higho Õ o Õ

utilizations but unsatisfactorily high probabilities of hand-off dropping. This agrees with the theoretical results.With ks6, the proportion of wideband traffic is significantly larger than the case of ks9 and wideband

traffic faces more severe hand-off dropping probabilities. Therefore, previous hard bounds on hand-off droppingprobabilities can be met only with P s0.05 which is shown in Fig. 11. We also note the increase in theo Õ

wideband portion of cell capacity utilization matches the analytical results shown in Fig. 6.In practical application of the P -based admission scheme, the network administrator should track the ratioo Õ

k of the narrowbandrwideband arrival rates. Then, according to the required values of hand-off droppingŽ .probabilities, appropriate P value can be determined either by iteratively solving the system of Eq. 17 ando Õ

Ž .calculating P bounds with Eq. 14 or by performing table lookup with pre-calculated QoS values.hd

5. Conclusion

We have analyzed the QoS parameters for mixed wideband and narrowband traffic in wireless cellularnetworks using a distributed event-based adaptive admission control scheme. Exact treatment of this problemrequires solving multidimensional Markov chains and is not practical to use in real-time admission control. Wehave also analyzed the role of the QoS tuning parameter P in the call admission process. Under complete cello Õ

capacity sharing the QoS experienced by different call types with heterogeneous bandwidth and mobilityrequirements are related. Furthermore, in a mixture of wideband and narrowband real-time traffic, the hand-offdropping probability experienced by the wideband traffic depends on the ratio of the arrival rates and also onmobility parameters of different traffic types and is usually much larger than the hand-off dropping probabilityfor narrowband calls. Therefore, the tuning parameter P must be set to satisfy the hard constraints on hand-offo Õ

dropping probability requirement for wideband calls first. We have also shown that our analysis is extensible tomore than two types of calls. The results of our approximate analysis have been verified by simulations. Thesimulation results agreed well with those of the mathematical models for the hand-off dropping probability, newcall blocking probability and cell capacity utilization.

Future work includes hot-spot performance analysis of the SAF-based admission algorithm, analysis of thedirectional SAF distribution and QoS control for calls with unknown mobility factors.

Appendix A. Estimating bandwidth for hand-off events

In order to reserve bandwidth for hand-off events, the probabilities of visiting the surrounding cells at eachhop of the mobile during the lifetime of a call must be determined.

Let t be the number of traversed cells by a type j call during its entire lifetime. The probability of the callvisiting more than ky1 cells during its lifetime is given by:

my 1 ky1` m h hj j j

P t)ky1 s s . A.1Ž . Ž .Ýj ž / ž /m qh m qh m qhj j j j j jmsk

1Assuming that the probability for a mobile to leave a hexagonal cell through anyone of the edges to be .6

The probability for a type j call to move to Ring 1 on hand-off given that it is originally in Ring 0 will be equalŽ .to 1. Other than that, a type j call will move from Ring i with i)0 to a neighboring cell on hand-off with the

following probabilities:Ž . Ž . Ž .1. r i s 2 iq1 r 6 i , for i)0, is the probability for the call to move to a cell in Ring iq1,1Ž . Ž . Ž .2. r i s 2 iy1 r 6 i , for i)0 is the probability for the call to move to a cell in Ring iy1 and2


Ž .3. r i s1r3, for i)0, is the probability for the call to move to a cell in the same ring as the original cell, i.e.3

Ring i. We shall denote it as r since it is a constant.3Ž . Ž . ŽNote that r i qr i qr s1 for any call in Ring i with i)0 given that a hand-off is successfully1 2 3

.executed .Consider a random walk in the hexagonal topology in which a call is allowed to make infinite hops from cell

to cell.Ž .Then, the joint probability P i,k that the call will visit a cell in Ring i after ky1 hand-offs is given by thew

following recurrent relation:

w x w xP i ,k sP 0,ky1 is1 qr iy1 P iy1,ky1 iG2Ž . Ž . Ž . Ž .w w 1, j w

w x w xqr iq1 P iq1,ky1 iG0 qr P i ,ky1 iG1 , A.2Ž . Ž . Ž . Ž .2, j w 3, j w

w xwhere the value of expr is 1 when expr is true, and 0 if false.Ž . Ž .Without loss of generality we shall consider a call to start at the central Cell 0,0 . Then, P 0,1 s1,w

Ž . Ž . Ž .P p,1 s0 for p)0, P 1,2 s1 and P q,2 s0 for q/1, which are the boundary conditions for thew w w

system under investigation. Also, the inequality k) i holds for all i.w x Ž . ` ` Ž . i kNow, consider the generating function 7 G x, y sÝ Ý P i,k x y of the recurrence relation givenis0 ks0 w

Ž .in Eq. A.2 subject to the boundary conditions given above, we have,` ` ` ` `

i k k i kP i ,k x y s P 0,ky1 y xq r iy1 P iy1,ky1 x yŽ . Ž . Ž . Ž .Ý Ý Ý Ý Ýw w 1 wis0 ks1 ks2 is2 ks3

` ` ` `

i k i kq r iq1 P iq1,ky1 x y qr P i ,ky1 x y . A.3Ž . Ž . Ž . Ž .Ý Ý Ý Ý2 w 3 wis0 ks3 is1 ks3

Ž . 6 Ž .Let us limit the terms in the summation in Eq. A.3 to ksK steps and is I rings with I-K . Then, bymatching of coefficients corresponding to x i y k for all i’s and k’s with the bounds described, a system ofŽ . Ž .K Iq1 linear equations with unknown probabilities P i,k can be obtained and solved.w

Ž .Let us define now P i,k as the probability that a call of type j will visit Ring i after ky1 hand-offs whichj

is given by:

P i ,k sP i ,k PP t)ky1 . A.4Ž . Ž . Ž . Ž .j w j

Ž .The solutions P i,k carry the bandwidth requirements and hence provide reservation information for each ringj

at each hop for traffic type j.

References

w x1 A.S. Acampora, M. Naghshineh, An architecture and methodology for mobile-executed handoff in cellular ATM networks, IEEEŽ . Ž .Journal on Selected Areas in Communications 12 8 October 1994 1365–1375.

w x2 J. Chen, M. Schwartz, Two-tier resource allocation for a multimedia micro-cellular mobile system: performance summary, in: Proc.Ž .IEEE Int. Symp. on Person, Indoor and Mobile Radio Communications PIMRC’95 , 1995, vol. 3, pp. 1067–1072.

w x3 M. Naghshineh, M. Schwartz, Distributed call admission control in mobilerwireless networks, IEEE Journal on Selected Areas inŽ . Ž .Communications 14 4 May 1996 711–717.

w x4 M. Naghshineh, A.S. Acampora, QOS provisioning in micro-cellular networks supporting multimedia traffic, in: Proc. IEEEINFOCOM’95, 1995, pp. 1075–1084.

w x5 M. Naghshineh, A.S. Acampora, Design and control of micro-cellular networks with QOS provisioning for data traffic, WirelessŽ . Ž .Networks 3 4 1997 249–256.

6 Note that the value of K can be chosen by limiting the probability type j calls having more than K steps to be smaller than somepredefined value.


w x6 B. Epstein, M. Schwartz, Reservation strategies for multi-media traffic in a wireless environment, in: Proc. 1995 IEEE 45th VehicularTechnology Conference, Chicago, IL, July 1995, pp. 165-169.

w x7 G.R. Grimmett, D.R. Stirzaker, Probability and Random Processes, Oxford University Press, London, 1994.w x8 R. Guerin, H. Ahmadi, M. Naghshineh. Equivalent capacity and its application to bandwidth allocation in high-speed networks, IEEE

Ž . Ž .Journal on Selected Areas in Communications 9 7 1991 968–981.w x9 G. Kesidis, J. Walrand, C.S. Chang, Effective bandwidths for multiclass Markov fluids and other ATM sources, IEEErACM

Ž . Ž .Transactions on Networking 1 4 1993 424–428.w x10 D.A. Levine, I.F. Akyildiz, M. Naghshineh, A resource estimation and call admission algorithm for wireless multimedia networks

Ž . Ž .using the shadow cluster concept, IEEErACM Transactions on Networking 5 1 1997 1–12.w x11 J-P.M.G. Linnartz, On the performance of packet-switched cellular networks for wireless data communications, Wireless Networks 1

Ž .1995 129–137.w x12 J. Misic, S.T. Chanson, F.S. Lai, Event based resource estimation in admission control for wireless networks with heterogeneousˇ ´

Ž . Ž .traffic, Mobile Computing and Communications Review 1 4 1997 .w x Ž13 E.C. Posner, R. Guerin, Traffic policies in cellular radio that minimize blocking of handoff calls, in: Proc. 11th Teletraffic Cong. ITC

.11 , Kyoto, Japan, September 1985.

Jelena Misic received her bachelor’s degree in Electrical Engineering in 1982 and master’s and Ph.D. degree in Computer Engineering inˇ ´1987 and 1993 respectively, all from University of Belgrade, Yugoslavia. Before joining HKUST she was the head of the Vinca InstituteNetwork Research Group and an Adjunct Assistant Professor of Computer Science at University of Belgrade. She is the member of IEEEComputer Society.

Dr. Misic’s research interests include wireless networks, high speed networking, wireline and wireless-ATM, parallel computerˇ ´architectures and algorithms.

Samuel T. Chanson received his Ph.D. degree in Electrical Engineering and Computer Sciences from theUniversity of California, Berkeley in 1975. He was a faculty member at the School of Electrical Engineering,Purdue University for two years before joining the Department of Computer Science at the University of BritishColumbia where he became a full professor and director of its Distributed Systems Research Group. In 1993Professor Chanson joined the Hong Kong University of Science & Technology as professor and Associate Head ofthe Computer Science Department. He has consulted widely for industry and government institutes in Canada,USA, China, Korea, Taiwan and Japan on communication technologies and has served on the program committeesof many international conferences on distributed systems and computer communications. He was a generalco-chair of the 1998 IEEE International Conference on Distributed Computing Systems and will be the conferenceco-chair of FORTErPSTV in 1999. Dr. Chanson is currently serving on the editorial boards of IEEErACMTransactions on Networking, New Generation Computing and also the Journal of Computing and Information.

Ž .Dr. Chanson’s research interests include computer communications particularly protocols and high speed networks , multimediaCommunication, parallel programming and Internet technologies and has published more than 120 papers in the above areas. He is theDirector of Cyberspace Center at HKUST.

Frederick S. Lai received his BEng and MPhil degrees both in Computer Science from the Hong Kong University of Science andTechnology in 1996 and 1998 respectively. He is currently research assistant with the same institute.

admission control for wireless multimedia networks with hard call level quality of service bounds

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