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Admission control for differentiated servicesin 3G cellular networks

Onno J. Boxma a , b, Rudesindo Nunez-Queija c, b , 1,Adriana F. Gabor a , b , 2, Hwee-Pink Tan a , , 3

aEURANDOM, P.O. Box 513, 5600 MB Eindhoven, The Netherlandsb Eindhoven University of Technology, Department of Mathematics and Computer

Science, 5600 MB Eindhoven, The Netherlandsc

CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands

Abstract

Third generation wireless systems can simultaneously accommodate ow transmis-sions of users with widely heterogeneous applications. As radio resources are limited,we propose an admission control rule that protects users with stringent capacity re-quirements (streaming traffic) while offering sufficient capacity over longer time

intervals to delay-tolerant users (elastic traffic). Using time-scale decomposition,we develop approximations to evaluate the performance of our differentiated admis-sion control strategy to support integrated services with capacity requirements in arealistic downlink transmission scenario for a single radio cell.

Key words: Third generation wireless systems, differentiated admission control,time-scale decomposition.

Corresponding author. Authorship listed in alphabetical order.Email addresses: [email protected] (Onno J. Boxma), [email protected]

(Rudesindo Nunez-Queija), [email protected] (Adriana F. Gabor),[email protected] (Hwee-Pink Tan).1 Presently also aliated with TNO Information and Communication Technology,The Netherlands. No longer affiliated with Eindhoven University of Technology.2 No longer affiliated with EURANDOM.3 Present address: Centre for Telecommunications Value-chain Research, Lloyd In-stitute, Trinity College Dublin, Dublin 2, Ireland.

Preprint submitted to Performance Evaluation 3 April 2007


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1 Introduction

Third Generation (3G) cellular networks such as UMTS and CDMA2000 areexpected to support a large variety of applications, where the traffic theycarry is commonly grouped into two broad categories: Elastic traffic corre-sponds to the transfer of digital documents (e.g., Web pages, emails, storedaudio / videos) characterized by their size, i.e., the volume to be transferred.Applications carrying elastic traffic are exible, or elastic, towards capac-ity uctuations, the total transfer time being a typical performance measure.Streaming traffic corresponds to the real-time transfer of various signals(e.g., voice, streaming audio / video) characterized by their duration as well astheir transmission rate. Stringent capacity guarantees are necessary to ensure

real-time communication to support applications carrying streaming traffic.

Various papers have been published recently that study wired links carryingintegrated (elastic and streaming) traffic. In terms of resource sharing, the clas-sical approach is to give head-of-line priority to packets of streaming traffic inorder to offer packet delay and loss guarantees [7,5,11]; alternatively, adaptivestreaming traffic (that is TCP-friendly and mimics elastic traffic) is consideredin [9,3,13]. Markovian models have been developed for the exact analysis of

these systems [11,14]. However, they can be numerically cumbersome due tothe inherently large dimensionality required to capture the diversity of userapplications. Hence, various approximations have been proposed [7,13], whereclosed-form limit results were obtained that can serve as performance bounds,and hence yield useful insight.

In this study, we consider downlink transmissions of integrated traffic in asingle 3G radio cell and propose an admission control strategy that allocatespriority to streaming traffic through resource reservation and guarantees thecapacity requirements of all users while maximizing the data rate of each elas-tic user. The location-dependence of the wireless link capacity adds to thedimensionality problem already inherent in the performance analysis of corre-sponding wireline integrated services platforms. We describe the system modelin Section 2 and develop an approximation based on time-scale decompositionin Section 3 to evaluate the user-level performance. We dene two base stationmodels based on abstractions of the system model in Section 4 and present nu-merical results comparing both models in Section 5. Some concluding remarksare outlined in Section 6.

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2 System model

We consider a 3G radio cell (e.g., UMTS/W-CDMA) with a single downlinkchannel whose transmission power at the base station (resource) is sharedamongst users carrying streaming and elastic traffic. We assume that the basestation transmits at full power, denoted by P , whenever there is at least oneuser in the cell. In addition, a part of the total power, P s P , is statically re-served for streaming traffic, where unclaimed power is equally shared amongstall elastic users. Note that although the resource that can be maximally guar-anteed for on-going elastic traffic is P e = P P s , they are permitted to usemore than P e . However, the surplus is immediately allocated to streamingtraffic when a new streaming user arrives.

With W-CDMA technology, the base station can transmit to multiple users

simultaneously using orthogonal code sequences. Let P u P be the powertransmitted to user u . The power received by user u is P ru = P u u , whereu denotes the attenuation due to path-loss. For typical radio propagationmodels, u for user u at distance u from its serving base station is proportionalto (u )

, where is a positive path-loss exponent.

As a measure of the quality of the received signal at user u, we consider theenergy-per-bit to noise-density ratio , E bN 0 u , given by

E b

N 0 u=

W

Ru

P ru

+ I au + I

ru

,

where W is the CDMA chip rate, Ru is the instantaneous data rate of user u, is the background noise (assumed to be constant throughout the cell) and I ru isthe inte r -cell interference at user u caused by simultaneous interfering trans-missions received at user u from the base station in the serving cell. For linearand hexagonal networks, it can be shown [12] that I ru increases as u increases.On the other hand, intr a -cell interference, I au , is due to simultaneous trans-missions from the serving base station of user u using non-orthogonal codes(with total power P au ) to other users in the same cell received at user u . Quan-titatively, we can write I au = P au u , where is the code non-orthogonalityfactor.

To achieve a target error probability corresponding to a given Quality of Ser-vice (QoS), it is necessary that E bN 0 u u , for some threshold u . Equivalently,the data rate Ru of each admitted user u is upper-bounded as follows:

Ru W P u u

u ( + P au u + I ru ). (1)

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Accordingly, for a given P u , and user-type, the feasible data rate of useru depends on its location (through u and I ru ) and the intra-cell interferencepower, P au .

2.1 Location-dependence

According to Eq. (1), the transmission power, P u , needed to support the ca-pacity requirement, r u , of user u is given by:

P u r u u [P au u + + I ru ]

W u P u . (2)

Ideally, given perfect knowledge of the location of each user u at the basestation, a maximum number of users can be admitted by allocating exactly P u to each user u . However, in reality, only the quantized location of eachuser in the cell is known. This is obtained, e.g., by dividing the cell into J disjoint segments, where we assume that the path-loss, intra-cell and inter-cell interference are the same for any user in segment j = 1 , . . . , J , denoted by( j , I a j , I r j ), respectively. As J increases, the location quantization becomesner and approaches the ideal case ( J = ); on the other hand, the specialcase of J =1 corresponds to the case where user-location is unknown.

Accordingly, we assume that elastic and streaming users arrive at segment

j as independent Poisson processes at rates j,e and j,s , with capacity re-quirements of r j,e > 0 and r j,s > 0 respectively. Elastic users in segment jhave a general le size (or service requirement) distribution with mean f j,e(bits) and, similarly, the holding times of streaming users may be taken tohave mean 1/ j,s (secs). The total arrival rates of elastic and streaming usersto the cell are denoted by e = J j =1 j,e and s =

J j =1 j,s . The minimum

energy-to-noise ratio, u , may depend on the user type and location [1], andwill be denoted by j,e and j,s for elastic and streaming users in segment j ,respectively.

2.2 Resource Sharing

Given the transmission power, P u , the mechanism via which the total power,P , is shared amongst all users (resource sharing) determines the total intra-cellinterference power experienced at user u , P au . When the base station transmitsto all users in the cell simultaneously, each user u experiences the maximumintra-cell interference power, given by P -P u ; on the other hand, if time isslotted and the base station transmits only to one user in each time slot ( time

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sharing ), then there will be no interference power. Accordingly, we have thefollowing expressions for P au :

P au

= P P u , simultaneous transmission to all users in the cell;

< P P u , simultaneous transmission to some users in the cell;

= 0 , no simultaneous transmission ( time -sharing ).

2.3 Admission Control

We propose an admission control strategy that ensures the required capacity r uof each admitted user u is satised. Let N j,e and N j,s denote the number of elas-tic and streaming users in segment j respectively, and dene N j = N j,e + N j,s .We further dene the vectors N e = ( N 1,e , . . . , N J,e ) and N s = ( N 1,s , . . . , N J,s )and let N e and N s be the total number of elastic and streaming users in thecell respectively. Let ( j , j ) be the minimum transmission power required byan (elastic, streaming) user in segment j to sustain a capacity requirementof (r j,e , r j,s ), respectively. Depending on the resource sharing mechanism em-ployed, ( j , j ) can be evaluated using Eq. (2).

Streaming users are always accommodated with exactly their required capac-ity, consuming a total power of

P s (N s ) =J

j =1N j,s j .

Hence, the capacity of elastic users must be achievable with power P e = P P s .Since all elastic users receive an equal portion of the available power, weconclude that

N e j P e ,

must hold for all j with N j,e > 0, or equivalently,

N e j 1(N j,e > 0) P e , j. (3)

The indicator function 1E equals 1 if expression E holds and is 0 otherwise.Note that the J conditions in (3) only limit the total number of elastic usersN e , but that the maximum number of users does depend on the entire vector

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N e . Similarly, the fact that elastic users share power equally, together with theminimum power restrictions of both elastic and streaming users, imply that

N e j 1(N j,e > 0) + P s (N s ) P, j. (4)

Conditions (3) and (4) completely determine the admission policy: a newly-arrived user will be accepted only if the resulting system state, ( N e , N s ),satises all 2J conditions. Alternatively, these conditions may be formulated interms of the required power for each user type. Similar to P s (N s ), we determinethe transmission power required by elastic requests:

P e(N e , N s ) N e max j :N j,e > 0

{ j } .

Note that this expression depends on the system state, ( N e , N s ).

Our admission control policy for streaming users can now be formulated asfollows: a newly-arrived streaming user in segment i will be admitted if

P e(N e , N s + e i ) + P s (N s + e i ) P, (5)

where the vector e i has its i th component equal to 1 and all other componentsare 0.

For elastic users, we must incorporate the power reservation restrictions as

well. If we dene

P s (N s ) max {P s , P s (N s )} ,

then a newly-arrived elastic user in segment i will be admitted if

P e(N e + e i , N s ) + P s (N s ) P (6)

While the admission control proposed in [7] is similar, it results in equal block-

ing probabilities for both types of traffic. Due to resource reservation in ourcase, the blocking probabilities will depend on both the user type and location.

2.4 Rate allocation

While streaming users are accommodated with exactly their required capac-ities, i.e., r j,s in segment j , the date rates allocated to elastic users dependon the number, type and location of other users. The available transmission

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of ne reduces to a simple truncated geometric distribution:

P (N Qe = ne | NQs = n s ) =

e(n s )n e (1 e(n s ))1 e(n s )n

Q, maxe (n s ) , (10)

where nQ, maxe (n s ) = P P s (n s )) / and e(n s ) = ee (n s ) is the total depar-ture rate of elastic requests from the cell.

We emphasize that, assuming quasi-stationarity, (9) and (10) are valid forgeneral distributions of elastic requests [6]. Note that these expressions areinsensitive to the le size distributions, other than through their means. As afurther remark, we observe that stability is of no concern in our model, sinceN Qe is bounded due to the assumption that r j,e > 0. Often, when applying atime-scale decomposition, the issue of stability is of considerable importance,giving rise to an additional assumption commonly referred to as uniform sta-bility [5].

Remark 1 According to Eq. (8), the departure rate of elastic requests dependson the system state, ( n e , n s ). However, to apply Eq. (9) and (10), the depar-ture rate can depend on the system state through n s only. We illustrate how this can be achieved with various resource sharing mechanisms in Section 4.

3.1.2 Unconditional marginal distributions

Next, we consider the dynamics of streaming ows. When N Qs = n s , stream-ing ows depart at a rate j n j,s j,s . When a new streaming ow arrives insegment i, due to admission control, it is either accepted or blocked. Underour approximation assumptions, the probability of acceptance in segment i,AQi,s (n s ), is given by:

P P e(N Qe , n s + e i ) P P s (n s + e i ) | NQs = n s .

Hence, the effective arrival rate of streaming ows in segment i , Qi,s (n s ), isgiven as follows:

Qi,s (n s ) = i,s AQi,s (n s ).

As a side remark, note that AQi,s (n s ) = 1 if P s (n s + e i ) P s , since the admis-sion control on elastic ows ensures that N Qe j 1(N j,e > 0) P P s for all j .

In general, there is no closed-form expression for the equilibrium distributionof N Qs and we must assume exponential or phase-type holding time distribu-

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tions and resort to standard methods to (numerically) solve the equilibriumdistribution of a nite-state Markov process. Note that the dimension of thisprocess N Qs is much smaller than that of the original process ( N e , N s ): thecomponent N e is eliminated in the approximation. However, if we applyuniform admission control for streaming traffic by taking j independentof j [see the earlier Footnote 4], then AQi,s (n s ) AQs (n s ) is independent of iand depends on n s only through the total number of streaming ows. N Qs canthen be shown to be balanced [4] and can be reduced to the framework of [6].It follows that, for arbitrary holding time distributions of streaming ows, and0 n s nmaxs = P :

P (N Qs = n s ) = cQs

n s 1

k=0AQs (k)

J

j =1

( j,s )n j,s

n j,s !, (11)

with j,s = j,s / j,s and cQs = P (N Qs = 0) can be determined by normaliz-ing (11) to a probability distribution. Letting s = j j,s , we further obtainthe distribution of the total number of active streaming ows (still for uniformadmission control):

P (N Qs = n s ) = cQs

(s )n s

n s !

n s 1

k=0AQs (k), (12)

which in this case results again in a simple expression for the normalizingconstant:

cQs =n maxs

n s =0

(s )n s

n s !

n s 1

k=0AQs (k)

1

.

To conclude this section, we now calculate several relevant performance mea-sures (not restricting anymore to uniform admission control) by un-conditioningon N Qs . In general, the unconditional distribution for the number of elasticusers is

P (NQe = n e) = n s

PQ

(n e | n s )P (NQs = n s ). (13)

The unconditional blocking probabilities in segment i are

pQi,s =n s

(1 AQi,s (n s ))P (N Qs = n s ), (14)

for streaming ows; similarly, for elastic ows, we have:

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pQi,e =n s

(1 AQi,e (n s ))P (N Qs = n s ).

3.2 Fluid Approximation

The uid approximation (from the perspective of elastic ows), denoted byA (F , J ), complements the quasi-stationary approximation: We now assumethat the dynamics of elastic ows are much slower than those of streamingows, i.e., the j,s and j,s are much larger than the j,e and 1/f j,e . This as-sumption is valid when we consider the combination of voice calls (streaming)and large le transfer (elastic) applications. The dynamics of streaming owscan then be studied by xing the number of elastic ows in each segment. This

approximation will be reected in the notations by adding a superscriptF

.Similar to A(Q, J) , we will construct an approximating 2 J -dimensional pro-cess under the assumption that N F s immediately reaches steady state, when-ever N F e changes.

3.2.1 Conditional distribution of streaming traffic

We x the number of elastic ows in each segment: N F e = n e . Under the

uid approximation assumption, we can model the streaming ows as aJ -class Erlang-loss queue with nite capacity:

P F (n s | n e) P (N F s = n s | NF e = n e)

= cF s (n e)J

j =1

n j,s j,sn j,s !

, (15)

where j,s = j,s j,s . As before, we emphasize that the above expression depends

on the holding time distribution only through its mean. The constant cF s (n e)can again be determined by requiring that (15) adds to 1 when summing(for xed n e) over all n s such that P e(n e , n s ) + P s (n s ) P . For uniformadmission control, i.e., i independent of i, this results in an elegantform of the distribution for the total number of streaming users (a truncatedPoisson distribution), as well as for the normalization constant:

P (N F s = n s | NF e = n e) = cF s (n e)

(s )n s

n s !,

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and

cF s (n e) = (n F, maxs (n e )

k=0

(s )k

k!) 1,

where nF, maxs (n e) is the maximum number of streaming users for which P e(n e , n s )+P s (n s ) P .

3.2.2 Unconditional marginal distributions

Next, we consider the dynamics of elastic ows. When N F e = n e > 0, elasticows in segment j (if any) experience an average data rate (recall that ne isthe sum over all components of the vector n e):

r j,e (n e) E [r j,e (ne , N F s ) | NF e = n e]

=n s

r j,e (ne , n s ) P F (n s | n e), (16)

where the summation is taken over all n s for which P e(n e , n s ) + P s (n s ) P .The (state-dependent) departure rate of elastic ows from segment j is

n j,e r j,e (n e)/f j,e .

In order to fully describe the dynamics of the elastic ows, we now determinethe arrival rate, which also depends on the state n e because of the employedadmission control. Under our approximation assumptions, the probability of acceptance in segment i is given by:

AF i,e (n e) P (P s (NF s ) + P e(n e + e i , N

F s ) P | N

F e = n e),

and, consequently, the effective arrival rate of elastic ows in segment i is

F i,e (n e) i,e A

F i,e (n e).

As for the quasi-stationary approximation, in general, there is no closed-formexpression for the distribution of N F e . However, under additional assumptions,N F e is balanced [4]. This is the case, for example, if we assume perfectly or-thogonal codes ( = 0) and apply uniform admission control for elastic trafficby taking j independent of j . In this case, the dynamics of N F s dependson N F e only through the total number of elastic users N e , so if we dene

h(n s ) = P P s (n s ),

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then, we can write

E [h(N F s ) | NF e = n e] = E [h(N

F s ) | N

F e = ne] g(ne).

If we further dene

j =W j

j,e [ + I r j ],

then, from Eq. (7) and (16), we obtain

r j,e (n e) r j,e (ne) = j g(ne)

ne.

Furthermore, AF i,e

(n e) is independent of i and depends on n e only through thetotal number of elastic ows, i.e., AF i,e (n e) AF e (ne).

It follows that, for arbitrary le size distributions, and 0 ne nmaxe = P e :

P (N F e = n e) = cF e

n e

k=1

k AF e (k 1)g(k)

J

j =1

j,e j

n j,e

, (17)

with j,e = j,e f j,e and cF e = P (N F e = 0) can be determined after normaliza-tion. We further obtain the distribution of the total number of le transmis-

sions (still for uniform admission control and = 0):

P (N F e = ne) = cF e

j

j,e j

n e n e

k=1

k AF e (k 1)g(k)

, (18)

leading to a simple expression for the normalizing constant as before:

cF e =n maxe

n e =0 j

j,e j

n e n e

k=1

k AF e (k 1)g(k)

1

.

Remark 2 If the codes are not perfectly orthogonal ( > 0), we can still apply the above analysis in case the background noise and inter-cell interference arenegligible ( j + I r j


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We conclude this section with the following unconditional performance mea-sures:

P (N F s = n s ) =n e

P F (n s | n e)P (N F e = n e). (19)

The unconditional blocking probabilities in segment i are

pF i,e =n e

(1 AF i,e (n e))P (NF e = n e), (20)

and

pF i,s =

n e(1 AF i,s (n e))P (N

F e = n e).

4 Specic models

Based on the abstraction of the model in terms of (a) location-dependenceand (b) resource sharing mechanism, we can dene variants of the base stationmodel, where our objective is to evaluate the performance gain achieved withlocation-awareness and time-sharing so as to ascertain if the added processingcomplexity at the base station is justied.

4.1 CDMA model

In this model, the base station does not maintain location information of eachuser (i.e., J =1), and transmits simultaneously to all users. As such, each useru is distinguished only in terms of its type (i.e., streaming ( u s) vs elastic(u e)). Hence, the system state ( N e , N s ) reduces to (N e , N s ) and we candrop the subscript j from the notations. In addition, due to simultaneous

transmission to all users, P au = P -P u , and Eq. (1) can be written as follows:

Ru W P u

u [(P P u ) + + I ru

u ],

which can be re-written as follows:

P u Ru ( + I

rmax

min + P )W + R u

. (21)

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For linear and hexagonal networks and typical propagation models, u = minand I ru = I rmax when user u is located at the edge of the cell.

Accordingly, we can dene the minimum power required by an (elastic, stream-ing) user to sustain capacity requirements of ( r e , r s ) as follows:

=r e ( + I

rmax

min + P )W + r e

,

=r s ( + I

rmax

min + P )W + r s

. (22)

Eq. (3) and (4) can be written as follows:

N e P e ,

N e + N s P. (23)

By substituting Eq. (22) into Eq. (23) and dening r = max( r e , r s ), we obtainthe following:

N er e + N s r s P (W + r )( + I

rmax

min + P ). (24)

4.1.1 Equivalent wired link analysis

According to Eq. (24), if we dene c P (W + r )(

+ I rmax min

+ P ), then the downlink trans-

mission scenario in the CDMA model can be approximated by a wired linkwith capacity c shared amongst streaming and elastic requests, where cs =P sP c is reserved for streaming requests. Details of the analysis of this modelbased on the quasi-stationary and uid approximations (denoted by A(Q)and A(F) respectively) can be found in [10].

4.1.2 General analysis

Referring to Remark 1, to apply the quasi-stationary approximation, the de-parture rate of elastic users from the cell should only depend on the systemstate ( N s , N e) through N s . From Eq. (8), we have the following expression:

e(N e , N s ) =W [P P s (N s )]

e[(P P P s (N s )

N e ) ++ I rmax

min ].

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It is not straightforward to obtain an approximation, e(N s ), for e(N e , N s ).On the other hand, the uid approximation developed in Section 3.2 can beapplied for this model.

4.2 HSDPA model

Based on our denition in Section 1, each streaming (elastic) user u has a xed(minimum) capacity requirement, denoted by r u . According to our resourcereservation policy, while each streaming user transmits at xed rate r u , thetransmission rate of an elastic user u , Ru ( r u ), depends on the resourceunclaimed by streaming traffic, given by P -P s (N s ). From Eq. (1), Ru can bemaximized by minimizing P au . One approach to do so is to apply time-sharingamongst elastic users.

If we aggregate all elastic users, the resource sharing mechanism is such thatthe base station transmits using (almost-)orthogonal codes to all users, wherethe aggregate elastic user may be assigned several codes. Within the aggregateuser, elastic users sharing the same code are served in a time-slotted fashionso that they do not interfere with one another, but only with elastic usersusing different codes and streaming traffic. This resource sharing mode issimilar to UMTS / HSDPA, where up to N c = 4 codes can be shared amongstdata/elastic users. We assume that N c = 1 in our study.

For the HSDPA model dened here, the base station has the capability tomaintain quantized location information (at different levels of granularity)and also supports time-sharing resource sharing amongst elastic requests asdescribed above.

4.2.1 Impact on admission control

According to the above resource sharing policy, the received signal at eachstreaming user u in segment j is interfered by simultaneous transmissions toall other users, i.e., P au = P -P u and from (2) we obtain

j =r j,s j,s [P j + + I r j ]

(W + r j,s j,s ) j.

For an elastic user u in segment j , we have P au = P s (N s ) since its receivedsignal is only interfered by streaming users. Hence, the power required by anelastic user in segment j to sustain its capacity requirement, r j,e , depends on

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P (W) (20, 0.2)

(W) 6.09x10 -14

W (chips /s) 3.84x10 6

dB 2

UMTS and traffic parameters

P s (W) 10

0.5

r e (kbps) 128r s (kbps) 128

Propagation Model Okumura-Hata Model [2]

Inter-cell InterferenceModel

Hexagonal network withmaximum tx. power [12]

Link budget Table 8.3 [1]

Table 1UMTS cell and traffic parameters for performance evaluation.

within the cell is computed based on the conservative approximation for ahexagonal network [12].

Elastic (streaming) users arrive at the cell according to a Poisson process atrates e ( s ), capacity requirement r e (r s ), target energy-to-noise ratio e ( s ),mean le size f e (holding time 1 s ) and are assumed to be uniformly distributed

over the cell. In addition to the mean number of users, (E[ N e], E[N s ]), andblocking probabilities, ( pe , ps ), for each class of traffic, we dene the stretch ,S e , for each admitted elastic user by normalizing the expected residence time,E [Re], by the mean le size, f e , i.e., S e = E [R e ]f e =

E [N e ] e (1 pe ) (cf. Littles Theorem).

A summary of the cell and traffic parameters is given in Table 1.

In [10] and [8], through simulations, we have demonstrated that the user-performance obtained with the basic CDMA and HSDPA model is almostinsensitive to the actual distribution of the traffic parameters. This justiesthe application of the approximation techniques we develop, which depend onthe traffic parameter distribution only through the mean values. In addition,we also demonstrated the accuracy of the approximations, particularly for theextreme (quasi-stationary and uid) traffic regimes.

Here, we focus on the comparison of the basic CDMA model and the HSDPAmodel for the base station based on simulation as well as the approximations.Unless otherwise stated, we assume that ( ds , se) are exponentially distributedwith mean 1 s and f e respectively.

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5.1 Simulation Procedure

We develop a simulation program for our model by considering arrival / depar-ture events of traffic requests (elastic or streaming). Each simulation scenario

is dened according to the following procedure:

1. Fix the level of location quantization, J :J =1 : no location information;J > 1 : location information available.

2. Fix the total offered traffic by choosing the loading factor , l > 0, where ue + us = l c,ue = ef e and us = s r s s ;

3. For each l, x the traffic mix , u elc , by choosing ue ,0 ue l c;

4. For each traffic mix, select ( e , s ) to t one of the following traffic regimes:a. Quasi-stationary Regime ( S(Q,J) , cf. Section 3.1);b. Fluid Regime ( S(F,J) , cf. Section 3.2);c. Neutral Regime ( S(N,J) , ts neither a. nor b.)

We generate 5 sets of simulation results for each scenario, for which the samplemean for each performance metric is computed and used for performancecomparison.

5.2 Impact of time-sharing (J=1)

We begin by investigating the performance gain achieved with time-sharing bycomparing the performance obtained for the basic CDMA model and HSDPAmodel without location-awareness for various traffic regimes.

5.2.1 Quasi-stationary regime

We plot ( pe , ps ) and (E[N e], S e) as a function of the traffic mix, u ec

, 0 ue c in Fig. 1 and 2 respectively. We note that, since it is not straightforwardto apply the quasi-stationary approximation to the CDMA model (cf. Section4.1.2), we utilize the equivalent wired link analysis to obtain the correspondingquasi-stationary approximation.

Based on the simulation results, we observe a performance gain achieved as aresult of time-sharing in terms of reduced blocking probabilities, queue lengthand sojourn time. This gain is expected since, for a given number of streamingrequests, time-sharing amongst elastic ows reduces the intra-cell interference

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power experienced by each elastic user, thereby increasing the data rate perelastic user. This gain is marginal when elastic load is low, since the additionalinterference experienced by an elastic user due to other elastic users (withouttime-sharing) is insignicant.

In terms of the accuracy of approximations, we observe that the performanceobtained with the HSDPA model is well-tracked by the corresponding approx-imation; on the other hand, the equivalent wired link analysis results in overlyconservative estimates of the performance for the CDMA model.

0 0.2 0.4 0.6 0.8 10

0.02

0.04

0.06

0.08

0.1

0.12

Normalized offered elastic load, ue /c

B l o c

k i n g p r o

b a

b i l i t y f o r e

l a s

t i c

f l o w s ,

p e A(Q)A(Q,1)S(Q,1) CDMAS(Q,1) HSDPA

0 0.2 0.4 0.6 0.8 10

0.02

0.04

0.06

0.08

0.1

0.12


B l o c

k i n g p r o b

a b i l i t y f o r s

t r e a m

i n g

f l o w s ,

p s

A(Q)A(Q,1)S(Q,1) CDMAS(Q,1) HSDPA

Fig. 1. Blocking probability for elastic (left) and streaming requests (right) vs nor-malized offered elastic load obtained for quasi-stationary regime ( J =1).

0 0.2 0.4 0.6 0.8 10

2

4

6

8

10


E x p e c

t e d n u m

b e r o

f e

l a s t i c

f l o w s ,

E [ N

e ]


0 0.2 0.4 0.6 0.8 10

0.5

1

1.5

2

2.5

3

3.5

Normalized offered elastic load, ue /c S

t r e

t c h o

f e a c h a

d m

i t t e d e

l a s t

i c f l o w ,

S e

( s e c /

M b i


Fig. 2. Number of active elastic requests (left) and stretch of each admitted elas-tic request vs normalized offered elastic load obtained for quasi-stationary regime(J =1).

5.2.2 Fluid regime

We plot ( pe , ps ) and (E[N e], S e) as a function of the traffic mix, u ec , 0 ue c in Fig. 3 and 4 respectively.

As with the quasi-stationary regime, we observe a performance gain achievedas a result of time-sharing in terms of reduced blocking probabilities, queuelength and sojourn time. In terms of the accuracy of approximations, the

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blocking performance obtained with both models is well-tracked by the cor-responding approximations. However, the approximations achieved more op-timistic estimates of the queue length and sojourn time of elastic users.

0 0.2 0.4 0.6 0.8 10

0.02

0.04

0.06

0.08

0.1

0.12


B l o c

k i n g p r o

b a

b i l i t y f o r e

l a s

t i c

f l o w s , p

e

A(F,1) CDMAA(F,1) HSDPAS(F,1) CDMAS(F,1) HSDPA

0 0.2 0.4 0.6 0.8 10

0.02

0.04

0.06

0.08

0.1

0.12


B l o c

k i n g p r o

b a

b i l i t y f o r s

t r e a m

i n g

f l o w s ,

p s


Fig. 3. Blocking probability for elastic (left) and streaming requests (right) vs nor-malized offered elastic load obtained for uid regime ( J =1).

0 0.2 0.4 0.6 0.8 10

1

2

3

4

5

6

7


E x p e c

t e d n u m

b e r o

f e

l a s

t i c

f l o w s ,

E [ N

e ]


0 0.2 0.4 0.6 0.8 10

0.5

1

1.5

2

2.5

3


t r e

t c h o

f e a c

h a

d m

i t t e

d e

l a s

t i c f l o w ,

S e

( s e c /

M b i


Fig. 4. Number of active elastic requests (left) and stretch of each admitted elasticrequest vs normalized offered elastic load obtained for uid regime ( J =1).

5.2.3 Neutral regime

We plot ( pe , ps ) and (E[N e], S e) as a function of the traffic mix, u ec , 0 ue c in Fig. 5 and 6 respectively.

As with the extreme traffic regime, we observe a performance gain achievedas a result of time-sharing in terms of reduced blocking probabilities, queuelength and sojourn time. For each performance metric, we note that the quasi-stationary (uid) approximation upper (lower) bounds the performance ob-tained in the neutral traffic regime, where a tighter bound is obtained withthe HSDPA model.

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0 0.2 0.4 0.6 0.8 10

0.02

0.04

0.06

0.08

0.1

0.12


B l o c

k i n g p r o

b a

b i l i t y

f o r e

l a s

t i c

f l o w s ,

p e

A(Q) CDMAA(Q,1) HSDPAA(F,1) CDMAA(F,1) HSDPAS(N,1) CDMAS(N,1) HSDPA

0 0.2 0.4 0.6 0.8 10

0.02

0.04

0.06

0.08

0.1

0.12


B l o c

k i n g p r o

b a

b i l i t y

f o r s

t r e a m

i n g

f l o w s ,

p s


Fig. 5. Blocking probability for elastic (left) and streaming requests (right) vs nor-malized offered elastic load obtained for neutral regime ( J =1).

0 0.2 0.4 0.6 0.8 10

2

4

6

8

10


E x p e c

t e d n u m

b e r o

f e

l a s

t i c

f l o w s ,

E [ N

e ]


0 0.2 0.4 0.6 0.8 10

0.5

1

1.5

2

2.5

3

3.5


t r e

t c h o

f e a c h a

d m

i t t e d e

l a s t

i c f l o w , S

e ( s e c

/ M b i


Fig. 6. Number of active elastic requests (left) and stretch of each admitted elastic

request vs normalized offered elastic load obtained for neutral regime ( J =1).5.3 Impact of location-awareness (HSDPA model)

Next, we investigate the performance gain achieved with location-awarenessby comparing the performance obtained for the HSDPA model with variousdegrees of location quantization, J . We dene each segment j as the annulusbetween concentric rings of radius j 1 and j such that j = jJ J , 1 j J .Since user arrivals are uniformly distributed over the cell, their arrival rate ineach ring j is j =

2j 2j 1

2J

, where 0 = 0.

5.3.1 P=20W

We plot ( pe , ps ) and (E[N e], S e) as a function of the traffic mix, u ec , 0 ue c, for S(N,J) in Fig. 7 and 8 respectively for J =1, 2 and (correspond-ing to the case of exact location information) for a neutral traffic regime. Weobserve that the cell performance obtained with simulation is lower bounded(well approximated) by A(F,J=1) (A(Q,J=1) ), and that S(N,J) is almost

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invariant with the value of J . Hence, no signicant performance gain is achievedthrough exploiting more accurate location information in this case, and there-fore, the performance can be approximated using location-unaware approxi-mations ( J =1).

0 0.2 0.4 0.6 0.8 10

0.02

0.04

0.06

0.08

0.1

0.12

0.14


B l o c

k i n g p r o

b a

b i l i t y f o r e

l a s

t i c

f l o w s ,

p e

A(Q,J=1)A(F,J=1)S(N,J=1)S(N,J=2)S(N,J= )

0 0.2 0.4 0.6 0.8 10

0.02

0.04

0.06

0.08

0.1

0.12

0.14


B l o c

k i n g p r o

b a

b i l i t y f o r s

t r e a m

i n g

f l o w s ,

p s


Fig. 7. Blocking probability for elastic (left) and streaming requests (right) vs nor-malized offered elastic load obtained with approximation and simulation for HSDPAmodel (J =1,2, , P=20W, neutral regime).

0 0.2 0.4 0.6 0.8 10

0.5

1

1.5

2

2.5

3


E x p e c

t e d n u m

b e r o

f e

l a s

t i c

f l o w s ,

E [ N

e ]


0 0.2 0.4 0.6 0.8 10

0.5

1

1.5

2


t r e

t c h o

f e a c

h a

d m

i t t e

d e

l a s t

i c f l o w ,

S e

( s e c /

M b i


Fig. 8. Number of active elastic requests (left) and stretch of each admitted elasticrequest vs normalized offered elastic load obtained with approximation and simula-tion for HSDPA model ( J =1,2, , P=20W, neutral regime).

5.3.2 P=0.2W

In order to demonstrate the performance gain with exploiting user location, werepeat the simulations for the case of P = 0.2W, and plot ( pe , ps ) and (E[N e],S e) as a function of the traffic mix, u ec , 0 ue c, for S(F,J) in Fig. 9 and10 respectively. In this case, we note that as cell partitioning becomes ner(increasing J ), the performance obtained with S(F,J) is improved signicantly(e.g., reduced blocking and sojourn time).

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0.2 0.4 0.6 0.80

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16


B l o c

k i n g p r o

b a

b i l i t y

f o r e

l a s

t i c

f l o w s ,

p e S(F,J=1)S(F,J=2)S(F,J= )

0.2 0.4 0.6 0.80

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16


B l o c

k i n g p r o

b a

b i l i t y

f o r s

t r e a m

i n g

f l o w s ,

p s

S(F,J=1)S(F,J=2)S(F,J= )

Fig. 9. Blocking probability for elastic (left) and streaming requests (right) vs nor-malized offered elastic load obtained with simulation for HSDPA model ( J =1,2, ,P=0.2W, uid regime).

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

0.5

1

1.5

2

2.5


E x p e c

t e d n u m

b e r o

f e

l a s

t i c

f l o w s ,

E [ N

e ]

S(F,J=1)S(F,J=2)S(F,J= )

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

0.5

1

1.5

2

2.5


t r e

t c h o

f e a c

h a

d m

i t t e

d e

l a s

t i c f l o w ,

S e

( s e c

/ M b i

S(F,J=1)S(F,J=2)S(F,J= )

Fig. 10. Number of active elastic requests (left) and stretch of each admitted elasticrequest vs normalized offered elastic load obtained with simulation for HSDPAmodel (J =1,2, , P=0.2W, uid regime).

6 Conclusions

Third generation wireless systems can simultaneously accommodate users car-rying widely heterogeneous applications. Since resources are limited, particu-larly in the air interface, admission control is necessary to ensure that all ac-tive users are accommodated with sufficient bandwidth to meet their specicQuality of Service requirements. We propose a general traffic managementframework that supports differentiated admission control, resource sharingand rate allocation strategies, such that users with stringent capacity require-ments (streaming traffic) are protected while sufficient capacity over longertime intervals to delay-tolerant users (elastic traffic) is offered. This frame-work permits users within each type to be distinguished according to theirdistance from the base station through cell partitioning, and also supports atime-sharing resource sharing mode to improve rate allocation to elastic trafficwhile guaranteeing the capacity requirements of all users.

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Since the exact analysis to evaluate the performance of such an integratedservices system is non-tractable in general, we dene extreme traffic regimes(quasi-stationary and uid) for which time-scale decomposition can be appliedto isolate the traffic streams, from which known results from uid queueingmodels are used to approximate the performance for each user type. For theextreme traffic regimes, simulation results suggest that the performance is al-most insensitive to traffic parameter distributions, and is well approximatedby our proposed approximations. In addition, we also demonstrate the per-formance gain achieved by exploiting location information about each user,as well as applying time-sharing amongst elastic users to improve their rateallocation.

7 Acknowledgments

The support of Vodafone is gratefully acknowledged. This research is partiallysupported by the Dutch Bsik/BRICKS project and is performed within theframework of the European Network of Excellence Euro-NGI. Much of theresearch was performed while Adriana F. Gabor and Hwee-Pink Tan wereaffiliated with EURANDOM.

References

[1] H. Holma and A. Toskala, WCDMA for UMTS, Radio access for third generation mobile communications . John-Wiley and Sons, 2001.

[2] Y. Wang and T. Ottosson, Cell search in W-CDMA, IEEE Journal on Selected Areas in Communications , vol. 18, 2000, pp. 14701482.

[3] P. Key, L. Massoulie, A. Bain, and F. Kelly, Fair internet traffic integration:network ow models and analysis, Annales des Telecommunications , vol. 59,2004, pp. 13381352.

[4] T. Bonald and A. Proutiere, Insensitive bandwidth sharing in data networks,

Queueing Systems , vol. 44, 2003, pp. 69100.[5] F. Delcoigne, A. Proutiere, and G. Regnie, Modeling integration of streaming

and data traffic, Performance Evaluation , vol. 55, 2004, pp. 185209.

[6] J. W. Cohen, The multiple phase service network with generalized processorsharing, Acta Informatica , vol. 12, 1979, pp. 245284.

[7] N. Benameur, S. B. Fredj, F. Delcoigne, S. Oueslati-Boulahia, and J. W.Roberts, Integrated admission control for streaming and elastic traffic,Lecture Notes in Computer Science , vol. 2156, 2001, pp. 6981.

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[8] R. Nunez-Queija and H. P. Tan, Location-based admission control fordifferentiated services in 3G cellular networks, Proc. of the 9th ACM-IEEE MSWiM , 2006, pp. 322329.

[9] T. Bonald and A. Proutiere, On performance bounds for the integration of elastic and adaptive streaming ows, Proceedings of the ACM SIGMETRICS / Performance , 2004, pp. 235245.

[10] O. J. Boxma, A. F. Gabor, R. N unez-Queija, and H. P. Tan, Performanceanalysis of admission control for integrated services with minimum rateguarantees, Proc. of 2nd NGI , 2006, pp. 4147.

[11] R. Nunez-Queija, J. L. van den Berg, and M. R. H. Mandjes, Performanceevaluation of strategies for integration of elastic and stream traffic, Proc.ITC 16 , 1999. Eds. D. Smith and P. Key. Elsevier, Amsterdam, pp. 10391050.

[12] T. Bonald and A. Proutiere, Wireless downlink data channels: Userperformance and cell dimensioning, Proc. of the ACM MOBICOM , 2003,pp. 339352.

[13] P. Key and L. Massoulie, Fluid Limits and Diffusion Approximations forIntegrated Traffic Models, Technical Report MSR-TR-2005-83, MicrosoftResearch, June 2005.

[14] R. Nunez-Queija, Processor-Sharing Models for Integrated-Services Networks .PhD thesis, Department of Mathematics and Computer Science, EindhovenUniversity of Technology, 2000.

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