Connection Admission Control for Flow Level QoS in Bufferless Models

Sindor R ~ c z , Tanxis Jakabfy, Jinos Farkas and Csaba Anta1 Traffic Analysis and Network Performance Laboratory

Ericsson Research Budapest, Hungary

{ Sandor.Racz, Tarnas. Jakabfy, Janos.Farkas, Csaba.Anta1) @ericsson.com

Abstract- Admission control algorithms used in acces net- works for multiplexed voice sources are typically based on aggregated system characteristics, such as aggregate loss proha- Mi@. Even though the relation of these aggregate performance measures to the performance of specific flows is not trivial, it has gained limited attention so far. We propose an admission control method that provides flow level QoS guarantees. The proposed method is based on Gaussian approximation applied for the bufferless multiplexing model. We show that the flow level packet loss violation probability can be approximated as the quantile of a normal distribution and we give a method to calculate its mean and variance. The obtained admission control formula includes the moments of the activity factor distribution.

I. INTRODUCTION

The most important design objectives of connection admis- sion control algorithms are fast execution time and conserva- tive but accurate operation. The prerequisites of fast algorithms are simplicity, both in terms of traffic model and applied queuing model. Even with simple models, approximations are required to get a feasible algorithm. The cost of simplicity, however, is often reduced accuracy.

Admission control mechanisms are crucial in networks carrying delay/jitter sensitive traffic, The most important real- time application for operators is undoubtedly voice. Voice over IP service is provided by both fix and mobile networks. Even though admission control is not needed in the backbone due to the high transmission speed and the applied dimensioning methods, it is still important to control admitted traffic in access networks.

In the analysis of aggregated voice sources, a generally accepted traffic model is the periodic O N - O ~ source model. Voice coders generate packets periodically when the speaker is talking; and silence suppression algorithms (or voice activity detection) are used to detect silent intervals when only silence indication packets are sent with much less frequency. A simple and efficient queuing model for ON-OFF sources is bufferless multiplexing, which is applicable when the buffers are small so queuing at ON-OFF time scale can be neglected, but they are large enough to avoid packet scale queuing effects [11. It is intuitively clear that bufferless multiplexing j s a reasonable modet for aggregated voice sources because strict

delay and jitter requirements usually motivate short buffers and the multiplexing gain due to large buffers is rarely significant.

QoS requirements for bufferless multiplexing, which are necessary input to admission control algorithms, can be based on packet loss probabihty for the total traffic aggregate. In some papers f i e workload loss ratio is calculated directly [23, but it i s even more general to approximate packet loss prob- ability by the system saturation probability [21-[61. Previous analytical results on bufferless model are summarized e.g. in [61.

Calculation of aggregate loss probability for bufferless mul- tiplexing allows many simplifications in the traffic description, The distribution of the duration of ON and OFF periods can be arbitrary. Furthermore, it is sufficient to provide the ratio of ON and om periods, their separate characterization is not required. A common descriptor to characterize ON-

OFF sources is the activity factor [71. Activity factor is defined as the ratio of the total duration of ON periods and the total lifetime of the flow. In case of voice connections, the activity factor means the portion of time when the speaker is busy talking if voice activity detection algorithms operate optimally. The activity factor of a flow depends on several e'ifects and it can vary flow by flow. However, if aggregate loss requirement is applied these variations even out, so a constant activity factor, which typically takes values from 0.4-0.6 [SI, [9], provides a sufficient characterization of voice sources.

Even though the aggregate loss requirement makes analytic work tractable, it fails to provide flow level QoS assurances. As admission control is designed for aggregate loss requirement, the loss rate of individual flows may violate their requirement even if they are admitted by the admission control. A specific example for such violation is due to the varying activity factor of voice sources [lo], [ll]. There may be time intervals when the activity factor of many ongoing flows is larger than the average activity factor. Flows in these periods will experience high loss.

The goal of this paper is to define a new QoS requirement and a related admission control algorithm that reflects the gen- eral need of providing flow level QoS assurances. Due to the new problem formulation, the applied traffic model has to be revised as well. We assume that the ON-OFF operation of voice sources is characterized solely by the activity factor, but we

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consider its random nature when designing the new connection admission control algorithm. Our proposed algorithm is based on Gaussian approximation applied for bufferless systems [61, extending it to guarantee flow level QoS. The new method considers the variance and higher order statistics of the activity factor.

The rest of the paper is structured as follows. The related work is presented in the next section. We describe the con- sidered system and its model in Section 111. In Section IV, we introduce the flow level QoS measure and propose a cor- responding connection admission control algorithm. Section V shows an exampIe application of the proposed results in a UTRAN system. Finally. in Section VI we conclude the paper.

11. RELATED WORK

Methods related to effective bandwidth [61 and network calculus [12] are extensively studied in the literature for determining capacity need of flows in QoS enabled packet networks. The effective bandwidth expression describes the minimum bandwidth that is needed to fulfill the QoS criteria of the flow. The effective bandwidth, which is between the average and peak rate of the flow, IS generally used in tiadi- tional dimensioning and admission control methods. Effective bandwidth was determined for many traffic types, for example periodic sources, fluid sources, ON-OFF sources [61. The network calculus also determines the capacity need of flows in a packet network [12]. In the network calculus method, rate envelopes ai-e used for packet arrivals and services in the network. The deterministic network calculus is a worst- case analysis method, which gives upper bounds for packet delay. By introducing stochastic bounds for packet delay, which slightly weakens the QoS requirement. better network utilization can be achieved. Stochastic network calculus was proposed to solve this problem (see e.g. [13]).

Li. Burchard and Liebeherr established a link between effec- tive bandwidth and network calculus in [141. They showed that a general formulation of effective bandwidth can be expressed within the framework of stochastic network calculus, where both arrivals and service are specified in terms of probabilistic bounds. In [lS]. the authors determined stochastic bounds for the service experienced by a single flow when resources are managed for aggregates of flows. Using statistical network calculus, per-flow bounds are calculated for backlog, delay, and the burstiness of output traffic.

The above techniques were developed for the analysis of a wide variety of systems, However, they do not exploit all information that we assume to be available in a voice-only system or in a multi-service system where voice service has differentiated treatment, for example in a DifBerv IP network. In this paper, we utilize traffic and system properties of voice services. Beside the periodic ON-OFF structure of flows, strict delay requirement and short buffer we also consider the random nature of activity factor of flows.

Measurement and analysis of ON-OFF parameters of voice sources have been the subject of research, especially in relation to mobile communication systems. In [ll], the distribution

of voice activity factor is presented based on measurements performed in a GSM network. Jiang and Schulzrinne measured and analyzed the distribution of ON and OFF durations of voice flows in a VoIP system [16]. Jug1 and Boche 1173 also took into account the fluctuation of voice activity factor in order to calculate the capacity of the air interface in CDMA based systems. They modeled the activity factor of users as a uniform disuibution and showed that the fluctuation of activity factor affects the performance of the air interface. Measurement based analysis was also carried out to find the sources of the fluctuation of the activity factor. The activity factor of a flow depends on the user behavior and also on the applied transport protocol. Furthermore, in case of voice connections it also depends on the voice activity detection algorithm and on the operation of voice coders [16], [IS]. Regarding user behavior the sex of the speakers, their language and personality also affect the activity factor 191, [19]. Sun and Ifeachor [20] studied the effect of these differences on the perceived voice quality in IP networks.

111. SYSTEM AND MODEL DESCRIPTION

The subject of the paper is a FIFO queue fed by periodic ON-OFF sources. Firstly, we describe the parameters of the studied system; we then give the characterization of traffic sources. Finally, we introduce the flow level quality of service requirement to be applied at the development of the admission control algorithm and we describe the model of the system.

The FZFO'server is characterized with capacity C' and a buffer of length B. Packets of ON-OFF sources are character- ized with a constant packet size b. Periodic ON-OFF sources generate packets with a deterministic inter-arrival time T in state ON. also called as source period; and they do not generate any packets in state OFF. In most practical cases, the duration of ON periods of ON- OFF sources are independent, so we assume this property in the analysis,

The random activity factor of flow i is denoted by at and the common distribution function of activity factors is F ( z ) . The activity factors are assumed to be iid random variables. For example, Westholm and Olin provide the distribution of the activity factor in 1111 based on measurements of voice sources in a GSM system (E la] = 0.58) and the distribution of ON and OFF period lengths. An example system is illustrated in Fig. 1, where call

arrivals and departures are marked by vertical lines and packet arrivals are marked by small bars. In this system, a call admission control algorithm limits the maximum number of parallel flows to N = 4. As mentioned above, the actual value of the activity factor can be different for each flow. For example, the activity factor of flow4 is close to 0.6, which means that the source sends packets during 60% of the duration of flow-I. However, the activity factor of flow-J' is close to 0.9, meaning that the source almost always sends packets.

After the definition of how the system works, the next step i s to introduce the flow level quality of service requirement.

periods and the duration o€ OFF

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Fig. 1. An example system: the maximum number of parallel flows is 4

We assume that the system that we study has a strict delay requirement D. That is, all packets that have longer delay than D are dropped at the receiver. Under these circumstances a packet is dropped if the buffer is overflown or if it suffers longer delay than D in the buffer.

The per flow QoS requirement can now he defined as a per flow packet drop requirement, denoted by E, considering dropped packets both i n the FIFO buffer and in the receiver.

The fraction of dropped packets depends on the number of parallel flows. In generaI. it increases if the number of parallel flows increases, as Fig. 2 shows. In order to get a conservative admission control that operates independently of the call arrival rate, we must assume that the number of flows in the system is always the maximum allowed by the admission conlrol. i.e. the system is always fully loaded.

The fraction of dropped packets also depends on the activity factors of ongoing flows even in a fully loaded system. The activity factor can take any value in (0, 1) interval in practi-

65

60

---E 55 I e 50 "6

a

L I n

D 0% !4c 0 10 20 30 40 50 80 70 80 90 1W 110

time [sec]

Fig. 2. Fraction of dropped packets of a Bow: N = 61, T= 20ms. D= 8ms, B= Ems, C=6721;bps, b=336bit. F ( x ) = Uniform(O.l,0.9)

cal cases [l 11. Therefore, if packet loss rate was required to be less than E for all flows then we would need to calculate with an activity factor of 1 for each flow in the admission control. However, this would inherently exclude any gain from the multiplexing of voice sources. As a reasonable compromise, we assume that the d probability of the violation of the E packet drop rate requirement is small.

Finally. the parameters of the studied system are summa-

Our system model is as follows. We study a bufferless multiplexer with capacity of serving Z = CT/b packets in a source period. which multiplexes Ar ON-OFF soitrces wilh random activiry fucror. If more packets arrive in a source period T than the system capacity 2 then all packets are considered lost, which is a worst case assumption that is vafid when the buffer size B is lager than the delay requirement D. We allow arbitrary activity factor disfribution. The parameters used in the model are summarized in Table 11.

rized in Table I.

TABLE I SYSTEM PARA METERS

c B N D

6 5

ai b T -

System descriptors server capacity kbps size of the buffer ms max number of admitted ON-OFF sources packet delay requirement m S max allowed packet drop rate probability of not fulfilling drop requirement Descriptors of individual sources random activity factor; cli - F ( s ) packet size bit packet inter-arrival time (source period) ms

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TABLE I1 PARAMETERS O F THE MODEL

System descriptors 2 = CTjb server capacity N max number of admitted ON-OFF sources

5 E max allowed packet drop rate

probability of not fulfilling drop requirement Descriators of indwidual sources

a, random activity factor: ai - Frzci

Iv. ADMISSION CONTROL ALGORITHM FOR FLOW LEVEL Q O S GUARANTEES

Analysis of models where the traffic descriptor, which is the activity factor in our case, is also random can be performed according to the law of total probability. As a first step a QoS hnction is evaluated under the condition of fixed activity factors. Using the density function of activity factors we can remove the conditioning and obtain the probability 6 of QoS violation.

Accordingly. we firstly derive a &OS function that indicates whether the fraction of dropped packets is below E assuming fixed values of random activity factors cy1 = a l , . . . = U,V for the ongoing flows

0, fraction of dropped packets is below E; &(ai, . . . , a ~ ) = { 1, otherwise.

That is, QoS violation is indicated by Q = 1. In the next step, we can take into account the randomness

of the activity factor. Denote f(q, . . . , U N ) the joint density function of the random activity factors. The probability that the system does not provide flow level QoS requirement for any of the ongoing flows can be calculated as follows:

6 = 1 Q(a1,. . . ,UN) f(a1,. . . , a r ~ ) d a . l . . .da,v. ( I )

In the following two subsections, we propose a method to evaluate the value of 6. In Section IV-A, we present an accurate QoS function based on Gaussian approximation [6] . We then provide a method to evaluate efficiently the integral in (1) in Section IV-B.

A. Evaluating QoS function for @xed activity factors

the fraction of dropped packets is fulfilled if:

a1 v . . . r4N

According to the bufferless model, the QoS requirement on

(2)

which is the QoS defined on aggregation of flows. The distribution of the number of sources in state ON de-

pends on the values of the activity Factors. Denote ai the constant activity factor of source i . The distribution of the number of sources in state ON follows the sum of N independent Bernoulli random variables with parameter ai, i.e.

P[the number of sources in state ON 1 21 5 E ,

P[the number of sources in state ON 5 Z] =

(3)

where X, is a Bernoulli random variabIe with parameter p . The calculation of the distribution of the sum of Bernoulli

random variables was extensively studied in the literature. Two well-known approximations of the sum in (3) are the Chernoff bound and the Gaussian model [61. In this paper. we use the Gaussian approximation, which applies the central limit theorem and approximates the sum of the Bernoulli random variables with normal distribution. This means that

\ i= 1

t4)

Finally, we can define the QoS function Q , which indicates whether the fraction of dropped packets is below E, as follows:

0 dthenvise, (5)

where the a(.) and W 1 ( x ) denote the standard normal distribution function and its inverse. The +(z; p: g2) denotes the distribution function of a normally distributed random variable with mean p and variance r2,

B. Evaluating QoS function for random acrivig factors We now provide the second step of the analysis. In this step,

we take into account the randomness of the activity factor. The random activity factors of N sources al, . . . a, are iid random variables. The value of the flow level QoS measure S can be obtained by substituting (5) into (1) and using the joint density function of the activity factors:

The direct calculation of 8 is very complicated and results in very complex formula even for small values of N . This motivates the application of an accurate and fast approximation o f 6 .

Before we derive an admission control algorithm for general distributions of the activity factor, we show an illustrative example far the above equations. Let us consider an example system multiplexing N = 50 connections and having capacity 2 = 40. Let E be 0.1%. The activity factors of the connections are independent and identically distributed Bernoulli variables: Xa,. Let the ai parameters have the following distribution:

P [ai = 0.41 = IP [ai = 0.61 = 0.5

Applying (3) and (4) for the case when the activity factor of all connections equals to 0.4 we get

Packet drop probability = 1 - P [E Xo.4 5 401 x

40 - 50 x 0.4 =:

50 x 0.4 x 0.6 2 1 - @

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If -39 connections have an activity factor of 0.6 then

flows still fulfill the drop requirement. However, if 30 connections have the larger activity factor then P [ ~ 0 . 6 + ~ 0 . 4 ) 2 401 = 0.12%~ so flows vioIate the drop requirement. Ohviousty. if even more connections have an activity factor of 0.6 then the drop requirement cannot be fulfilled. For example, if all connections have the larger activity factor (0.6) then B

B [ (x::~ x0.6 + z::so xO.4) 2 401 0.10%, SO

XO.6 2 401 w 2.96%. Calculating ( 5 ) we get that

Q (ai!. . . ~ 0 5 0 ) = 1, if #(ai = 0.6) 2 30.

That is, the packet loss requirement is not met if more than 29 sources have an activity factor of 0.6 (and the rest have activity lactor of 0.4).

Now d can be calculated based on (6) and (1). The proba- bility of each particular realization in case of our example is F , e.g. p [ a l = 0.4,. . . ~ a 5 0 = 0.4) = 6. n u s 1

6 = pial al ,a2 a?, . . . ,050 = 0401 x Q l I,. @SO

& ( a l > a z , . . . .a50) = - 2ko (ii) = 4.2%.

Thus, the probability of the violation of the 0.1% drop requirement is 4.2%.

We now proceed to the calculation of 6 for general distri- bution of the activity factor. For the sake of easier calculation

of 6 let us introduce Y = ~ ~ - . We derive 6 in

the following steps: We show that J' is normally distributed independently of

We determine the expected value and the variance of Y

and calculate b = P [Y 2 @-'( 1 - E ) ] .

Z - E,"_, ai

E;:, Oi(l - ai)

the distribution of activity factors;

using the first moments of the activity factor;

The following two lemmas give the formal description of the above described solution method.

z - c , " = , ~ i Lemma 1: The distribution of Y = 4zzZFz follows a normal distribution with negligible error. Sketch ofthe Proof.- The derivation has three steps:

N The random variables a.i and ai(l - ai) are

The random variable F ai( 1 - ai) is also normally

The ratio of two normal random variables approximately

The first step directly follows from the central limit theorem. The proof for the second step is described in Appendix in detail. The ratio of two correlated normal random variables, in our case the numerator and the denominator of y , is studied in 1211. Hinkley examined the exact: distribution and showed that

normally distributed for lar e N ;

distributed;

follows a normal distribution too.

a normal approximation can be applied when the denominator is greater than zero even if the numerator and denominator are correlated. Applying these results we obtain the lemma. [3

Lemma 2: The first and the second moments of Y can be calculated as infinite Taylor:

where pi and o2 denote the i-th moment and the variance of the activity €actor, and

Z - N U A(Q) =

J-

1 _ - 9 (2 - N a ) ( l - 2a) (Na(1 - u))312 2 ( N a ( 1 -U))$/? .

3

Higher coefficients of the Taylor series can also be calculated, due to Iack of space we do not present them here.

ProoJ First, we determine the Taylor expansion of the function

f (x l , . . . , XN), which is defined as follows:

This function is symmetric in z l , . I ~ , ZN and takes 00 if at least one of the zi is 0 or 1. The symmetric property makes the Taylor expansion easy. The structure of the Taylor expansion of f (XI,. . . , Z N ) around 11 = a,. . . ,XN = a is the following:

i= 1 N

C(a) (Zi - + D ( a ) 1 (Xi - a) (Zj - 0.) -t i=l i#3

N

E ( a ) (Zi - a ) 3 + F ( a ) (Xi - U)' (23 - a ) +

I277

and the value of the coefficients is as follows: A(a) = f ( ~ ! . . . , C L )

2.5 1

Evaluating this we get the formulae of the statement. Now we provide the Taylor expansion of the hnction

f 2 (XI ! . . . ,SA,) around 2 1 = a , . . . ,ZN = a. The firs1 terms of tne Taylor expansion are the following:

N

f 2 (XI,. . . , ZN) = A'(.) + 2A(a)B(a) (zi - U ) -k i=1

N 2 [B2(u) + ZA(a)C(a)] (Xi -a) +

i= 1 N

[2A(a)D(a) + B'(Q.)] F, (Zi - a ) (zj - a) -t

7 y (.a - a)' (Zj - a) + f = l ifJ

Now we apply the function f (z l , . . . , Z N ) to the random activity factors. Denote p1 the expectation value and U' = ,U? - p: the variance of the random activity factors a,, i = 1,. . . : N . We calculate lE[ f (a l , . . . : C Y N ) ] using the Taylor expansion of the function f ( X I , . , . , ZN):

A(p1) + C(p1)No' + E(p1)A-E [(a - pi)3] + . . . Similarly, the second moment of ~ ( c Y I , . . . , a ~ ) can be

calculated as:

= A2(pi) + [B2(pi) + 2-4(pi)C(pi)] N o 2 + [2A(pi)E(p1) +2B(m)C(p1)1 [(e - p1I3] +. . .

m Two example distributions of the activity factor are used

to illustrate the numerical properties of the proposed method. The first one is a measured GSM speech activity distribution published in i l l ] and depicted in Fig. 3. The second one is the uniform distribution family with various parameters.

I o 0.1 0.2 0.3 04 o 5 0.6 07 0.8 0.9 1

Activity laclor of GSM speech

Fig. 3. measurements

Density function of activity factors of GSM speech based on

In Fig. 4, the distribution of cr is according to GSM speech measurements [ll], while in Fig. 5 it is uniform over the interval [0.48,0.68]. Fig. 4 and 5 illusrate that the distribution of Y is close to a normal distribution even for small value of Ar ( N = 10). Our proposed distribution is also shown in the figures. The fitted distribution is a normal distribution with expected value and variance got from the exact distribution. It is seen in Fig. 5 that the proposed and the fitted distribution run together very close to the exact distribution. The GSM speech activity factor distribution is spread over much wider interval than the examined uniform distribution, which causes tbe small difference between our proposed and the exact distribution in Fig 4. However, the exact and the fitted distributions run together in this figure, which illustrates that J' has normal distribution.

Note that Fig. 4 and 5 illustrate the accuracy of the proposed method for N = 10. For larger N the error is even smaller.

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

n 0.5 1 1.5 2 2.5 3

Fig. 4. shown in Fig. 3, N = 10, Z = 8, E = 0.001

Distribution of y : activity factors have the GSM speech distribution

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0.9 ~ Exact distribution I..........

0.8 - Proposed distribution ~

Fitted distribvt!on +

07 - - F3 0 6 -

vj 0.5 -

0.3

0.2

~

-

1 1 1 1.2 1.3 1.4 1 5 X

Model naramiera

L

1.5

wfr& higher- delay {han a predefined target delay value should be less than E

ity EaStors of c c k c t i o n s we ”selected” E U C ~ that the ag- sregated QoS requirement is violated should be less than d

AT r

I

1.6 : 1.7 1.8

Fig. 5. Distribution of y : a - U(0.48.0.68), N = 10. Z = 8, E = 0.001

C. nie proposed connection admission control algorithm

Applying the results of the previous sections, the new admission control algorithm can be defined. Firstly, the input parameters of the admission control algorithm should be determined. As Table 111 shows, the activity factor should be characterized by its mean, variance and the third moment of the distribution, i.e. p1, 0’ and p3. To determine these parameters measurements are required, or the distribution published in [l 11 can be used. The remaining input parameters are the drop requirement E , the allowed violation probability 6 of this requirement and the system capacity Z, which all are fixed system parameters. The only variable input of the admission control is the number of actual connections N .

Once ihe input parameters for the flow level admission control are determined, we are ready to define the real- time part of the algorithm. The admission control algorithm should calculate the probability of larger drop rate than the requirement at the actual number of flows. If it is larger than its allowed maximum then the new connection is blocked, otherwise it is admitted. The actual probability of drop rate violation, d ~ , can be calculated according to (6) and using the results proposed in Lemma 1 as follows:

6 N =I- ib (@-1 (1 - €) ; p = E [Y] , 2 = E [YZ] - IE [Y]2) . (7)

The expected value and variance of Y shodd be determined based on Lemma 2. If d~ < 6 then the QoS decision is ”Accept”, otherwise it is ”Reject”.

p*

TABLE III COMPARISON OF THE MODELS

1 Aggregation level model I Flow level modci QnSmasure I Th e probability that a packet I The probabilitv that activ-

- . - , . .. . ..

QoS input I E E , d Activitv desc. I UI I I , , . IT1 I , ? I , -. , F. , - . r*

output 1 Accepi or Relect I

The proposed admission control has fast execution time because the obtained formuIa includes only basic operations.

Table I11 also shows the parameters of the usual aggregated QoS models id addition to the proposed flow level model. The admission criteria for fulfilling the aggregate QoS requirement using Gaussian approximation is expressed in [6] (see (3.13)). It has the following form with our notations:

This expression reinforces our previous statement that activity factor is considered only with its mean value in the aggregate QoS model.

It is interesting to see the daggr probability of violating the packet loss requirement E if h e aggregate admission control algorithm is used by the same E setting. The probability c5aaggr can he obtained from (7) by substituting E from (8) assuming equality:

daggr = 1- @ (0; p = E [Y] - A (pi), 6’ = IE [Y’] - E [J’]’) ,

where A ( p L 1 ) is defined in Lemma 2. If E[Y] equaIs to the first term of its Taylor series A ( p 1 ) then Jaggy = 50%. which means that flows violate the drop requirement with 50% probability.

Now we show for two sample activity factor distributions how the capacity requirement changes i f we change the number of multiplexed sources and the value of 6 .

Table IV and Table V show the capacity requirements if the system has to carry N multiplexed voice flows. In Table IV uniform activity factor distribution over (0.2-0.8) is used. Table V belong to the case when the activity factor distribution is based on measured GSM speech. The packet drop requirement E = 1% and the 6 probability of violating packet drop requirement runs from 0.001% to 50%.

We can see that the results of the two tables are similar. We found that the small difference between the two tables can be attributed to the different mean values of the activity factor distributions (0.5 in Table IV: 0.58 in Table V). For example, if N = 40 and d = 50% then the difference is 3 units.

The capacity requirement significantly changes if small d values (< 1%) are used instead of the d = 50% setting. For

TABLE rv CAPACITY REQUIREMENT FOR N SOURCES WITH UNIFORM ACTIVITY

FACTOR DISTRIBUTION OVER 0.2-0.8 AND E = 1%

Unifo

N=20 N=40 N=60 N=80

N=100 N= I20 N=140 N=lM) N=180 N=2M

Ily dstributed activity factor over 0.2-0.8 6

50% 1% 0.170 0.01% 0.001% 15 17 17 18 18 27 30 30 31 31 39 42 42 43 43 50 53 54 55 55 61 65 66 67 67 73 76 77 78 79 83 87 89 89 90 94 99 1 0 0 101 102 105 110 111 112 113 I16 I21 122 123 124

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TABLE V CAPACITY REQUIREMENT FOR N SOURCES WITH ACTIVITY FACTORS

DiSTRlBUTlON BASED ON MEASURED GSM S P E E C H A N D E = 1%

I GSM soeech activitv factor distribution I

N=20 X=40 N=60 N=XO N=100 N=120 N=140 N=160 N=180 N=200

b 50% 1% 0.1% 0.01% 0.001% 17 18 19 19 19 30 33 33 33 31 44 46 47 47 48 56 59 60 61 61 69 73 73 74 75 82 86 87 87 88 94 98 100 I00 101 107 111 112 113 114 119 121 125 126 127 132 137 138 139 140

example, if N = 200 and 6 changes from 50% to 0.001% then the difference is 8 units at both activity factor distributions.

Fig. 6 shows the plot of 6 against the variance of activity factor at three capacity values (2 = 40;41:42). The activity factors in different cases have the same expected value (0.5) and they have uniform distribution in different ranges. The figure shows that higher vanance of the activity factor causes larger 6 value, i.e. more capacity is needed to achieve the same QoS. For example, if the variance grows from 0.003 to 0.03 then 6 increases from 0.8% to 9.3% at 2 = 40.

V. APPLICATION

Our results can be applied for example in Universal Mobile Telephony System (UMTS), of which architecture is illustrated in Fig. 7.

A UMTS network consists of three main components: Care Network (CN). UMTS TerrestriaI Radio Access Network (UTRAN) and User Quipment (UE). Core network provides switching, routing, management functions and Uansit for user traffic, A Node B of UTRAN terminates the air interface and forwards the traffic to the Radio Network Controller (RNC). Voice connections then enter the core network via a Media

j ' j 0 0.005 0.01 0.015 0.02 0.025 0.03

Variance of the aclivityfaclor

Fig. 6. uniformly distributed and N = 60. E = 0.1%

6 probability vs. the variance of activity factor. Activity factor is

Fig. 7. UMTS architecture

Gateway (MGW). They are terminated for example in a PSTN after leaving CN as shown in the figure.

UTRAN is an access network for which our results can be applied directly, for example for the lub interface which is the interface between the RNC and the Node B. The radio protocols that are used to convey the data flows re- sult in deterministic inter-arrival times with random offsets between packets transferred through the lub interface. The delay requirement of packets is strict and typically below the packet inter-arrival time which is 20 m s in the case of voice connections. A voice packet has approximately 5 -8 ms delay requirement in UTRAN [22] . This strict delay requirement has to be cut back by the transmission delay and h e remaining part can be the queuing delay. The queuing delay is small enough that only a buffer with length of some nas worth to be used. The strict QoS requirement allows us the application of bufferless models at ON-OFF time scale as explained for example in [23], [241.

In this section, we investigate the effect of the application of the proposed method in UTRAN. For this purpose the activity factor distribution of [I 13 is applied. This distribution is displayed in Fig. 3.

Fig. 8 shows the capacity need of a Aow versus the number of flows for different values of 6. The loss requirement is E = 0.001. In the aggregated QoS case the activity factor is constant (0.58), which is the mean of the GSM speech distribution. This case is shown by dashed line in the figure,

1 ,

l i

.. 0 50 1Do 150 200 250 300

Numberofflows (N)

Fig. 8. Effect of difference in QoS requiremenls: c = 0.001

1280

where (2) gives the QoS requirement. The two other lines show the predefined ow level requirements, i.e. 6 = 50% or 6 1%. The jumps in these curves are due to the fact that the result

[4] G. Mao, D. Habibi. "Loss performance analysis for heteropzneous On- Off sources with application to connection admission controL"IEEEL4CM Tmmucsions OPT Netwurkzng, d. 10. no. 1, February 2092.

[51 A. M. Makwski. "Bounding on-mf sources - variability ordering and majorization to the rescue:' %chicut research repnrf. 2001.

when the flow level Q ~ S is considered

is calculated as the ratio of two integer numbers (Z IN) . It can be seen in the figure that the ignorance of flow Ievd

QoS practically gives the same results as setting 6 = 50% in the flow level model. That is, if aggregate QoS measures are considered only then practically half of the OMIS IS do not meet rhe requirement. Setting 5 = 1% means that 99% of the flows have to fulfill the QoS requirement. The uppermost curve shows the results for this setting. It can be concluded from the figure, that the capacity requirement of a flow increases slightly, but the majority of the flows meet the requirements.

These results show that the application of flow levet QoS is needed in call admission control in order to ensure that most of the flows fulfill the QoS requirements. Our proposed method can be easily implemented in existing admission control algorithms in UTRAN.

VI. CONCLUSION The aim of our work was to deveIop an admission control

[6 ] E P. Kellj-, "Notes on effective bandwidths." Stochartic Networks: 77teov and .4pp/Icn!ims. Oxford Umv. Press. 1996.

(71 3CPP. "Methodology for measuring impaa on voice activity factor.'' TR 26.9783 V4.0.0. March 2001,

[SI P. Tran-Gia. K. Leibnitz. "Telatraffic models and planning in wireless IF networks," IEEE "reless Comniiinicarions and Networking Conference, New Orleans. 1999.

[9 ] M. Arvedson, M. Edlund. 0. Eriksson. A. Sordin. A. Furuskf, "Packet or circuit switched voice radio bearers - A capacity evaluation for GERAN." MPRG WidesJ Svmposium. Blucksbirrg, June 2001.

[IO] S. Ni. "Network capacity and quality of service management in F m M A cellular systems." P1t.D. Dksertntion, Helsinki Univversiry, February 2001.

[ 111 T. Westholm. B. Olin. "A model for GSM speech," XJW SJ*mposim an Perfomia~ice Evaiimtion of Comprrter and Telecommunicarion System, pp. 458-62. 2001.

1121 I.Y. Lz Boudec, "Application of network calculus to guaranteed service networks.'' IEEE Transactions on Information Theov, Vol. 44, pp. 1087- 1096. 1998.

[I31 A. Burchard. J. Liebehem. S.D. Patek. "A calculus for end-to-end statistical service guarantees," Technical Reporr, Crrtiversi& of M r g i n i o , CS-2001- 39. May 2002.

[ 141 C. Li, A. Burchard. J. Liebeherr, "Network calculus with effective band- width," Technical Report, Uniltmity of Erginia CS-2003-20, November

algorithm that relies on a flow levet QoS definition. We modeled the aggregation of with the bufferless multiplexing model. The applied flow level QoS

2003. [IS] J. Liebeherr, S.D. Patek, A. Burchard. "Stalishcal Per-Flaw Sertice

BMnds in a Network wlth Aggregate Provisioning:' E E E Infocom. sm Francisco. April 2003.

voice

requirement allows the violation of the predetermined packet loss requirement with a small probability. Packet loss violation occurs at the rare cases when ongoing flows have large activity factors.

We proposed an admission control method that guarantees per flow QoS. The proposed method is based on Gaussian approximation applied for the bufferless multiplexing model. We have shown that the packet loss violation probabiIity can be approximated as the quantile of a normal distribution. The parameters of the normal distribution are obtained with the Taylor expansion of a random variable, which is the function of the random activity factors ai. The obtained admission control formula includes the moments of the activity factor distribution. , .

We analyzed the relation of the flow level admission control to the conventional aggregate level admission control method for the example of UMTS Terrestrial Radio Access Networks.

ACKNOWLEDGMENT

The authors would like to thankLars Westberg, Istvan Szab6 and Balks Ger6 for their helpful suggestions and constructive comments.

REFERENCES [l] E L. Presti. Z.-L. Zhang, J.F. Kurose, D.F. Towsley, "Source time scale

and optimal bufferhandwidth tradeoff for heterogeneous regulated traffic in a network node." IEEWACM Trrmsactim on Nemoding. Vol. 7, No. 4. pp. 490-501. August 1999.

[2] I. Bir6, E N6meth. Z. Heszberger, M. Maninecz. "Bandwidth requirement estimators for QoS Lpuaranteed packet networks," Infeenrationd Network Optim'zation Conference, Evry/Paris. 2003.

131 N. k"r. S. Ben Fredj. S. Oueslati and J. Roberts, "Quality of service and flow level admssion control in the Internet," Neiworks, Voi 40, pp. 57-71, 2002.

[I61 W. Jiang and H. Schulzrinne, "Analysis of On-Off patterns i n VoIP and their effect on voice traffic aggregation," ICCCN, 2000.

[17] E. Jugl, H. Boche, "Effect of the fluctuation of the voice activity factor on CDMA system capacity," internotional Workshop on Mobile Commiinications IWMC'W, Chrmia, Creie, pp. 310-320, June 1999.

[ 181 E Beritelli, S. Casale, G. Ruggeri, S. Serrano, "Performance evaluntion and comparison of G.729/AMlVFuzzy voice activity detectors," IEEE Signal Processing Letters, Vol. 913, pp. 85 -88, March 2002.

[19] E Beritelli, S, Casale, A. Cavallaro, "A robust voice activity dDetector for wireless communiwtions using soft computing," IEEE Jounral on Selected Areas in Commufaicalions, Special Issue on Signal Processkg fur Wireless Commtnications, vol. 16, N . 9. December 1998.

1201 L. Sun. EX. Ifeachor, "Perceived speech quality prediction for voice over IP-based networks:' IEEE Intermtimud Cmference oti Communi- cations, New York, pp. 373-2577., April 2002.

[21] D. V. Hinkley. "On the ratio of two correlated normal random variables." Biumetrika, 56, pp. 635-639, 1969.

[22] 3FPP, "Delay hdpet within the access stratum," TR 25.853 V4.0.0. March 2001.

[23] S.-Q. Li. "Study of information loss i n packet voice systems," IEEE Tramuc6ions on Communicatiow. vol. 37. no. I I , November 1989.

[24] S. Malomsoky. S. Rim, S. Nddas. "Connection admission control in UMTS radio access networks," Computer Comrmmnicaiiunr, Vol. 26, pp. 1907-191 7, 2003.

APPENDIX

Assume an XN normally distributed random variable with expectation /L,V and variance 0;. We are interested in the distribution of if ,UN - m. The Taylor expansion of the square root function at ,uAr is

Substituting 2 with the random variable X N in the series we get

1281

where the x; denotes the chi-square distribution with two

In our case X,y has to be substituted with E,”: ai ( 1 -a i ) .

degrees of freedom.

The cwfficients of ~5 in (U) tends to zero if N + 03:

where p j denotes the j - th moment of the activity factor.

formation of with expectation fi and variance e.

Finally this means that for large AT the square root trans- ai(l - ai) tends to a normal distribution N

1282