Charging Schemes for ATM Networks Based on

Charging Schemes for ATM Networks Based on Virtual Effective Bandwidths Jelena Miˇsi´c Samuel T. Chanson Department of Computer Science The Hong Kong University Of Science and Technology Clear Water Bay, Kowloon, Hong Kong Abstract

traffic is only loss sensitive. A traffic source is commonly characterized by traffic descriptors such as the peak rate, average rate, and average burst length. Also specified is the quality of service descriptors, which are usually either cell loss probability, delay, or delay jitter. Charging in ATM networks has been addressed in [10, 11]. In [10], both usage-sensitive and time-sensitive charging are considered in the framework where cell loss probability is the only QoS criterion. One value of cell loss probability is associated with a buffer, and multiple buffers are needed for various types of traffic. In [11], time-sensitive charging is considered using only delay as the QoS criterion. This approach charges for the combination of buffer and bandwidth allocation. However, since no cell loss is allowed, statistical multiplexing is prevented, and therefore network resources can not be used efficiently. In the connection admission phase of an ATM network, the amount of resources allocated to the connection is based on the specified traffic pattern and the QoS bound. If the traffic characteristics do not change throughout the duration of a connection, time-sensitive charging can be effectively used. The problem is in determining the appropriate traffic descriptor and its value to accurately estimate network usage and provide enough information for charging traffic with different QoS bounds. One possible traffic descriptor which can be used for charging (as well as in CAC) is the effective bandwidth, defined as the minimum bandwidth required by a source to satisfy its QoS requirements. Effective bandwidths have been investigated mostly using two approaches: spectral expansions for Markov fluid models [2, 5], and theory of large deviations (for calculating large buffer asymptotics) [4, 12]. Both approaches assume an infinite buffer, and equal QoS requirement for all the connections. Under these assumptions the criterion for admission of a connection is simple: If the sum of effective bandwidths of the arriving call and the existing connections is less than the capacity of the output channel, the new connection can be admitted. However, when QoS bounds are different, a set of parallel FIFO queues is needed which share the output link’s bandwidth using some scheduling policy, such as the packetized general processor sharing policy (PGPS) [9]. Connection requests with the same QoS requirement are placed in the same queue. The drawbacks of this approach include complex implementation (in particular, the need for a scheduler) and low buffer utilization. The charging problems related to this approach are: – Various QoS descriptors are not related, e.g., it is not known what the cell loss probability bound means in terms

In this paper, we propose charging schemes for ATM networks based on the concept of virtual effective bandwidths (VEB). VEBs were initially developed by the authors to support real-time Connection Admission Control (CAC) in a framework where traffic sources with different quality of service (QoS) requirements are multiplexed into the same finite length queue [6]. VEBs allow different QoS requirements to be related which is important for charging purposes. We propose three charging schemes which can be included in real-time CAC: the first one depends solely on the resource requirements of the call; the second is dependent on resource as well as QoS requirements of the call; the third is dependent on the current traffic intensity of the other connections also. Keywords: ATM networks, QoS, charging, Connection admission control.

1

Introduction

Among the various issues related to ATM research, the problem of appropriate charging for different types of traffic has not received much attention, although it must be solved if ATM is to be offered as a public service. Charging schemes can generally be classified into two categories: usage-sensitive charging and time-sensitive charging. In a usage-sensitive charging scheme, the user pays according to the required QoS and to the number of packets sent. The general framework for usage-sensitive pricing (see [1] and its references) is based on the elements of microeconomic theory [7]. In this approach, network services with different QoS are priced dynamically according to user demand. However, algorithms which implement this kind of pricing are complex and therefore not suitable for ATM networks, where charging must be implemented in real-time together with CAC. On the other hand, the telephone network often uses time-sensitive charging, i.e., charges are based on connection time. Time-sensitive charging requires less overhead in monitoring and computation than usage sensitive charging and is therefore more appropriate for ATM networks. Parameters that are related to charging in ATM networks are the distance between the source and destination, holding time (i.e., length of call), traffic characteristics, type and value of QoS bound(s), and traffic intensity of the network at the moment of call arrival. Network traffic can be grouped into two broad classes – real-time and non-real-time, based on their properties and requirements. Real-time traffic is sensitive to average delay, delay variations, and cell loss, while non-real-time 1

0-8186-7780-5/97 $10.00 1997 IEEE

of delay and delay jitter and vice versa. – Charging is dependent on the scheduling policy also, e.g., the amount of time given to each queue. In this paper we consider charging in the situation when N traffic classes with (possibly) different QoS requirements are multiplexed into a single ATM queue (with cell loss control implemented using the Partial Buffer Sharing Mechanism (PBS) [3]), sharing the same buffer and the total bandwidth of the link. We define a capacity domain as the union of all connections with the same QoS criterion. We will characterize a target QoS traffic class (capacity domain) t with the following descriptors: (a) sum of effective average arrival rates of the connections within t, and (b) QoS requirement of t. In order to model the charging descriptor which reflects the value of the target capacity domain QoS descriptor as well as the occupancy of the other capacity domains, the effective bandwidth of a connection is determined within a capacity domain. This parameter represents the fraction of the capacity domain allocated to the source. Hence we will refer to it as virtual effective bandwidth (VEB). The VEB of a source depends on the traffic descriptors of the source, the QoS bound for the associated capacity domain, and the sum of the effective average arrival rates of connections in the other capacity domains. In this way, we can consider capacity domains as linear combinations of VEB’s, and represent them as P 0 i Ai i(Qd)  1, where Ai corresponds to the number of class i connections (all connections within a traffic class have the same traffic descriptors), and 0i(Qd) denotes the VEB of class i connections with regard to the value of QoS descriptor Qd. All traffic sources are assumed to be ON-OFF. However, when we analyse the behavior of a target connection, the background traffic is approximated as Poisson (see section 2). We estimate how the average queue length, queue length jitter (defined as the ratio of standard deviation of queue length and the mean queue length), and aggregate traffic losses change under different Poisson traffic intensities. The changes in QoS descriptors depend on the buffer size, threshold position and the ratio of low and high priority cells. We then use these results to determine values of QoS descriptors for combinations of various classes of ON-OFF sources, which we model as an ON-OFF Poisson sources with exponentially distributed ON and OFF times. These expressions relate value of the QoS descriptor with the number and type of ON-OFF connections within capacity domain, and therefore expressions for effective bandwidth within a domain, with respect to the given value of QoS descriptors, can be derived. The expressions for VEBs show that the QoS bounds are related. For example, if delay and delay jitter bounds are given, we can calculate the equivalent QoS limit on target connection loss. Because a simple relationship exists between the VEB’s in a domain and the sum of effective average rates in the other domains, the capacity domains can be simply managed. Therefore, both time-sensitive charging and real-time connection admission control can be implemented efficiently. The rest of the paper is organized as follows. Section 2 gives basic assumptions and definitions. In Section 3 QoS descriptors are determined for PBS queue for various

ON-OFF class 1 ON-OFF class 2 QoS class 1 ON-OFF class K

ON-OFF class 1

Q

T

ON-OFF class 2 QoS class N ON-OFF class K

Figure 1: PBS queue with a combination of Poisson traffic and N classes of ON-OFF traffic sources.

intensities of Poisson input traffic. Section 4 analyses the PBS queue using a combination of Poisson traffic and various classes of ON-OFF sources. In Section 5 we discuss the virtual effective bandwidths (VEBs) for three classes of performance criteria: average queue length, queue length jitter, and loss probabilities. In Section 6 we discuss the properties of capacity domains and VEBs related to charging. In Section 7 we propose three simple charging policies based on VEB which can be used for time-sensitive charging. They also allow charging to be integrated with CAC. Finally, Section 8 concludes the paper.

2

Background

In this section we consider a PBS queue fed by N traffic classes with different QoS requirements (Fig. 1). Each QoS traffic class j consists of K classes of ON-OFF sources (‘ON-OFF classes’) and comprises one capacity domain. Each ON-OFF class (i) within the QoS class (i.e., the capacity domain) j consists of Aij independent and identical ON-OFF Poisson sources. Each ON-OFF class i source has exponentially distributed ON and OFF periods, and is represented with a triplet ( i ; i; it), where i is the transition rate from the OFF state to the ON state, i is the transition rate from an ON state to an OFF state, and it is the average cell generation rate while the source is in the ON state. The probabilitygenerating function (PGF) of the cell generation process with the source in the ON state is f (x) = et(x 1) . The activity factor of the source is pion = i +i i , and the average arrival rate of the connection is pionit . Let the traffic intensities for low and high priority traffic be itl and ith , respectively. Then the probability of cell arrival from a connection at a slot boundary (given that there is an arrival from this connection) is pih = ithith , for a +itl itl , for a low-priority high-priority cell, and pil = ith+ itl cell. In subsequent analysis we shall assume that for all types of sources, pih = ph = 1=3, and pil = pl = 2=3. In order to obtain specific values of QoS descriptors (average queue length, queue length jitter, low- and highpriority cell loss probabilities) for the target capacity domain t 2 [1::N ], we shall concentrate on the ON-OFF sources in that domain, and model other the N 1 capacity domains as ‘background’ traffic. We model the PGF of the background traffic from capacity domains j , (j 2 [1::N ]; j 6= t), by the following expression:

0-8186-7780-5/97 $10.00 1997 IEEE

Φ(x)

=

N X

AX 1;j






AX K;j

PK

e

i=1 pi it(x 1)

j = 1 p1;j =0 pK;j =0 j 6= t K Y  Ai;j  pi;j A p pi;j pion (1 pion ) i;j i;j i=1




log C N log Qd = f (λ)

log C t log C 1 Example b

δ Qdb

(1)

For large Ai;j and small pion , Φ(x) becomes Φ(x) = P P exp( j 6=t i Ai;j pion (eit (x 1) 1)), with an error less than 1% when Ai;j  10 and Pion  0:5, and less than 5% when Ai;j  3 and Pion  0:5. The first and second moments of the background traffic PGF are P N P A p  and PN P A p  (1 +  ), it j 6=t i i;j ion it j 6=t i i;j ion it respectively. In practice, however, it is small (0.065 for 10Mbps connection rate and outgoing line capacity of 155Mbps, or 0.016 for the same connection rate and outgoing line capacity of 622Mbps), hence we can approximate eit (x 1) with 1 + it(x 1), and the PGF of the background traffic P becomes P the PGF of a Poisson process, Φa (x) = exp( j 6=t i Ai pion it (x 1)). This approximation has the same average as the original input process, but with smaller variance. For large number of connections with diversity of peak rates and high capacity of the output channel, the difference in variance should not differ by more than a few percents. The average arrivalPrate P of the background traffic Poisson process is sl = j 6=t i Ai;j pion it. We shall refer to the average arrival rate of the background traffic as s , and the number of sources within the target QoS P class P as Ai . The total average arrival rate is tot = j i Ai;j pion it : The average arrival rate within the capacity domain t is ct = PKi=1 Ai;t pionit (in the text that follows we shall refer to the average arrival rate within the target capacity domain as c ). However, as will be shown in Section 5, the impact of the connections with high peak rates on QoS descriptors varies exponentially with the connection peak rate. Therefore, the Poisson approximation of the input process has to be modified such that connections contribute to the total average arrival rate with their ‘effective’ average arrival rates instead of their real average arrival rates.

2.1

log Qd=log K1 + K2 λ

log Qd

Relationship between effective average arrival rate, effective bandwidth and virtual effective bandwidth

Consider the situation depicted in Fig. 1. Assume that all QoS traffic classes are characterized with the same QoS descriptor Qd which may be cell loss probability, average queue length or queue length jitter. Each QoS class j will have a different value of Qd, Qdj = Cj (without loss of generality, we assume C1 < C2 : : : < Ct : : : < CN ). We concentrate on the target QoS traffic class (capacity domain) with the required value of QoS descriptor Ct , the background traffic arrival rate s , and the average domain arrival rate c . Let’s assume that the transfer characteristics log Qd = f (), which relates the input traffic (Poisson) arrival rate

Example a

δ Qda

log K1 + K 2 λs

δ Qda /K2

δ Qdb / K2

log K1

λs

λs+ λc

λ

Figure 2: Representation of effective average arrival rate, effective bandwidth and virtual effective bandwidth

with the consumed value of the QoS descriptor, may be approximated by a linear function log(Qd) = log K1 +K2  in the vicinity of  = s + c , as shown in Fig. 2. (In fact, both K1 and K2 are functions of , but for the sake of clarity, we shall consider them as constants for the time being). We shall use this transfer characteristics to model a target ON-OFF connection from the aspect of the amount of QoS descriptior (Qd) it consumes. According to Fig. 2, the amount of Qd spent on the background traffic is log K1 + K2 s . The available amount of Qd for the target capacity domain is ∆Qd = log Qd1 log K1 K2 s . The target connection within the target capacity domain consumes some amount of Qd, denoted as Qd. As will be shown in Section 5, Qd = pion (eK2 it 1), where pion represents the connection activity factor, and it is the average arrival rate when the connection is active (for ON-OFF source this is equivalent to the peak rate). For small peak rates, Qd = pionit K2 , which means that a connection with an average arrival rate pionit consumes an amount of Qd which is linearly proportional to its average arrival rate (this is shown as example a in Fig. 2). However, for high peak rates, Qd grows exponentially with the connection peak rate, and has higher slope than K2 . In that case, Qd K2 > pion it (this is shown as example b in Fig. 2).

eff The value Qd K2 = it corresponds to the effective average arrival rate of the connection with respect to the consumed amount of traffic descriptor and to the transfer characteristics for the aggregate traffic, log Qd = log K1 + K2 . The total amount of effective average arrival rates for connections from all capacity domains is determined by the most stringent value of Qd (in the example shown in Fig. 2 this value is C1 ). The total amount of QoS descriptor is equal to log C1 log K1 , and the total amount of effective arrival log C1 log K1 rates is equal to eff . tot = K2 Then, effective bandwidth (Qd) of the connection with respect to the tightest value of QoS descriptor Qd = C1 is

0-8186-7780-5/97 $10.00 1997 IEEE

defined as:

(Qd) = ∆Qd Qd

=

1

Qd

log C1

log K1

=

eff it : eff tot

(2)

average queue length

Effective arrival rates and effective bandwidths have additive property across all capacity domains. Since the amount of traffic from the various QoS classes varies in time, and the tightest value of the QoS descriptor may change, it is useful to define the effective bandwidth of the connection with respect to its QoS class, as well as the amount of traffic in the other capacity domains. We define the virtual effective bandwidth 0 (Qd) of an ON-OFF connection within a given target capacity domain as the ratio of the amount of Qd consumed by the target connection and the available amount of Qd for the target capacity domain t, t 2 [1::N ]:

7

6

5

4

3

2

0(Qd)

=

Qd

∆Qdt

=

log Ct

Qd (3) log K1 K2 eff s

eff it (log Ct log K1 K2 eff s )=K2 where Ct is the value of Qd for capacity domain t, and eff s is the sum of effective average arrival rates in all the

1

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

load

=

non-target capacity domains.

3

PBS queue QoS descriptors for the Poisson input process

Figure 3: Average queue length and its approximation eD0Q +D1Q +D2Q 2 with D0Q = 0:946, D1Q = 9:599 and D2Q = 11:2744 (R2 = 0:9970).

generating function G(x) = PQIn 1 [6], probability j for queue length distribution was derived  ( j ) x j =0

(buffer size is denoted by Q and queue threshold is T). After obtaining stationary distribution of the queue length, the relevant moments of the distribution as well as cell loss probabilities for aggregate traffic can be calculated. The average queue length is Qav = G0(1), and the variance of the queue length is: V arQ = G00(1) + Qav Q2av : Knowing the average queuep length and its variance, we can compute the jitter as: J = V arQ =Qav : Figs. 3 and 4 show the average queue length and jitter as functions of the average arrival rate of the input traffic. Since the analytical results for the queue length distribution are very complex, these functions are approximated using standard regression method in the range of average arrival rates of input traffic from 0.6 to 0.95. As a measure of the adequacy of approximation, the determination coefficient (R2 ) [8] was computed. Values calculated from the PGF are shown by dots, and exponential approximation is given by the full line. In all examples the following values are used: Q=50, T=40, pl = 2=3. Fig. 5 shows low priority cell loss probabilities as functions of the average arrival rate of the input traffic. For the range of average arrival rate of input traffic from 0.6 to 0.95, this function is also approximated by exponential function using linear regression method. A similar graph was constructed for high priority cell loss and approximated by the Bh Bh Bh 2 function eD0 +D1 +D2  , where D0Bh = 172:144, D1Bh = 228:234, and D2Bh = 78:510 (determination coefficient R2 = 0:99997).

queue length jitter

2

1.8

1.6

1.4

1.2

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

load

Figure 4:

eDJ +DJ  0:99948). 0

1

Queue length jitter and its approximation with D0J = 1:791, D1J = 1:817 (R2 =

0-8186-7780-5/97 $10.00 1997 IEEE

from pi active sources to ai active sources in the next time P i KiAi = 1 [6]). slot ( A ai =0 pi ;ai Expression 4 gives the joint distribution of queue length, losses and the number of active ON-OFF sources. The average queue length in this case is:

low priority cell losses

.1000000000e-3 1e-05

A AK X X Wx0 (1; 1; : : :; 1) =


G0x (1)p :::pK ;eff
s p =0 pK =0  K  Y Ai ppi (1 pion )Ai pi (5) pi ion 1

1e-06

1

Qav

1e-07 1e-08

=

1

1

1e-09 1e-10 1e-11

i=

1e-12 1e-13

The variance of the queue length is:

1e-14

AK X


G00(1)p :::pK ;eff
(6) s p =0 pK =0  K  Y Ai pp (1 pion )Ai pi + Qav Q2 av pi ion i=1 pV arQ The jitter is equal to J = Qav :

1e-15

1e-17 0.6

0.65

0.7

0.75

0.8

0.85

0.9

Figure 5: Low priority cell loss probability and its apBl Bl Bl 2 proximation eD0 +D1 +D2  , with D0Bl = 133:438, D1Bl = 197:296, and D2Bl = 69:001 (R2 = 0:99995).

In this section, the QoS descriptors are derived for a PBS queue fed by N QoS traffic classes (Fig. 1). Each QoS traffic class j consists of K classes of ON-OFF sources and comprises one capacity domain. Each ON-OFF class i of sources within the QoS class j consists of Ai;j independent and identical ON-OFF Poisson sources (as presented in Sec. 2). Under the assumption that the offered load is less than 1, and that the queue can reach steady state, the steady state PGF of queue length and the state of ON-OFF sources are defined below (detailed derivation is presented in [6]) :

A X 1

p1 =0






AK X pK =0

 K  Y Ai ppi (1 pion)Ai pi ion i=1


G(x)p :::pK ;eff s 1

1

The low priority cell loss probability is :

Bl

Derivation of QoS descriptors in the presence of ON-OFF sources

W (x; u1; : : :; uK ) =

=

1

0.95

load

4

A X 1

V arQ

1e-16

(4)

Ai pi
( X KiAi uai ) pi ;ai i ai =0

where G(x)p1 :::pK ;eff is the steady state generating s function obtained for p1 ; p2 ; : : :; pi; : : :; pK sources from classes 1; 2; : : :; i; : : :; K respectively, being constantly turned ON in the presence of Poisson traffic with effective average arrival rate eff s . i is associated with the i-th class of The coefficient KiA pi ;ai ON-OFF sources and denotes the probability of switching

A X

AK X


Bl;p :::pK ;eff s p =0 pK =0  K  Y Ai ppi (1 pion )Ai pi ion i=1 1

=

1

1

pi

(7)

where Bl;p1 :::pK ;eff denotes the low priority cell loss s probability for p1 ; p2 ; : : :; pi; : : :; pK sources from classes 1; 2; : : :; i; : : :; K respectively, being constantly turned ON in the presence of background traffic with effective average arrival rate eff s . The high priority cell loss probability is determined in a similar manner.

5

Virtual effective bandwidths

Results (5), (6), and (7) must be further simplified in order to model the capacity domain satisfying the condition PK A 0 (Qd) = 1, where 0 (Qd) denotes the VEB of i i=1 i i the target ON-OFF class i connection with respect to the QoS descriptor Qd. VEB based on low priority cell loss probability. We will simplify expression (7) using the exponential approximation shown in Fig. 5, log(Bl ) = D0Bl + D1Bl  + D2Bl 2 . Furthermore, at the point  = tot , the transfer characteristics can be approximated with a linear function with the same slope, i.e., log(Bl )  [2D2Bl tot + D1Bl ] + [D0Bl

D2Bl 2tot]:

Expression (7) can then be rewritten as:

AK "Y K (A p )pi X i ion e Bl =


pi ! p =0 pK =0 i=1 A X 1

1

0-8186-7780-5/97 $10.00 1997 IEEE

Ai pion

#




(8)

eff K Kt +s ) eDBl DBl tot
e[2DBltot+DBl ](p  t +:::p P s e i Ai pion
e[DBl DBltot] e[2DBl tot+DBl ]eff Bl Bl A AK [2D tot+D ] t X X (e A1 p1on )p



p! 2

0

=

2

2

1

1

1

2

0

2

2

1

1

2

1

1

VEB(Bl)

1

1 pK =0 Bl Bl (e[2D2 tot+D1 ]Kt AK pKon )pK

p1 =0






pK !

0.007

[2D Bl tot +D Bl ]it

1 If the values e 2 pion  0:5 and Ai the previous summation can be expressed as:

 10,

0.006 0.005 0.004 0.003

Bl

=

s e D0Bl D2Bl2tot] e[2D2Bl tot+D1Bl ]eff (9) =K P A p iY Bl Bl [2D  +D ] e i i ion eAi pion e 2 tot 1 it i=1 [

0.002 0.001 -8 -7 -6

Previous limitation means that for connections with high peak rates (e.g., 0.016, which corresponds to 10Mbps peak rate and 622 Mbps outgoing line capacity), the activity factor must be less than 0.3. Taking logarithm of both PK sides, we obtain i=1 Ai 0i(Bl ) = 1, where 0i(Bl ) (the VEB of the target ON-OFF class i connection with respect to the low priority cell loss limit) is given by

pion (e[2DBl tot+DBl ]it 1) [D0Bl D2Bl 2tot] [2D2Bl tot + D1Bl ]eff s 2

log Bl

1

(10)

Similar expressions can be derived with high priority cell loss probability as the QoS descriptor. Graphical representation of the VEB with low priority cell loss probability as QoS descriptor in the case of a single capacity domain is shown in Fig. 6. Exponential approximation is determined for tot = 0:85. Effective average arrival rate of ON-OFF connection. By combining the results from Section 2.1 with Eqn. 10, we can extract the expressions for the consumed amount of QoS descriptor and effective average arrival rate as Bl = Bl pion (e[2D2Bl tot+D1Bl ]it 1) and eff it = [2D2Bl tot+D1Bl ] , respectively. VEB based on average delay and delay jitter. Effective bandwidths based on average queue length and queue length jitter can be obtained using exponential approximations (shown in Figs. 3 and 4), in the same manner as PK those for losses; i=1 Ai 0i(Qav ) = 1, where 0i(Qav ) (the VEB of the target class i ON-OFF connection with respect to the average queue length) is given by:

pion (e[2DQ tot+DQ ]it 1) Q DQ 2 ] [2DQ  + DQ ]eff [D0 s 2 tot 2 tot 1 2

log Qav

1

(11)

Also, 0i (J ) which denotes the VEB of the target class i ON-OFF connection with respect to queue length jitter is given by

0i(J ) =

pion (eDJ it 1) log J D0J D1J eff s 1

(12)

log10(Bl)

0.002 0.004 0.006 0.008

-5 -4

0.01 connection peak rate 0.012 0.014 -3 0.016

Figure 6: VEB for one capacity domain as a function of the source peak rate (pon = 0:2) and low priority cell loss probability as QoS criterion.

Graphical representation of the VEB with average queue length and queue length jitter as QoS criteria in the case of a single capacity domain are shown in Figs. 7 and 8 respectively (tot = 0:85).

6

Properties of capacity domains

VEBs provide a basis for obtaining the relationships between different QoS bounds. This is important for charging schemes based on specified QoS requirements. The following example shows how a real-time connection with given delay and delay jitter requirements can obtain information about the limit on its cell loss behavior. In the example, we will consider a PBS queue with Q=50, T=40 and pl = 2=3. For simplicity, we will assume that there is only one capacity domain, i.e., s = 0. Suppose that the imposed limit on average queue length is Qav = 1. According to the transfer characteristic Qav = f () for Poisson input traffic shown in Fig. 3, this limit corresponds to the total effective arrival rate tot = 0:75, and to the jitter limit J = 1:53 (Fig. 4), and low priority cell loss limit Bl = 0:5
10 9 (Fig. 5). The effective bandwidths of the connection with peak rate 0.004 and activity factor pon = 0:2 are 0(Qav ) = 0(J ) = 0(Bl) = 0:0011. Consider a source belonging to QoS traffic class t, with burstiness 1=pon, and peak rate t . Assume that the QoS descriptor Qdt for the traffic class t is given by Qdt = K1;Qdt eK2;Qdt  and that the QoS descriptor bound is Qdt = Ct. Then the virtual effective bandwidth of the source is given by the following expression:

0-8186-7780-5/97 $10.00 1997 IEEE

VEB(Qav)

VEB(J)

0.006

0.008 0.007

0.005

0.006 0.004 0.005 0.004

0.003

0.003 0.002 0.002 0.001

0.001 0

1 1

1.2 2

1.4 3

Qav

1.6

0.002 0.004 0.006 0.008

4 5 6

1.8 2

0.01 connection peak rate 0.012 0.014 7 0.016

2.2

Figure 7: VEB for one capacity domain as a function of source peak rate (pon = 0:2) and average queue length as QoS criterion.

0l (Qdt) =

pon (eK ;Qdt t 1) ; t log K C;Qd K2;Qdt eff st t 2

(13)

1

where

eff st =

N X K X j = 1 i=1 j 6= l

Ai;j eff it :

Therefore, the VEB depends on the traffic parameters of the source, the value of QoS descriptor for the given capacity domain, and the sum of the effective average arrival rates of all connections in the other traffic classes. In the presence of multiple capacity domains, the total effective PN P eff average traffic rate is: eff tot = j =1 i Ai;j it :

7

Charging Policies

In this section we will present charging policies based on: – traffic descriptors of the connection only, – traffic descriptors and QoS requirements of the connection, and – traffic descriptors, QoS requirement of the connection, and intensity of traffic in all capacity domains.

7.1

0.002 0.004 0.006 0.008

J

Charging policy based on the traffic descriptors of the call only

From the fairness point of view, traffic intensity in the other capacity domains should not be taken into consider-

0.01 connection peak rate 0.012 0.014 0.016

Figure 8: VEB for one capacity domain as a function of source peak rate (pon = 0:2) and queue length jitter as QoS criterion.

ation for charging. In this case, a connection should be charged only on the consumed amount of QoS descriptor Qd, or equivalently on its effective average arrival rate Qd eff it = K2Qd . However, the transfer characteristics for a particular QoS descriptor is approximated by a linear approximation (in the log scale) Qd = K1 eK2 , around the point eff tot . Therefore, K1 and K2 depend on the value and slope of the transfer characteristic at the point determined by total effective arrival rate. They also include information about the buffer length, PBS threshold position, and outgoing line capacity. Since the slope of the transfer characteristics for all QoS descriptors except queue length jitter decreases with total load, Qd and eff it will decrease slightly when the total load increases. This means that the values of these charging descriptors decrease as the utilization of the outgoing link increases. The charging unit can be determined according to one of two policies: – based on the normalized server rate which is equal to 1 (or total amount of QoS descriptor K2 log K1 log K1 ), or – based on the current maximum admissible traffic rate which is imposed by the tightest QoS bound eff = Ct (or the amount of QoS descriptor loglmax 1 log Qd t K2Qd K1Qd log K1 ). The second approach tends to discourage data-transfer users from establishing connections when real-time connections are present (see Fig. 2).

0-8186-7780-5/97 $10.00 1997 IEEE

7.2

Charging policy sensitive to the traffic descriptors and QoS requirement of the connection

The third scheme provides charging which is dependent on the current network traffic intensity. For this type of charging, a ‘scaled VEB’ (SVEB) descriptor is proposed. All charging descriptors can be computed during the call negotiation phase and returned to the user. The relations among different QoS bounds for VEB provide a sound basis for simple, real-time charging schemes for ATM connections.

In this case, the appropriate charging descriptor is the VEB of the connection. To exclude the information about connections in other capacity domains, eff s should be set to 0. Therefore, connections with same traffic descriptors will be charged differently if they have different QoS requirements.

7.3

References [1] R. Cocchi, S. Shenker, D. Estrin, L. Zhang. “Pricing in Computer Networks: Motivation, Formulation and Example”. IEEE/ACM Trans. Networking, 1(6):614– 627, 1993.

Charging policy sensitive to the traffic descriptors, QoS requirement and current traffic intensity

This type of charging is harder to implement than the previous ones since the traffic intensity changes when a call arrives or terminates and must be recalculated. The appropriate charging descriptor is the ratio of the amount of the QoS descriptor consumed by the connection and the available amount of QoS descriptor across all capacity domains. For a particular connection within target domain t with QoS descriptor bound Ct , let us assume that the occupancy of capacity domain changes at time instances t0 ; t1; : : :tk ; : : :tQ , where t0 denotes the time of target call arrival, tQ denotes the time of target call termination, and tk ; 0 < k < Q denotes instances of other call arrivals or terminations. Then, the ‘scaled’ charging descriptor for the connection at time tk ; 0  k  Q can be defined as:

(Qdt ; tk ) =

p (eK Pcl t 1) P onP A (t )p (eK Qdt t

[3] H. Kroner, G. Hebuterne, P. Boyer, A. Gravey. “Priority Management in ATM Switching Nodes”. IEEE Journal on Selected Areas in Communications, 9(3):418–427, 1991. [4] G. Kesidis, J. Walrand, C. S. Chang. “Effective Bandwidths for Multiclass Markov Fluids and Other ATM Sources”. IEEE/ACM Trans. Networking, 1(4):424– 428, 1993.

2

t log KC 1

PN PK

Qdt

j

i i;j k ion

2

K  where j =1 i=1 Ai;j (tk )pion (e 2Qdt t 1) denotes the occupancy of all capacity domains at tk . We will refer

to this descriptor as a ‘scaled VEB’ or SVEB. The total price of the connection is then proportional to the value PQ 1 (Qd ; t )(t t k k+1 tk ). This policy tends to disk =0 courage users from making connections when the network is heavily loaded.

8

[2] R. J. Gibbens, P. J. Hunt. “Effective Bandwidths for the Multi-Type UAS Channel”. Queuing Systems, 9:17–28, 1991.

Conclusions

In this paper we have investigated the possibility of charging ATM connections using traffic descriptors that are similar to those used in connection admission control. We have derived expressions for virtual effective bandwidths which allow different QoS requirements to be related. This is important for charging purposes. The two other features of VEB which are important to pricing are that VEB has an exponential relationship with connection peak rate which imposes penalty for underutilization of link capacity, and VEB increases with the traffic intensity outside the capacity domain. We have proposed three charging schemes. The first one is insensitive to the network traffic intensity and is based only on the characteristics of the connection being charged. The second scheme is dependent on the traffic descriptors as well as the QoS requirement of the connection.

1)

[5] A. Elwalid, D. Mitra “Effective Bandwidth of General Markovian Traffic Sources and Admission Control of High Speed Networks”. IEEE/ACM Trans. Networking, 1(3):329–343, 1993. [6] J. Miˇsi´c, S. Chanson. “Multiparameter QoS Admission Control for ATM Queues with Partial Buffer Sharing Mechanism”. technical report HKUST-SC9607, Dept. Of Computer Science, The Hong Kong University of Science and Technology, March 1996. [7] W. Nicholson. Microeconomic Theory Basic Principles and Extensions. Dryden Press, 1989. [8] W. W. Hines and D. C. Montgomery. Probability and Statistics in Engineering and Management Science, third edn, New York: John Wiley and Sons, 1990. [9] A. K. Parekh, R. G. Gallager. “A Generalized Processor Sharing Approach to Flow Control in Integrated Services Networks: A Single Node Case”. IEEE/ACM Trans. Networking, 1(3):344–357, 1993. [10] H. Saito. “Resource Management and Charging in ATM Networks”. Computer Networks and ISDN Systems, 28:641–644, 1996. [11] S. H. Low, P. P. Varaiya. “A New Approach to Service Provisioning in ATM Networks”. IEEE/ACM Trans. Networking, 1(5):547–553, 1993. [12] G. de Veciana, J. Walrand. “Effective Bandwidths: Call Admission, Traffic Policing, and Filtering for ATM Networks”. Queuing Systems, 20:37–59, 1995.

0-8186-7780-5/97 $10.00 1997 IEEE