Jitter characterization in admission control and pricing issues in integrated multiservice networks.

INTRODUCTION

In recent years, a variety of mobile computers equipped with wireless communication devices have become popular. Mobile users want to have diverse services and applications handy. These services include file transfer, videoconferencing, electronic mail, graphical user interfaces, remote file systems, etc. They require different levels of quality of service (QoS) measured in terms of delay, jitter, transmission error rate. Broadband technologies have emerged, making possible the integration of data, voice and multimedia applications.

The concept of multiservice cellular network is then used to denote the integrated infrastructure dedicated to support these applications and services. In fact, multiservice networks refer to networks carrying multimedia, voice, data and video traffic (1), (2). Their architecture integrates broadband and wireless mobile networks such that they are suitable for multimedia and mobile applications with bursty traffic (1).

The convergence of the Internet, the multiservice network and the traditional POTS (Plain Old Telephone Service), raised the problem of charging and pricing. Learning from the Internet, network operators are now aware that pricing is needed not only to recover costs, but also as a method of control. Therefore, in the last five years, a whole series of research (3-6) has been done in the pricing and charging area. However, these works are more or less adapted to the third-generation solutions with various QoS guarantees.

With the end of the public funding of the Internet, the problem of tariffs in computer networks became crucial. The transition towards a commercial Internet emphasized the need to cover the infrastructure costs through an access cost and possibly a usage-based cost. Therefore, numerous papers have been published on Internet engineering and economics; they give a good overview and introduction to the various models and frameworks (7). We refer the reader to references (3-6) for a more detailed and complete review of pricing schemes.

Generally, users can be billed according to several factors going from the type of service to the usage via the allocated resources (or a measurement such as effective bandwidth), the duration of the call, the flow, the call beginning, the distance, the number of calls, etc. Often, the price is given as a function of a combination of several of these factors.

Globally, pricing schemes can be gathered in two categories:

* Static pricing: this kind of pricing sets a flat fee per unit of resource that is independent of the resource usage or the network state. The fixed price can also be an average resulting from a dynamic scheme.

* Dynamic pricing: the price is in general per unit of resource and varies with the network state.

The effective bandwidth pricing is a dynamic pricing scheme based on the concept of effective bandwidth (8-14). Basically, the idea is to apply a tariff including a price per unit of time, a price per unit of volume and a connection price. At connection time, the user chooses a tariff corresponding to its expected mean rate. If the user sends more or less than the declared rate, it pays a higher price. Even if in (12) the authors show the efficiency of this model from the competing point of view, some disadvantages are noted. For instance, the user must declare its expected flow, the connection admission algorithm uses the parameters declared by the user; if this latter send more than the declared rate, he/she is penalized at the same time by the loss of its packages and by a higher tariff. A more detailed presentation of the model will be done in later.

This paper analyses the pricing framework of multiservice networks and proposes an improved pricing scheme based on the effective bandwidth concept by taking into account more QoS parameters.

2. Basic concepts and background: In integrated networks, pricing schemes are strongly related to connection admission. Indeed, pricing requires having a good idea of the resources used (or expected to be used) by each connection, which enables a control of connection admission. Generally, connection admission is based on an estimation of the queue/buffer length probability. In this section, we present some concepts related to the estimation of the queue/buffer length probability and its application to connection admission control (15), (16).

Cell loss asymptotic: With the development of ATM, there has been a lot of work to compute the buffer length probability or the asymptotic overflow probability. In this section, we summarize results obtained by Likhanov and Mazumdar (17), extending earlier works from Courcoubetis and Weber (18).

Consider N independent, identical, stationary and ergodic sources, each with input rate [[lambda].sub.n,j] where j refers to the jth source and n to the nth time slot. We assume that the time is discrete and that the input rates have some regularity properties (17). The total amount of work offered by the jth source during time interval [0,t) is [X.sub.t,j] = [t-1.summation over (n=0)][[lambda].sub.n,j] and the amount of work offered from all sources is [X.sub.t.sup.(N)] = [N.summation over (k=0)][X.sub.(t,k)].

Let [M.sub.t](s) denote the moment generating function of [X.sub.(t,1)], i.e. [M.sub.t](s) = E[[e.sup.[s[X.sub.(t,1)]]]]. Suppose that the sources access a buffer of size NB with output rate NC. The stationary workload [W.sup.(N)] is given by: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] where [X.sub.-t.sup.(N)] denotes the total of cells arrivings in the interval (-t,0]. Then as N[right arrow][infinity],

P{[W.sup.(N)]>NB} = 1/[square root of [2[pi]N[[sigma].sup.2][s.sub.0.sup.2]]][e.sup.-[NI.sub.[t.sub.0],[s.sub.0]](C,B)](1 + 0(1/N)) (1)

where

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

and

[[SIGMA].sup.2] = [[[partial derivative].sup.2]/[[partial derivative][s.sup.2]]]log(E[e.sup.s[X.sub.t,1]]) = [[[M.sub.t.sup."]([S.sub.0])]/[M([S.sub.0])]] - [[(Ct + B)].sup.2] (3)

In the previous definition, by abuse of notation, we suppose that 0[less than or equal to][s.sub.0],[t.sub.0][less than or equal to]+[infinity]

In (19), the term [[sigma].sup.2][s.sub.0.sup.2] is approximated by 2[I.sub.[t.sub.0],[s.sub.0]](C,B). Thus Eq. (1) can be rewritten:

P{[W.sup.(N)]>NB} = 1/[square root of [4[pi]N[I.sub.[t.sub.0],[s.sub.0]](C,B)]][e.sup.-[NI.sub.[t.sub.0],[s.sub.0]](C,B)](1 + 0(1/N)) (4)

Connection admission control and pricing: The effective bandwidth concept was introduced by Hui (20) and Guerin et al. (21). Combined with the work from (17-19), it is used by Kelly et al. (8), (10), (22) in their investigation of linear acceptance region for certain buffered resources and in the design of pricing schemes. We recall some results obtained by Courcoubetis et al. (23).

Many source types without priority: Suppose that the arrival process at a broadband link is the superposition of independent identically distributed sources of J types. Let [N.sub.i] = N[n.sub.i], i = 1,..., J, be the number of sources of type i and let n = ([n.sub.1],..., [n.sub.i],..., [n.sub.j]) (the [n.sub.i] are not necessarily integers). The link is serviced by a buffer NB at rate NC. Parameter N is the scaling parameter (size of the system).

Adapting the notations from the previous section, we define [X.sub.(t,j)] as the total amount of work offered by a source of type j during time interval [0,t) and [M.sub.(t,j)](s) as the moment generating function of [X.sub.(t,j)] i.e., [M.sub.(t,j)](s) = E[[e.sup.s[X.sub.(t,j)]]], where E is the expected value operator. We recall that [X.sub.(t,j)] has stationary increments. Then the effective bandwidth of a source of type j is defined as follows:

[[alpha].sub.j](s,t) = 1/st logE[[e.sup.s[X.sub.t,j]]] = 1/st log([M.sub.t,j](s))

where s, t are system parameters which are defined by the context of the source.

More precisely, s and t are defined by Eq. (2), which can be rewritten;

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

Consider the QoS constraint on the overflow probability to be P(overflow) [less than or equal to][e.sup.-[gamma]] and assume [gamma]=N[[gamma].sub.0]. If a point ([N.sub.1],..., [N.sub.j]) = ([Nn.sub.1],..., [Nn.sub.j]) satisfies:

[J.summation over (j = 1)][n.sub.j][[alpha].sub.j](s,t)[less than or equal to]C + [1/t](B-[[gamma].sub.0]/s) = C* (6)

where [s.sub.0] and [t.sub.0] are defined by Eq. (5), then the QoS constraint on the overflow probability P(overflow)[less than or equal to][e.sup.-[gamma]] is satisfied. Thus Eq. (6) defines an acceptance region.

By taking into account the results presented in the previous section (Eq.(4)), the acceptance region can be …