Effective bandwidth and associated CAC procedure for traffic streams multiplexed over a VBR link

Abstract

In this paper we introduce the definition of the effective bandwidth for traffic streams that are multiplexed over a VBR link. We assume an arbitrary traffic mix multiplexed into a FIFO buffer, which has a service rate, regulated by VBR traffic parameters as opposed to the traditional CBR server capacity. In order to analytically obtain the generalized effective bandwidth we define an equivalent queuing model, which reduces the problem of the variable service rate multiplexer to a constant rate server. Following the Large Deviation Analysis of our equivalent queuing model we derive the effective bandwidth in terms of VBR link parameters. One of the appealing features of our method is that any dimensioning, resource allocation schemes that are based on the effective bandwidth concept but originally have been devised for CBR links can be easily extended to be applicable for VBR links as well. For example, one can easily build a Connection Admission Control (CAC) algorithm for a VBR link by reusing the existing methods based on the effective bandwidth concept. In this paper we also give an example for a CAC algorithm and for other practical application scenarios.

Introduction

The notion of effective bandwidth has become widely accepted as a measure of the resource requirements of bursty traffic in queuing networks [9], [11]. Intuitively, the effective bandwidth of a source can be considered as the minimum service capacity that has to be allocated for it in order to satisfy its QoS demands. This quantity depends on the statistical properties of the source, the traffic properties of the other traffic sources sharing the same resource, the QoS demands (e.g. target cell-loss rate) and on the resource itself (e.g. the buffer size).

The origin of the effective bandwidth concept lies in Large Deviation Theory. The theory has been used to prove that the tail of the queue length distribution in an infinite buffer that is emptied at a constant service rate decays exponentially [3], [5], [16] and the effective bandwidth is associated with the asymptotic exponential decay rate. Although the concept of effective bandwidth and the applicability of the large deviation theory in queuing networks are not restricted to the FIFO buffer with a constant service rate, the majority of research activities have been concentrated on this specific queuing system.

For example, in the domain of ATM networks this corresponds to the multiplexing of several VBR VCCs over a CBR VP. However the multiplexing over a VBR VP, which is often referred in the literature as the VBR over VBR case [4], [10], can be also interesting as it might be a more cost-efficient way of traffic aggregation, of course depending on the pricing policy.

Furthermore, with the introduction of the new ATM adaptation layer AAL2 [1] the multiplexing of bursty connections over a VBR link becomes even more interesting. The AAL2 adaptation layer enables the multiplexing of several AAL2 connections over an ATM VCC. This is going to be employed in the terrestrial part of third generation mobile access networks, where low bit-rate voice calls can be efficiently multiplexed over an ATM VCC. According to the current status of standards CBR VCC is assumed on the ATM level. However, as these VCCs will be rented by cellular operators, the question of cost-efficiency of applying VBR VCC instead of CBR arises in this context as well.

To apply a VBR over VBR multiplexing scenario necessitates the existence of CAC procedures for a VBR link. There are only a few papers available in the literature that give some proposals for the CAC procedure when VBR policed sources are multiplexed over a VBR link [4], [10]. On the one hand these solutions are subject to the constraint that the incoming traffic is also regulated by its corresponding VBR parameters, which is not necessary the case, for example, for AAL2 connections. On the other hand, here we do not intend to give a specific CAC procedure, rather we take the more general approach and we define and calculate the effective bandwidth formula when the traffic is multiplexed over a VBR link. As soon as we have a formula for the effective bandwidth, the existing CAC procedures for the CBR multiplexer case can be reused. Furthermore, the unified effective bandwidth concept also enables the direct comparison of the cost aspects of a VBR link versus a CBR one.

The paper is organised as follows. In Section 2, we review earlier results about the Large Deviation Analysis of a discrete time queue and we show how the effective bandwidth concept derives from the theory. In Section 3, we introduce our model for a FIFO queue with VBR server, which will be analysed in detail in Section 4. In Section 5, we reuse the Mosquito algorithm [6] to propose a measurement based CAC procedure for a VBR link. Finally in Section 6, further areas of possible applications and also results from calculations are presented.