Effective bandwidth and associated CAC procedure for traffic streams multiplexed over a VBR link
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.
Section snippets
Related work
As it is essential for the understanding of the later sections we give here a brief overview of the large deviation analysis of a discrete time queue, based on existing results available in the literature [12].
Let Xi denote the amount of work arrived in the ith time slot, Qi denotes the queue length at the end of the ith slot and s is the amount of work that the server can do in one slot. The service discipline is First-In-First-Out (FIFO). The queue length in the buffer is according to the
The FIFO queue with a VBR server
We consider the same discrete time queuing model as in the previous section, but now the service capacity varies in time according to the VBR link parameters and to the incoming traffic. The server is characterized by the three VBR metrics; the sustainable cell rate, the peak cell rate and the maximum burst size (m, p, b). In our slotted system this means that the mean and the maximum number of cells that the server can serve during one time slot is m and p, respectively. The evolutional
Definition of the effective bandwidth for a VBR server
In this section we give the definition of the effective bandwidth of an arbitrary traffic stream when it is multiplexed over a VBR link. The section is split into two parts. First we address the simpler case when the peak rate tends to infinity. Consequently the number of packets that can be served at a given time slot is limited only by the burst tolerance and the sustainable rate of the link and it is not effected by the peak rate. Then we analyse the queue length behaviour when also the peak
A measurement based CAC for the VBR link
The analytical calculation of the effective bandwidth requires the knowledge of the exact statistical behaviour of the traffic and even assuming this knowledge the calculation is tractable only for simple sources (e.g. Markovian). That is why measurement based techniques have great importance in practical applications.
In this section we propose a measurement based CAC procedure applicable in the VBR link environment. The proposed method is based on the Mosquito algorithm [6].
The basic concept
Numerical results
In this section we demonstrate our effective bandwidth definition for Markovian ON–OFF sources, in which case the exact value of the effective bandwidth can be calculated numerically.
Concluding remarks
In this paper, we gave the large deviation analysis of a queue which is served by a VBR link instead of the traditional constant server. We introduced an equivalent queuing system, which was easier to analyse, and which led us to the definition of the effective bandwidth of a traffic stream when it is multiplexed over a VBR link. Our unified effective bandwidth approach enables us to reuse the existing CACs that are based on the effective bandwidth concept for a VBR link as well. It can be also
References (16)
- B-ISDN ATM adaptation layer type 2 specification, Draft ITU-T Recommendation...
- ATM Forum Technical Committee, Traffic Management Specification, Version...
- D.D. Bottvich, N.G. Duffield, Large deviations, the shape of the loss curve and economies of scale in large...
- J.L. Boudec, A. Ziedins, A CAC algorithm for VBR connections over a VBR trunk, IEEE INFO-COM'97 Conference, 7–11 April...
- et al.
Buffer overflow asymptotics for a switch handling many traffic sources
Journal of Applied Probability
(1996) - S. Crosby, I. Leslie, J.T. Lewis, R. Russell, F. Toomey, B. McGurk, Statistical properties of a near-optimal...
- N.G. Duffield, M. Huggard, R. Russell, F. Toomey, C. Walsh, Fast bounds for ATM quality of service parameters,...
- D.N.C. Tse, R.G. Gallager, J.N. Tsitsiklis, Statistical multiplexing of multiple time-scale Markov streams, IEEE...
Cited by (6)
A solitary wave approach to parallel optimization for multi-agent systems and computer networks
2008, Proceedings - 5th International Conference on Fuzzy Systems and Knowledge Discovery, FSKD 2008A new problem-solving method for multi-agent systems and computer networks: Solitary wave propagation
2008, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)A generalized particle model and algorithm for dynamic optimization of bandwidth allocation in ATM networks
2007, Jisuanji Xuebao/Chinese Journal of ComputersParticle dynamics approach to multi-agent systems
2006, Conference Proceedings - IEEE International Conference on Systems, Man and CyberneticsA novel generalized particle approach to optimize ATM networks
2005, Proceedings of the Third IASTED International Conference on Communications and Computer Networks, CCN 2005