Nonparametric decision algorithms for CAC in ATM networks

Abstract

When performing call admission control (CAC) in ATM networks, the users are requested to declare their traffic descriptors on the basis of which the aggregated load is estimated. If this estimated load does not exceed the available node capacity, then calls are to be accepted and otherwise rejected. In the process of CAC, it is crucial that the network manager obtains correct information about the traffic characteristics declared by the users. Otherwise, the quality of service (QoS) can be severely deteriorated by accepting calls based on erroneous traffic descriptors. As traffic descriptors are usually obtained by measurements or statistical estimation, they are subject to errors or changes in time. Consequently, CAC must be viewed as a decision whether to accept or to refuse a certain traffic configuration, where the underlying traffic parameters are to be estimated from the samples of the aggregate traffic. This casts CAC as a nonparametric estimation problem first investigated by Gibbens et al. [R.J. Gibbens, F.P. Kelly, P.B. Key, IEEE J. Selected Areas Commun. 13 (6) (1995)]. As a result, when implementing a CAC algorithm, one is faced with the challenges of: (i) developing a good estimate of the tail of the aggregate traffic assuming that the true values of the traffic descriptors are given; and (ii) addressing the problem that the traffic descriptors themselves are random variables. In the latter case the tail estimation must be combined with a hypothesis testing method. To meet these challenges, in Section 1 of this paper a number of tail estimation techniques are listed which are based on statistical inequalities. Then a decision theoretic approach will be developed to perform CAC in the case of unknown traffic descriptors. This approach includes both parametric and nonparametric techniques. In developing these methods, the results of Gibbens et al. regarding the parametric case will be extended from homogeneous to heterogeneous traffic. The nonparametric decision algorithm will be implemented by a feedforward neural network which yields an asymptotically optimal Bayesian CAC function. More specifically, a two-layer neural network processes the samples of the aggregate traffic and yields an “accept” or “reject” decision at the output. Applying a special encoding scheme in the course of training, the outputs of the network will estimate the a posteriori probabilities needed for the Bayesian decision. In this way, CAC is performed as a decision function without the knowledge of the a priori distribution of the traffic descriptors. The paper contains the proof of this statement with some applications and simulation results regarding the different CAC algorithms.