Buffer losses vs. deadline violations for ABR traffic in an ATM switch: A computational approach

The B-ISDN will carry a variety of tra c types: the Variable Bit Rate tra c (VBR), of which compressed video is an example, Continuous Bit Rate tra c (CBR), of which telemetry is an example, Data tra c, and Available Bit Rate tra c (ABR) that represents aggregate data tra c with very limited guarantees on quality. Of these, VBR and CBR have timing constraints and need synchronous bandwidth; data tra c is relatively delay insensitive. In this paper, we consider the VBR, Data and ABR tra c types and obtain the cumulative distribution function (cdf) of the queueing delay experienced by a burst of ABR tra c in the output bu er of an ATM switch. The cdf is used to trade o bu er loss probabilities against deadline violation probabilities through adjusting the bu er size and (delay) deadline values. Large bu ers result in low losses but queueing delays can become excessive and cause a high level of deadline violations. Both losses and violations are detrimental and an operating point must be chosen to achieve a balance. In this paper we study the nature of the trade o . We develop a stochastic Petri net model assuming periodic burst arrivals for VBR and Poisson arrival processes for the Data and ABR tra c types at the burst level, and solve the model analytically (numerically) using a decomposition approach. This decomposition, along with the inherent decomposability of the tagged customer approach for obtaining the cdf opens up a possibility of carrying out fast computations using a parallel machine for selecting the operating point each time that a call is admitted.