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

The B‐ISDN will carry a variety of traffic types: the Variable Bit Rate traffic (VBR), of which compressed video is an example, Continuous Bit Rate traffic (CBR), of which telemetry is an example, Data traffic, and Available Bit Rate traffic (ABR) that represents aggregate data traffic with very limited guarantees on quality. Of these, VBR and CBR have timing constraints and need synchronous bandwidth; data traffic is relatively delay insensitive. In this paper, we consider the VBR, Data and ABR traffic types and obtain the cumulative distribution function (cdf) of the queueing delay experienced by a burst of ABR traffic in the output buffer of an ATM switch. The cdf is used to trade off buffer loss probabilities against deadline violation probabilities through adjusting the buffer size and (delay) deadline values. Large buffers 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 off. We develop a stochastic Petri net model assuming periodic burst arrivals for VBR and Poisson arrival processes for the Data and ABR traffic 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. This revised version was published online in June 2006 with corrections to the Cover Date.