A General Solution Technique for Discrete Queueing Analysis of Multi-Media Traffic on ATM

This paper presents a general solution technique for discrete queueing analysis of multi-media traac on ATM in multiple dimensions, using generating function approach. The queue has multiple deterministic servers with innnite buuer size. Each server represents a time slot on an ATM link for the transmission of one cell. The arrival process is modeled by a number of independent Markov chains and each characterizes the stochastic properties of diierent traac type. By decomposing the generating function of the queue we separate the evaluation of the characteristic roots. Further, to characterize the great diversity of time scales of variation in multi-media traac, we decompose the overall traac arrivals into multiple independent types. Each type is constructed by a number of i:i:d: two-state Markov chains and represents a diierent time scale of variation. Simple Kronecker product properties are then used to separate the evaluation of each individual root, so that the complexity involved to solve such a root is basically independent of the system size. As the system size becomes large, the main computational limit in this method is the memory size required to solve linear equations for the boundary terms. Complete solutions for the rst two moments of the queue are therefore constructed. In numerical examples, we calculate the mean and the variance of the queue for a four-dimensional Markov queueing process. A new concept of time scale decomposition is also introduced to simplify the numerical analysis of large systems. The new insight relation between the generating function approach and the queueing analysis of multi-media traac, exposed by this paper, is a fruitful starting point for further research.