A general solution technique for discrete queueing analysis of multi-media traffic on ATM

A generating function approach is used. The queue has multiple deterministic servers with infinite buffer 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 a different traffic type. The generating function of the queue is decomposed in order to separate the evaluation of the characteristic roots. Further, to characterize the great diversity of time scales of variation in multimedia traffic, the overall traffic arrivals are decomposed into multiple independent types. Each type is constructed by a number of i.i.d. two-state Markov chains and represents a different time scale of variation. Simple Kronecker product properties are then used to separate the evaluation of each individual root. 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 first two moments of the queue are constructed. In numerical examples, calculations are made of 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