A general solution technique for discrete queueing analysis of multimedia traffic on ATM

The author presents a general solution using a generating function approach. 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. By decomposing the generating function of the queue, the evaluation of the characteristic roots is separated. 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, so that the complexity involved to solve such a root is basically independent of the system size.>