Finite buffer discrete-time queues with multiple Markovian arrivals and services in ATM networks

An efficient computational procedure to calculate the queue size distribution in a finite buffer queuing system with a number of independent sources is presented. Each source is characterized by a finite state discrete-time Markov chain. An explicit expression for the queue size distribution is obtained directly. The method is based on computing the modified spectral expansion of the state distribution of the system. This representation requires evaluating the roots of the entire system characteristic function and solving a set of linear system equations. Exact results show that the cell loss probability depends only on the ratio of the buffer capacity to burst length. An approximation expression for the cell loss probability based on asymptotic analysis is also presented. Numerical results show that the approximation is accurate, especially when the system load is heavy. The effect of burst length on the cell loss probability is investigated