Martix geometric analysis of discrete time queues with batch arrivals and batch departures with applications to B-ISDN

This paper presents some extensions to the matrix geometric analysis method for performance evaluation of communication systems modeled via discrete time queues. The paper considers the case where the arrival streams generate periodic traffic with a period which varies according to an underlying modulating Markov process. The proposed algorithms evaluate the rate matrices which appear in the definition of the equilibrium distribution. A significant reduction in the computational complexity of the performance evaluation for servers with periodic arrival streams is obtained, by reducing the required size of the state space of the modulating Markov processes. The method is applicable to ATM systems with periodicities caused by the higher layer protocols, by traffic shaping, by ABR or UBR control mechanisms, etc.