A discrete-time single server queue with a two-level modulated input and its applications

Abstract

A discrete-time, single-server system with a two-level modulated input is considered. The time axis is divided into equal-length slots, and the service time is deterministic and equal to one slot. The probability-generating function of the number of calls in the system is derived. A special case of this queuing system with a two-level Markov modulated Poisson input is studied in detail. Some numerical results concerning the mean and the variance of waiting time of an arbitrary call are given. The MMPP (Markov modulated Poisson process) approach is used to study some cases other than that of the packetized voice system. An alternative to the determination of the four parameters of the MMPP is also presented. This approach produces better results than the method presented for the cases with long burst length and high source peak rate (broadband integrated services digital network). This queuing model can be applied to performance analysis of a discrete-time ATM (asynchronous transfer mode) system and can be used as an approximation for a continuous-time MMPP/D/1 system.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>