The Departure Process of a Discrete - Time Finite Capacity System with Correlated Arrivals Zhi

Queueing network models have proven to be very useful in the analysis of communication systems. The departure process of a queue in a queueing network is of special interest because it is the arrival process to other queues in the network. For high speed networks, correlation and burstiness are very important factors for system performance and thus the smooth Bernoulli process is no longer a good assumption for an arrival process of the network traffic in a discrete-time system. We have investigated the Markov Modulated Bernoulli process (MMBP), which can adequately capture the properties of both burstiness and correlation, as a model for the arrival processes of high speed network traffic. In this paper, the departure process of a discrete-time finite capacity queue, which has an MMBP arrival process, is derived. First, the MMBP /Geo/l/K queue is studied by using a multi-dimensional Markov chain. The MMBP /D /l/K queue, which is a special case, is also investigated. The queue length distributions and blocking probabilities for both systems are derived. Furthermore, the exact solution for the departure process of the MMBP /Geo/l/K queue is investigated by using the knowledge of the queue length distribution. The generating function of the interdeparture interval time and the first four moments of this quantity are obtained. Finally, the departure process was fitted to a two-state MMBP by using a four moments matching technique.