Some Properties of Queueing Systems with Fluctuating Traffic Intensity


IEICE TRANSACTIONS (1976-1990)   Vol.E71   No.7   pp.659-668
Publication Date: 1988/07/25
Online ISSN: 
Print ISSN: 0000-0000
Type of Manuscript: PAPER
Category: Systems and Control

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Multi-server queueing systems with traffic intensity which vary according to an irreducible Markov chain are considered. We will show that the probability distribution for the number of customers in these systems can be expressed by an algebraic sum of geometric series with appropriate coefficients satisfying some interesting properties. To study these properties a detailed analysis of the denominator of the partial generating functions of the number of customers in the system is presented. These coefficients allow us to explain the behavior of the system under different traffic conditions. First, we derive a general expression for the probability distribution and then compare this result with that of the Zukerman and Rubin's model. One special section is devoted to the case of an arbitrary number of phases. Some numerical results are also provided and discussed to support the theoretical results.