On Multiserver Queues with m-Phase Synchronous Fluctuation of Traffic Intensity


IEICE TRANSACTIONS (1976-1990)   Vol.E70   No.12   pp.1187-1194
Publication Date: 1987/12/25
Online ISSN: 
Print ISSN: 0000-0000
Type of Manuscript: PAPER
Category: Systems and Control

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The M(m)/M/K and M(m)/M/ models with synchronous fluctuation of traffic intensity are considered. The phase process is assumed to make changes according to an irreducible m-phase Markov chain. In contrast to the model with asynchronous fluctuation of parameters, phase changes may occur in synchronization with an arrival or beginning of a customer's service. We study mainly the steady-state regime of our models, and observe that, in general, closed form solutions for the limiting probabilities are difficult to obtain but their numerical computation is rather straightforward. We give a necessary and sufficient condition for the steady-state to be attained. For the model M(m)/M/K, it is shown that, for the case where the traffic intensity of one phase is greater than one (even if the average traffic intensity is less than one) the average queue length approaches infinity as the fluctuations among phases gets more sluggish. However, for the case where the traffic intensity for all phases is less than one, the queue length is moderate and not dependent as much on the rate of fluctuation among phases. Numerical examples are given and discussed. Finally, we point out that, our models may be more tractable than the asynchronous ones, when we try to generalize them to the case of general inter-arrival, service, or sojourn time distribution.