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On Multiserver Queues with mPhase Synchronous Fluctuation of Traffic Intensity
Walter SOTELO Kaiji MUKUMOTO Akira FUKUDA
Publication
IEICE TRANSACTIONS (19761990)
Vol.E70
No.12
pp.11871194 Publication Date: 1987/12/25 Online ISSN:
DOI: Print ISSN: 00000000 Type of Manuscript: PAPER Category: Systems and Control Keyword:
Full Text: PDF(586.4KB)>>
Summary:
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 mphase 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 steadystate 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 steadystate 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 interarrival, service, or sojourn time distribution.

