On Multiserver Queues with Synchronous Fluctuation of Traffic Intensity

Walter SOTELO  Akira FUKUDA  

IEICE TRANSACTIONS (1976-1990)   Vol.E70   No.10   pp.951-959
Publication Date: 1987/10/25
Online ISSN: 
Print ISSN: 0000-0000
Type of Manuscript: PAPER
Category: Engineering Science in General

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A study is presented on the generalization of the M/M/1 model with synchronous fluctuation of traffic intensity for the case of more than one server. The parameters of the queueing system fluctuates between two phases and the phase process is assumed to make changes according to an irreducible Markov chain. Phase changes may occur only when a customer arrives to the queue, further, his service time is also determined at his arrival instant. We compare our results to that of the asynchronous one and the comparison clearly shows that we can approximate the performance of the asynchronous model by that of the synchronous one and vice-versa. However, we point out that, to extend the M/M/K (M/M/) model with fluctuating parameters to the case of general interarrival, service, or sojourn time distribution, is easier in the case of the synchronous model than in the case of the asynchronous one since the latter introduces very considerable analytic complications. Two models, the M/M/K and M/M/, with synchronous fluctuation of parameters are analyzed in depth. Explicit results for the expected queue length are presented and discussed. Finally, numerical examples are used to support the theoretical analysis for a variety of traffic conditions.