A BULK SERVICE GI/M/1 QUEUE WITH SERVICE RATES DEPENDING ON SERVICE BATCH SIZE

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概要

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• We consider a bulk service GI/M/1 queue with service rates depending on service batch size. If there are n customers waiting at the completion of service, min(n, K) customers enter service. We show that the queue size and the service batch size at points of arrivals form an embedded Markov chain and the steady-state probabilities of this Markov chain have the matrix geometric form. We describe the rate matrix R of the matrix geometric solution procedure in a readily computable form. We obtain explicit analytic expressions for the steady-state queue length distribution at points of arrivals. Further we obtain the Laplace-Stieltjes transform and the moments of the stationary waiting time distribution of an arbitrary customer.

• 社団法人日本オペレーションズ・リサーチ学会の論文

著者

• Baba Yutaka

  Faculty Of Education Yokohama National University

関連論文

• A BULK SERVICE GI/M/1 QUEUE WITH SERVICE RATES DEPENDING ON SERVICE BATCH SIZE

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