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Factorization and Stochastic Decomposition Properties in Bulk Queues with Generalized Vacations

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Abstract

This paper considers a class of stationary batch-arrival, bulk-service queues with generalized vacations. The system consists of a single server and a waiting room of infinite capacity. Arrivals of customers follow a batch Markovian arrival process. The server is unavailable for occasional intervals of time called vacations, and when it is available, customers are served in groups of fixed size B. For this class of queues, we show that the vector probability generating function of the stationary queue length distribution is factored into two terms, one of which is the vector probability generating function of the conditional queue length distribution given that the server is on vacation. The special case of batch Poisson arrivals is carefully examined, and a new stochastic decomposition formula is derived for the stationary queue length distribution.

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Authors and Affiliations

  1. Laboratory for Manufacturing and Productivity 35-436, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA, 02139-4307, USA

    Seok Ho Chang

  2. Department of Communication Engineering, Graduate School of Engineering, Osaka University, Suita, 565-0871, Japan

    Tetsuya Takine

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  1. Seok Ho Chang
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  2. Tetsuya Takine
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Correspondence to Seok Ho Chang.

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AMS subject classification: 60K25, 90B22, 60K37

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Chang, S.H., Takine, T. Factorization and Stochastic Decomposition Properties in Bulk Queues with Generalized Vacations. Queueing Syst 50, 165–183 (2005). https://doi.org/10.1007/s11134-005-0510-9

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  • DOI: https://doi.org/10.1007/s11134-005-0510-9

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