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Markovian bulk-arrival and bulk-service queues with state-dependent control

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Abstract

We study a modified Markovian bulk-arrival and bulk-service queue incorporating state-dependent control. The stopped bulk-arrival and bulk-service queue is first investigated and the relationship with our queueing model is examined and exploited. Equilibrium behaviour is studied and the probability generating function of the equilibrium distribution is obtained. Queue length behaviour is also examined and the Laplace transform of the queue length distribution is presented. The important questions regarding hitting time and busy period distributions are answered in detail and the Laplace transforms of these distributions are presented. Further properties including expectations of hitting times and busy period are also explored.

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Authors and Affiliations

  1. Department of Mathematical Sciences, The University of Liverpool, Liverpool, L69 7ZL, UK

    Anyue Chen

  2. Department of Statistics and Actuarial Science, University of Hong Kong, Pokfulam Road, Hong Kong, HKSAR

    Anyue Chen

  3. Department of Mathematics, University of Queensland, Brisbane, Qld, 4072, Australia

    Phil Pollett

  4. School of Mathematical Science and Computing Technology, Central South University, Changsha, 410075, China

    Junping Li

  5. School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411105, China

    Hanjun Zhang

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  1. Anyue Chen
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  2. Phil Pollett
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  3. Junping Li
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  4. Hanjun Zhang
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Correspondence to Anyue Chen.

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Chen, A., Pollett, P., Li, J. et al. Markovian bulk-arrival and bulk-service queues with state-dependent control. Queueing Syst 64, 267–304 (2010). https://doi.org/10.1007/s11134-009-9162-5

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  • DOI: https://doi.org/10.1007/s11134-009-9162-5

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