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

  • Authors:

  • Anyue Chen;Phil Pollett;Junping Li;Hanjun Zhang

  • Affiliations:

  • Department of Mathematical Sciences, The University of Liverpool, Liverpool, UK L69 7ZL and Department of Statistics and Actuarial Science, University of Hong Kong, Hong Kong, HKSAR;Department of Mathematics, University of Queensland, Brisbane, Australia 4072;School of Mathematical Science and Computing Technology, Central South University, Changsha, China 410075;School of Mathematics and Computational Science, Xiangtan University, Xiangtan, China 411105

  • Venue:
  • Queueing Systems: Theory and Applications
  • Year:
  • 2010

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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.