RESEARCH ARTICLE

MX=M=c Queue with catastrophes and state-dependent control at idle time

  • Junping LI , 1 ,
  • Lina ZHANG 2
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  • 1. School of Mathematics and Statistics, Central South University, Changsha 410083, China
  • 2. School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China

Received date: 19 Feb 2016

Accepted date: 08 Oct 2016

Published date: 27 Nov 2017

Copyright

2017 Higher Education Press and Springer-Verlag GmbH Germany

Abstract

We consider an MX=M=c queue with catastrophes and state-dependent control at idle time. Properties of the queues which terminate when the servers become idle are first studied. Recurrence, equilibrium distribution, and equilibrium queue-size structure are studied for the case of resurrection and no catastrophes. All of these properties and the first effective catastrophe occurrence time are then investigated for the case of resurrection and catastrophes. In particular, we obtain the Laplace transform of the transition probability for the absorbing MX=M=c queue.

Cite this article

Junping LI , Lina ZHANG . MX=M=c Queue with catastrophes and state-dependent control at idle time[J]. Frontiers of Mathematics in China, 2017 , 12(6) : 1427 -1439 . DOI: 10.1007/s11464-017-0674-8

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