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

doi:10.1007/s11464-017-0674-8

Front. Math. China

2017, Vol. 12

Issue (6) : 1427-1439 https://doi.org/10.1007/s11464-017-0674-8

RESEARCH ARTICLE

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

Junping LI¹(

), Lina ZHANG²

¹. School of Mathematics and Statistics, Central South University, Changsha 410083, China
². School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China

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Abstract

We consider an M^X=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 M^X=M=c queue.

Keywords Markovian bulk-arriving queues equilibrium distribution queue size recurrence effective catastrophe

Corresponding Author(s): Junping LI

Issue Date: 27 November 2017

Cite this article:

Junping LI,Lina ZHANG. M^X=M=c Queue with catastrophes and state-dependent control at idle time[J]. Front. Math. China, 2017, 12(6): 1427-1439.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-017-0674-8
https://academic.hep.com.cn/fmc/EN/Y2017/V12/I6/1427

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