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

doi:10.1007/s11464-017-0674-8

Frontiers of Mathematics in China

2017, Vol. 12

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

本期目录

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.

Key words： Markovian bulk-arriving queues equilibrium distribution queue size recurrence effective catastrophe

收稿日期: 2016-02-19 出版日期: 2017-11-27

Corresponding Author(s): Junping LI

引用本文:

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

链接本文:

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

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