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

被引：25

作者：

Chen, Anyue ^{[1
,5
]}

Pollett, Phil ^{[2
]}

Li, Junping ^{[3
]}

Zhang, Hanjun ^{[4
]}

机构：

[1] Univ Liverpool, Dept Math Sci, Liverpool L69 7ZL, Merseyside, England

[2] Univ Queensland, Dept Math, Brisbane, Qld 4072, Australia

[3] Cent S Univ, Sch Math Sci & Comp Technol, Changsha 410075, Hunan, Peoples R China

[4] Xiangtan Univ, Sch Math & Computat Sci, Xiangtan 411105, Peoples R China

[5] Univ Hong Kong, Dept Stat & Actuarial Sci, Hong Kong, Hong Kong, Peoples R China

来源：

QUEUEING SYSTEMS | 2010年 / 64卷 / 03期

关键词：

Bulk-arrival and bulk-service queues; State-dependent control; Equilibrium distribution; Transient behaviour; Queue length distributions; Hitting times; Busy period distributions; BRANCHING-PROCESSES; NEGATIVE CUSTOMERS; INSTANTANEOUS IMMIGRATION; QUEUING-NETWORKS; RECURRENCE; DISASTERS; EXISTENCE; TIMES;

D O I：

10.1007/s11134-009-9162-5

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

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.

引用

页码：267 / 304

页数：38

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