An Analysis of the M/G/1 Retrial Queue with Negative Arrivals using a Martingale Technique*

被引：0

作者：

Berdjoudj L. ^{[1
]}

Aissani D. ^{[1
]}

机构：

[1] University of Bejaia, Bejaia

来源：

Journal of Mathematical Sciences | 2014年 / 196卷 / 1期

关键词：

Queue Length; Renewal Process; Busy Period; Retrial Queue; Single Server Queue;

D O I：

10.1007/s10958-013-1628-7

中图分类号：

学科分类号：

摘要：

We consider the M/G/1 retrial queue with negative arrivals. Using the technique of Baccelli and Makowski (1985, 1989) we define a martingale with respect to an embedded process. Using this, an analysis of the stationary behavior of the queue is possible. © 2013, Springer Science+Business Media New York.

引用

页码：11 / 14

页数：3

共 9 条

[1]

Artalejo J.R., A classified bibliography of research on retrial queues: progress in 1990–1999, TOP, 7, 2, pp. 187-211, (1999)

[2]

Artalejo J.R., Gomez-Corral A., On a single server queue with negative arrivals and request repeated, J. Appl. Probab., 36, pp. 907-918, (1999)

[3]

Baccelli F., Gomez-Corral A., Direct martingale arguments for stability: the M/G/1 case, Syst. Control Lett., 6, pp. 181-186, (1985)

[4]

Baccelli F., Makowski A.M., Dynamic, transient and stationary behaviour of the M/GI/1 queue via martingals, Ann. Probab., 17, 4, pp. 1691-1699, (1989)

[5]

Takacs L., Introduction to the Theory of Queues, (1962)

[6]

Falin G.I., Templeton J.G.C., Retrial Queues, (1997)

[7]

Gelenbe E., Production form queueing networks with negative and positive customers, J. Appl. Probab., 28, pp. 656-663, (1991)

[8]

Neuveu J., Martingales `a Temps Discret, (1972)

[9]

Roughan M., An application of martingales to queueing theory, Ph.D. Thesis, Department of Applied Mathematics, University of Adelaide, (1994)

← 1 →