The M/M/1 queue with mass exodus and mass arrivals when empty

被引：76

作者：

Chen, A ^{[1
]}

Renshaw, E ^{[1
]}

机构：

[1] UNIV STRATHCLYDE,DEPT STAT & MODELLING SCI,GLASGOW G1 1XH,LANARK,SCOTLAND

来源：

JOURNAL OF APPLIED PROBABILITY | 1997年 / 34卷 / 01期

关键词：

M/M/1; queue; catastrophe; mass immigration; q-process; recurrence; transience; idle probability; equilibrium probabilities; factorial moments;

D O I：

10.2307/3215186

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

An M/M/1 queue is subject to mass exodus at rate beta and mass immigration at rate {alpha(r); r greater than or equal to 1} when idle. A general resolvent approach is used to derive-occupation probabilities and high-order moments. This powerful technique is not only considerably easier to apply than a standard direct attack on the forward p.g.f. equation, but it also implicitly yields necessary and sufficient conditions for recurrence, positive recurrence and transience.

引用

页码：192 / 207

页数：16

共 17 条

[1] Abramowitz M., 1965, Handbook of Mathematical Functions, Dover Books on Mathematics
[2] Anderson W. J., 1991, CONTINUOUS TIME MARK
[3] Asmussen S, 2008, APPL PROBABILITY QUE, V51
[4] EXISTENCE AND UNIQUENESS CRITERIA FOR CONSERVATIVE UNI-INSTANTANEOUS DENUMERABLE MARKOV-PROCESSES
CHEN, A
RENSHAW, E
[J]. PROBABILITY THEORY AND RELATED FIELDS, 1993, 94 (04) : 427 - 456
[5] RECURRENCE OF MARKOV BRANCHING-PROCESSES WITH IMMIGRATION
CHEN, A
RENSHAW, E
[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1993, 45 (02) : 231 - 242
[6] MARKOV BRANCHING-PROCESSES WITH INSTANTANEOUS IMMIGRATION
CHEN, AY
RENSHAW, E
[J]. PROBABILITY THEORY AND RELATED FIELDS, 1990, 87 (02) : 209 - 240
[7] MARKOV BRANCHING-PROCESSES REGULATED BY EMIGRATION AND LARGE IMMIGRATION
CHEN, AY
RENSHAW, E
[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1995, 57 (02) : 339 - 359
[8] Cox D. R., 1965, THEORY STOCHASTIC PR
[9] GOSS D, 1985, FUNDAMENTALS QUEUEIN
[10] Hou Z. T., 1988, HOMOGENEOUS DENUMERA

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