Martingale Methods for Analysing Single-Server Queues

被引：0
作者：
M. Roughan
C.E.M. Pearce
机构：
[1] AT&T Labs – Research,Department of Applied Mathematics
[2] University of Adelaide,undefined
来源：
Queueing Systems | 2002年 / 41卷
关键词：
/; /1 queue; martingale queueing; phase; overload control;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper we presents a martingale method for analysing queues of M/G/1 type, which have been generalised so that the system passes through a series of phases on which the service behaviour may differ. The analysis uses the process embedded at departures to create a martingale, which makes possible the calculation of the probability generating function of the stationary occupancy distribution. Specific examples are given, for instance, a model of an unreliable queueing system, and an example of a queue-length-threshold overload-control system.
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页码：205 / 239
页数：34
相关论文
共 44 条
[1]  
Abate J.(1992)Numerical inversion of probability generating functions Oper. Res. Lett. 12 245-251
[2]  
Whitt W.(1986)Exponential martingales and Wald's formula for two-queue networks J. Appl. Probab. 23 812-819
[3]  
Baccelli F.(1985)Direct martingale arguments for stability: The Systems Control Lett. 6 181-186
[4]  
Baccelli F.(1989)1 case Ann. Probab. 17 1691-1699
[5]  
Makowski A.M.(1991)Dynamic, transient and stationary behaviour of the Stochastic Process. Appl. 38 99-133
[6]  
Baccelli F.(1989)1 queue via martingales Oper. Res. Lett. 8 229-236
[7]  
Makowski A.M.(1989)Martingale relations for the J. Appl. Probab. 26 345-362
[8]  
Baccelli F.(1992)1 queue with Markov modulated Poisson input Commun. Statist. Stochastic Models 8 733-741
[9]  
Makowski A.M.(1990)Queue length distributions from probability generating functions via discrete Fourier transforms Queueing Systems 7 253-268
[10]  
Daigle J.N.(1992)Multi-channel queueing systems with infinite waiting rooms and stochastic control Queueing Systems 11 255-272
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