The Embedded Random Walk in the Stationary M/M/1 Queue

被引：1

作者：

W. Stadje

机构：

[1] University of Osnabrück,Department of Mathematics and Computer Science

来源：

Methodology And Computing In Applied Probability | 2002年 / 4卷 / 2期

关键词：

simple queue; steady state; embedded Markov chain; exact distribution; monotonicity;

D O I：

10.1023/A:1020685423386

中图分类号：

学科分类号：

摘要：

We consider the stationary queue length process of the standard M/M/1 queue just after its jump times (i.e., the times of arrivals or departures). Simple formulas for the distribution of this embedded random walk with immediate reflection at zero are derived. We study the monotonicity properties of the corresponding expected values and point out an asymmetry between the number of arrivals and the number of departures until the n-th jump time.

引用

页码：143 / 151

页数：8

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