The interchangeability of ·/M/1 queues in series

Author:

Weber Richard R.

Abstract

A series of queues consists of a number of · /M/1 queues arranged in a series order. Each queue has an infinite waiting room and a single exponential server. The rates of the servers may differ. Initially the system is empty. Customers enter the first queue according to an arbitrary stochastic input process and then pass through the queues in order: a customer leaving the first queue immediately enters the second queue, and so on. We are concerned with the stochastic output process of customer departures from the final queue. We show that the queues are interchangeable, in the sense that the output process has the same distribution for all series arrangements of the queues. The ‘output theorem' for the M/M/1 queue is a corollary of this result.

Publisher

Cambridge University Press (CUP)

Subject

Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability

Cited by 7 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Queues, stores, and tableaux;Journal of Applied Probability;2005-12

2. On the departure processes of M/M/1/N and GI/G/1/N queues;Advances in Applied Probability;1992-09

3. The interchangeability of tandem queues with heterogeneous customers and dependent service times;Advances in Applied Probability;1992-09

4. Rare events in series of queues;Journal of Applied Probability;1992-03

5. On interchangeability for exponential single-server queues in tandem;Journal of Applied Probability;1990-06

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