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Summary: Queueing Systems 2 (1987) 387-392 387
PROBABILISTIC PROOF OF THE INTERCHANGEABILITY
OF ./M/1 QUEUES IN SERIES
V. ANANTHARAM
School of Electrical Engineering, Phillips Hall, Cornell University, Ithaca, NY 14853, U.S.A.
Received: 14 April 1987
Revised: 15 August 1987
Abstract
Given a .finite number of empty ./M/1 queues, let customers arrive according to an arbitrary
arrival process and be served at each queue exactly once, in some fixed order. The process of
departing customers from the network has the same law, whatever the order in which the
queues are visited. This remarkable result, due to R. Weber [4], is given a simple probabilistic
proof.
Keywords
Departure process, filtering theory, insensitivity, M/M/1 queues, point processes, queueing
theory, tandem queues.
1. Introduction
Given a finite number of empty ./M/1 queues, let customers arrive according
to an arbitrary arrival process, and be served at each queue exactly once, in some
fixed order, i.e., once they finish service at the first server they joint the queue at
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