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Journal of Applied Mathematics and Stochastic Analysis
Volume 9 (1996), Issue 2, Pages 171-183
http://dx.doi.org/10.1155/S1048953396000172

Stochastic analysis of the departure and quasi-input processes in a versatile single-server queue

University Complutense of Madrid, Mathematics Faculty, Department of Statistics and O.R., Madrid 28040, Spain

Received 1 July 1995; Revised 1 October 1995

Copyright © 1996 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper is concerned with the stochastic analysis of the departure and quasi-input processes of a Markovian single-server queue with negative exponential arrivals and repeated attempts. Our queueing system is characterized by the phenomenon that a customer who finds the server busy upon arrival joins an orbit of unsatisfied customers. The orbiting customers form a queue such that only a customer selected according to a certain rule can reapply for service. The intervals separating two successive repeated attempts are exponentially distributed with rate α+jμ, when the orbit size is j1. Negative arrivals have the effect of killing some customer in the orbit, if one is present, and they have no effect otherwise. Since customers can leave the system without service, the structural form of type M/G/1 is not preserved. We study the Markov chain with transitions occurring at epochs of service completions or negative arrivals. Then we investigate the departure and quasi-input processes.