Journal of Applied Mathematics and Stochastic Analysis
Volume 9 (1996), Issue 2, Pages 171-183
doi: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 J. R. Artalejo and A. Gomez-Corral. 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 j≥1. 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.