Stochastic analysis of the departure and quasi-input processes in a versatile single-server queue
type: Item
instance of: scholarly article
title: Stochastic analysis of the departure and quasi-input processes in a versatile single-server queue
zbMATH Open document ID: 0858.60083
DOI: 10.1155/S1048953396000172
published in: Journal of Applied Mathematics and Stochastic Analysis
publication date: 1997-03-18T00:00:00Z
full work available at URL: https://eudml.org/doc/47614
review text: Summary: 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 \(\alpha + j\mu\), when the orbit size is \(j\geq 1\). 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.
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 90B22
zbMATH DE Number: 938919
zbMATH Keywords: queueing
zbMATH Keywords: repeated attempts
zbMATH Keywords: negative arrivals
zbMATH Keywords: regenerative processes
zbMATH Keywords: generalized hypergeometric functions
author: Jesus R. Artalejo
author: A. Gómez-Corral
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 938919