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

Author:

Artalejo J. R.1,Gomez-Corral A.1

Affiliation:

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

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.

Publisher

Hindawi Limited

Subject

Applied Mathematics,Modelling and Simulation,Statistics and Probability

Cited by 6 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. An initiative for a classified bibliography on G-networks;Performance Evaluation;2011-04

2. A new solution for a queueing model of a manufacturing cell with negative customers under a rotation rule;Performance Evaluation;2011-04

3. A single-server discrete-time retrial G-queue with server breakdowns and repairs;Acta Mathematicae Applicatae Sinica, English Series;2009-09-08

4. AnMX/G/1 retrial queue with exhaustive vacations;Journal of Statistics and Management Systems;2000-11

5. G-networks: A versatile approach for work removal in queueing networks;European Journal of Operational Research;2000-10

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