OF E2/E2/1/m QUEUEING SYSTEM SUBJECT TO OPERATEDEPENDENT SERVER BREAKDOWNS

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  • Michal Dorda

Klíčová slova:

E2/E2/1/m, queueing, method of stages, server breakdown, Witness

Abstrakt

The paper deals with modelling of a finite single-server queueing system with a server subject to breakdowns. Customers interarrival times and customers service times follow the Erlang distribution defined by the shape parameter k=2 and the scale parameter 2λ or 2μ respectively. We consider that server failures can occur when the server is busy (so called operate-dependent failures). Further we assume that service of a customer is interrupted by the occurrence of the server failure (the preemptive-repeat discipline. We assume that random variables relevant to server failures and repairs are exponentially distributed. The queueing system is modelled using method of stages. We present a state transition diagram, a system of linear equations describing the system behaviour in the steady-state and formulas for several performance measures computation. To validate the mathematical model a simulation model was created using simulation software Witness. At the end of the paper some graphical dependencies are shown.

Stažení

Data o stažení nejsou doposud dostupná.

Reference

(1) BOLCH, G., GREINER, S., DE MEER, H., TRIVEDI, K. S. Queueing Networks and
Markov Chains – Modeling and Performance Evaluation with Computer Science
Applications (second edition). John Wiley & Sons, Inc., New Jersey, 2006.
(2) COOPER, R. B. Introduction to Queueing Theory (second edition). Elsevier North
Holland, Inc., New York, 1981.
(3) SHARMA, K. C., SIROHI, A.: Cost Analysis of the Unloader Queueing System with a
Single Unloader Subject to Breakdown with Two Types of Trailers. Opsearch 47(1); 93-
103, 2010.
(4) DORDA, M. Modelling and Simulation of Unreliable E2/E2/1/m Queueing System.
Sborník vědeckých prací Vysoké školy báňské - Technické univerzity Ostrava, Řada
strojní. 2011, č. 1, s. 49-55. ISBN 978-80-248-2051-4, ISSN 1210-0471 (Print), ISSN
1804-0993 (Online), ISSN-L 1210-0471.

Stahování

Publikováno

2012-07-13

Jak citovat

Dorda, M. . (2012). OF E2/E2/1/m QUEUEING SYSTEM SUBJECT TO OPERATEDEPENDENT SERVER BREAKDOWNS. Perner’s Contacts, 7(2), 15–21. Získáno z https://pernerscontacts.upce.cz/index.php/perner/article/view/1136

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