M/En/1/m queueing system subject to two types of failures

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27230%2F15%3A86094638" target="_blank" >RIV/61989100:27230/15:86094638 - isvavai.cz</a>

Result on the web

<a href="http://mme2015.zcu.cz/downloads/MME_2015_proceedings.pdf" target="_blank" >http://mme2015.zcu.cz/downloads/MME_2015_proceedings.pdf</a>

DOI - Digital Object Identifier

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Result language

angličtina

Original language name

M/En/1/m queueing system subject to two types of failures

Original language description

The paper deals with a finite single-server queueing system with a server subject to two classes of breakdowns – the first class is represented by non-preemptive failures, the second class by so-called catastrophes. The non-preemptive failures do not interrupt the service process; we consider that it is possible to finish the service of the customer before we begin to repair the server. The catastrophes interrupt the service of the customer and all the customers found in the system are flushed out of the system. Moreover, the system rejects all the customers when the server is under repair after the catastrophe (that means the system is always empty during the repair of the catastrophic failure). We consider that the customers enter the system according to the Poisson process and they can wait in a queue that has a limited capacity equal to m-1. The customers are served by the single server according to the FCFS service discipline, service times are Erlang distributed. Times between the non-preemptive failures and the catastrophes and times to repair are exponentially distributed. The queueing system is modelled as a multi-dimensional Markov chain for which we present a linear equation system to obtain stationary probabilities of the individual states of the system; the equation system is solved numerically via software Matlab. On the basis of the probabilities we are able to compute some performance measures. At the end of the paper we present some results of experiments carried out with the presented mathematical model in order to present its functionality.

Czech name

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Czech description

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Type

D - Article in proceedings

CEP classification

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OECD FORD branch

20104 - Transport engineering

Project

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Continuities

S - Specificky vyzkum na vysokych skolach

Publication year

2015

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection

Mathematical Methods in Economics, MME 2015 : 33rd international conference : conference proceedings : Cheb, Czech Republic, September 9-11, 2015

ISBN

978-80-261-0539-8

ISSN

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e-ISSN

neuvedeno

Number of pages

6

Pages from-to

139-144

Publisher name

University of West Bohemia

Place of publication

Plzeň

Event location

Cheb

Event date

Sep 9, 2015

Type of event by nationality

EUR - Evropská akce

UT code for WoS article

000387898900024