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

Kód výsledku v 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>

Výsledek na webu

<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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Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

20104 - Transport engineering

Projekt

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Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2015

Kód důvěrnosti údajů

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

Název statě ve sborníku

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

Počet stran výsledku

6

Strana od-do

139-144

Název nakladatele

University of West Bohemia

Místo vydání

Plzeň

Místo konání akce

Cheb

Datum konání akce

9. 9. 2015

Typ akce podle státní příslušnosti

EUR - Evropská akce

Kód UT WoS článku

000387898900024