Approximate anlysis of an unreliable M/M/c retrial queue with phase merging algorithm

Year 2016, Volume: 4 Issue: 3, 9 - 21, 30.09.2016

Meriem El Haddad Faiza Belarbi

Abstract

In this paper, we investigate an approximate analysis
of unreliable  retrial queue with  in which all servers are subject to
breakdowns and repairs. Arriving customers that are unable to access a server
due to congestion or failure can choose to enter a retrial orbit for an
exponentially distributed amount of time and persistently attempt to gain
access to a server, or abandon their request and depart the system. Once a
customer is admitted to a service station, he remains there for a random
duration until service is complete and then depart the system. However, if the
server fails during service, i.e., an active breakdown, the customer may choose
to abandon the system or proceed directly to the retrial orbit while the server
begins repair immediately. In the unreliable model, there are no exact
solutions when the number of servers exceeds one. Therefore, we seek to
approximate the steady-state joint distribution of the number of customers in
orbit and the status of the  servers for the case of Markovian
arrival and service times. Our approach to deriving the approximate
steady-state probabilities employs a phase-merging algorithm.

Keywords

Retrial queue, Multi server, Breakdown and repair of service

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