On the Analysis of Unreliable Markovian Multiserver Queue with Retrials and Impatience

Year 2019, Volume: 7 Issue: 2, 205 - 217, 15.10.2019

Meriem Elhaddad Faiza Limam-belarbi

https://doi.org/10.36753/mathenot.634506

Abstract

 This paper concerns an approximate analysis of a Markovian multiserver infinite source retrial queuing with impatience, in which all the servers are subject to breakdown and

repairs. Customer who find the total number of busy and failed servers equal to $s$,i.e, he is given to choice to enter a retrial orbit for an random amount of time before attempting to

reccess an available server or enter the queue of size $q$. Customer waiting in the queue start being served as an idle or repaired server assigned to them, they can also leave the queue and enter orbit due to impatience. Customers whose service is interrupted by a failure may have the option of leaving the system entirely or returning to the orbit to repeat or resume service. We assume that each server has its own dedicated repair person, and repairs begin immediately following a failure and all process are assumed to be mutually independent.

The simultaneous effect of customer balking, impatience and retrials is analyzed.  We try  to approximate the steady-state joint distribution of the number of customers in orbit and  the

number of customers in the service area using a phase-merging Algorithm.

Keywords

Retrial queue, Multi server, Impatient, Breakdown and repair of service, Phase merging algorithm

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