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

Abstract

This paper concerns an approximate analysis of a Markovian multiserver infinite source retrial queuingwith impatience, in which all the servers are subject to breakdown and repairs. Customer who find thetotal number of busy and failed servers equal to s,i.e, he is given to choice to enter a retrial orbit for anrandom 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, theycan also leave the queue and enter orbit due to impatience. Customers whose service is interrupted by afailure may have the option of leaving the system entirely or returning to the orbit to repeat or resumeservice. We assume that each server has its own dedicated repair person, and repairs begin immediatelyfollowing 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 approximatethe steady-state joint distribution of the number of customers in orbit and the number of customers inthe service area using a phase-merging Algorithm.