Unreliable Multi Server Retrial Queueing System with Reneging and Diverse Outgoing Services

This article explores a M/M/m unreliable retrial queue with reneging and diverse outgoing services.Incoming calls that arrive and discover all servers occupied join the orbit.The buffering incomings from the orbit retry their request after a while or leave the system without receiving service.When the orbit becomes empty, the idle server provides outgoing services.It is assumed that there are two categories of outgoing services.Due to unexpected circumstances, the server may breakdown.When a server undergoes breakdown, immediate repair process begins.Post-server breakdown, incoming calls go into orbit and retry service randomly, whereas the two variants of outgoing calls leave the system.The study utilizes a quasi-birth-death (QBD) process to analyse the stationary system size distribution.The steady state probabilities and the rate matrix are obtained through the matrix geometric method (MGM).Various performance metrics are evaluated for the proposed model.The study examines the impact of various system-based parameters on efficiency metrics with the help of numerical results.