Markovian Model of Unreliable Server Retrial Queue with Discouragement

Abstract

In this paper, we present the performance analysis of Markovian retrial queue with unreliable server by incorporating the features of balking and reneging. The customers may abandon the queue at the moment of busy server or at the departure epoch from the orbit zone. When the customers notice the server in busy state, they will join to the orbit zone and wait there to avail the service. After a random period, the customers from the orbit either may try for the re-attempts for the service or may renege from the system without getting the service. Markov model is developed by considering the inter-arrival, retrial and service times governed by the exponential distributions. The probabilities of the system states are determined by implementing recursive approach to solve the governing Chapman–Kolmogorov equations. The cost function is constructed which is further used to find the total expected cost and associated optimal service rate of the system. A numerical illustration is provided to explore the system metrics with respect to various system descriptors.