Performance Analysis of a Time-Sharing Queue with Server Breakdown, Discouraging Arrivals and Reneging

Abstract

This paper investigates a single-server time-sharing queueing system with server breakdowns, discouraging arrivals and customer reneging. Customers arrive according to a Poisson process with rate λ while the server is operational. During server breakdowns, the arrival rate is reduced to represent customer discouragement. The server operates under the time-sharing discipline, where all customers in the system receive an equal share of the available service capacity simultaneously. Service times are assumed to be exponentially distributed. The server is subject to random breakdowns and is restored after repair, while customers may abandon the system due to impatience through reneging. The proposed model is analysed using the Continuous-Time Markov Chain (CTMC) approach and the corresponding steady-state balance equations are formulated to obtain the steady-state probability distribution. Several system performance measures, including the expected number of customers in the system, average waiting time, server availability, throughput and reneging probability are derived. Numerical experiments are carried out to examine the effects of arrival rate, breakdown rate, repair rate and reneging rate on system performance. The proposed model provides a useful analytical framework for evaluating time-sharing service systems operating under server interruptions and impatient customer behavior with potential applications in computer systems, communication networks, cloud computing and other shared-resource environments.