Steady-state analysis of batch-size-dependent service queue with server breakdown, close-down time and multiple vacations

Department of Mathematics, Visvesvaraya National Institute of Technology, Nagpur 440010, India

^* Corresponding author: spiitkgp11@gmail.com

Received: 19 July 2024
Accepted: 12 February 2025

Abstract

For an efficient and cost effective utilization of the resources, queue length as well as server content distribution plays a noteworthy role. Dealing with manufacturing systems or telecommunications networks, we may encounter server’s breakdown which definitely effects queue length, waiting time of customers and cost of the system. We may also come across the situations where server performs the close-down works or may take the vacation of random time whenever enough number of customers are not available to start the service. The main objective of this paper is to analyze a queueing system with server’s breakdown, close-down time, multiple vacation and batch-size-dependent service mechanism. More precisely, we focus to derive the bivariate probability generating function of the joint queue and server content distribution at service completion epoch. We extract those probabilities and present them in a simplified form in terms of roots of the characteristic equation. We also obtain the probabilities at arbitrary epoch using which we acquire marginal distributions and performance measures. At the end, numerical examples with assorted significant distributions are provided which gives an insight to the readers and practitioners.