Transient and steady-state analysis of a queuing system having customers’ impatience with threshold

¹ School of Mathematics, Shri Mata Vaishno Devi University, 182320 Katra, Jammu and Kashmir, India
² Department of Mathematics, Faculty of Science, Menofia University, Shebin El Kom, Egypt
³ Department of Mathematics, College of Science, Taibah University, Madinah Munawwarah, Saudi Arabia

^* Corresponding author: rakesh.kumar@smvdu.ac.in

Received: 4 May 2018
Accepted: 13 November 2018

Abstract

In many practical queuing situations reneging and balking can only occur if the number of customers in the system is greater than a certain threshold value. Therefore, in this paper we study a single server Markovian queuing model having customers’ impatience (balking and reneging) with threshold, and retention of reneging customers. The transient analysis of the model is performed by using probability generating function technique. The expressions for the mean and variance of the number of customers in the system are obtained and a numerical example is also provided. Further the steady-state solution of the model is obtained. Finally, some important queuing models are derived as the special cases of this model.