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Transient performance analysis of a single server queuing model with retention of reneging customers

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In this paper, we study a single server queuing model with retention of reneging customers. The transient solution of the model is derived using probability generating function technique. The time-dependent mean and variance of the model are also obtained. Some important special cases of the model are derived and discussed. Finally, based on the numerical example, the transient performance analysis of the model is performed. | Yugoslav Journal of Operations Research 28 (2018), Number 3, 315–331 DOI: https://doi.org/10.2298/YJOR170415007K TRANSIENT PERFORMANCE ANALYSIS OF A SINGLE SERVER QUEUING MODEL WITH RETENTION OF RENEGING CUSTOMERS Rakesh KUMAR Department of Mathematics, Shri Mata Vaishno Devi University, Katra Jammu and Kashmir, India rakesh stat kuk@yahoo.co.in Sapana SHARMA Department of Mathematics, Shri Mata Vaishno Devi University, Katra Jammu and Kashmir, India sapanasharma736@gmail.com Received: April 2017 / Accepted: February 2018 Abstract: In this paper, we study a single server queuing model with retention of reneging customers. The transient solution of the model is derived using probability generating function technique. The time-dependent mean and variance of the model are also obtained. Some important special cases of the model are derived and discussed. Finally, based on the numerical example, the transient performance analysis of the model is performed. Keywords: Transient Performance Analysis, Mean and Variance, Probability Generating Function, Reneging, Probability of Customers’ Retention. MSC: 60K25, 68M20. 1. INTRODUCTION Queuing systems with customers’ impatience are used in modeling and analysis of a wide variety of real situations, for example, computer networks with packet loss, perishable inventory systems, call centres, hospital emergency rooms handling 316 Kumar, R., and Sharma, S., / Transient Performance Analysis critical patients, and impatient telephone switchboard customers. Customers’ impatience in queuing theory is extensively discussed by many researchers in terms of reneging and balking. The tendency of a customer not to join a queue upon arrival is called balking while in reneging, a customer joins the queue, waits for some time and leaves the queue without getting service if the wait is more than his expected wait. The pioneer researchers in the area of queuing with balking and reneging are Haight [6], [7], Ancker and Gaffarian [4], [3],