Cost and sensitivity analysis of transient Markovian queue with waiting server, heterogeneous vacation policy and reneged customers

Subject Areas : Stochastic Simulation Modeling

Mayank Singh ¹ , Madhu Jain ^{2 *} , Arumugam Azhagappan ³

1 - Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee 247667, India.
2 - Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee 247667, India
3 - Department of Mathematics, St. Anne’s College of Engineering and Technology, Anna University, Panruti, India.

Received: 2023-12-15 Accepted : 2025-01-11 Published : 2025-01-31

Keywords: Transient queue, Vacation, Reneging, Continued fractions, Cost optimization,

Abstract :

The impact of server unavailability during complete vacation (CV) and reduced service pace during working vacation (WV) periods is a significant concern for the service and manufacturing organizations. This study presents a performance model for a queueing system functioning under CV, WV, and impatience behavior of the customers. The key contribution of the present study lies in the feature that the server has options to choose either CV or WV, immediately after finishing the jobs of all customers. Due to slow service during the WV period, the customers may renege from the system without getting the service. This paper derives transient analytical expressions for the queue size distribution by using continued fraction (CF) and probability generating function (PGF) approaches. Furthermore, the formulae for various performance indices viz. expectation and variance of the queue length, throughput, cost function etc. are obtained. The practical applicability of the concern queueing model is explored by numerical analysis. Additionally, a cost optimization is conducted to determine the least cost associated with the optimal service rate.