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

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Article Type:
Research/Original Article (دارای رتبه معتبر)
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.

Language:
English
Published:
Journal Of Industrial Engineering International, Volume:19 Issue: 4, Autumn 2023
Pages:
70 to 85
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