Two parallel heterogeneous servers Markovian inventory system with modified and delayed working vacations

K. Jeganathan and M. Abdul Reiyas

Mathematics and Computers in Simulation (MATCOM), 2020, vol. 172, issue C, 273-304

Abstract: In this study, two servers namely server1 and server2 with working vacations are considered where one server is exclusively used for high priority customers and another for low priority customers. The modified working vacation is considered for server1 and delayed working vacation for server2 which is a main feature of this model. A high priority customer demands both item and service whereas a low priority customer demands only service. Items are replenished under (s,Q) ordering policy. In this system, the arrival of both types of customers is of independent Poisson processes and the service times of both types of customers are independent exponential distributions in which the service rates of both servers differ in regular service and working vacation time as well. The joint probability distribution of the inventory level, the statuses of both servers, the number of high priority customers in queue 1 and low priority customers in queue 2 are found to be in a steady state. Also, the distributions of waiting time of high priority and low priority customers are individually analyzed by Laplace–Stieltjes transform. The various measures of system performance in the steady state are obtained. The consequences are exemplified with numerical evidences. Mainly, some evidences portray the advantages of the feature of modified working vacation of the model compared to the features, like, simply vacations and non-delayed working vacations.

Keywords: Perishable goods; (s,Q) policy; Markov process; Two types of customers; Parallel queues; Heterogeneous servers; Modified and delayed working vacations (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:172:y:2020:i:c:p:273-304

DOI: 10.1016/j.matcom.2019.12.002

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