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

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  • Jeganathan, K.
  • Abdul Reiyas, M.

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.

Suggested Citation

  • Jeganathan, K. & Abdul Reiyas, M., 2020. "Two parallel heterogeneous servers Markovian inventory system with modified and delayed working vacations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 172(C), pages 273-304.
    • Handle: RePEc:eee:matcom:v:172:y:2020:i:c:p:273-304
    DOI: 10.1016/j.matcom.2019.12.002
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    References listed on IDEAS

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    1. P. Vijaya Laxmi & M.L. Soujanya, 2018. "Perishable inventory model with Markovian arrival process, retrial demands and multiple working vacations," International Journal of Inventory Research, Inderscience Enterprises Ltd, vol. 5(2), pages 79-98.
    2. Naishuo Tian & Zhe George Zhang, 2006. "Vacation Queueing Models Theory and Applications," International Series in Operations Research and Management Science, Springer, number 978-0-387-33723-4, April.
    3. Jeganathan, K. & Abdul Reiyas, M. & Prasanna Lakshmi, K. & Saravanan, S., 2019. "Two server Markovian inventory systems with server interruptions: Heterogeneous vs. homogeneous servers," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 155(C), pages 177-200.
    4. Naishuo Tian & Zhe George Zhang, 2006. "Applications of Vacation Models," International Series in Operations Research & Management Science, in: Vacation Queueing Models Theory and Applications, chapter 0, pages 343-358, Springer.
    5. I. Padmavathi & B. Sivakumar & G. Arivarignan, 2015. "A retrial inventory system with single and modified multiple vacation for server," Annals of Operations Research, Springer, vol. 233(1), pages 335-364, October.
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    Cited by:

    1. K. Jeganathan & S. Selvakumar & S. Saravanan & N. Anbazhagan & S. Amutha & Woong Cho & Gyanendra Prasad Joshi & Joohan Ryoo, 2022. "Performance of Stochastic Inventory System with a Fresh Item, Returned Item, Refurbished Item, and Multi-Class Customers," Mathematics, MDPI, vol. 10(7), pages 1-37, April.
    2. T. Harikrishnan & K. Jeganathan & S. Selvakumar & N. Anbazhagan & Woong Cho & Gyanendra Prasad Joshi & Kwang Chul Son, 2022. "Analysis of Stochastic M / M / c / N Inventory System with Queue-Dependent Server Activation, Multi-Threshold Stages and Optional Retrial Facility," Mathematics, MDPI, vol. 10(15), pages 1-37, July.
    3. Yuying Zhang & Dequan Yue & Wuyi Yue, 2022. "A queueing-inventory system with random order size policy and server vacations," Annals of Operations Research, Springer, vol. 310(2), pages 595-620, March.
    4. Kathirvel Jeganathan & Thanushkodi Harikrishnan & Kumarasankaralingam Lakshmanan & Agassi Melikov & Janos Sztrik, 2023. "Modeling of Junior Servers Approaching a Senior Server in the Retrial Queuing-Inventory System," Mathematics, MDPI, vol. 11(22), pages 1-31, November.

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