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Equilibrium Joining Strategies of Positive Customers in a Markovian Queue with Negative Arrivals and Working Vacations

Author

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  • Gopinath Panda

    (University of Central Florida)

  • Veena Goswami

    (Kalinga Institute of Industrial Technology)

Abstract

We study the economic analysis of a single server Markovian queueing system with positive and negative customers and multiple working vacations. Both positive and negative customers arrive in the system according to a Poisson process. Upon arrival, positive customers acquire some system information and decide whether to join or to balk the system based on the acquired information and a linear cost-reward structure. Negative customers on arrival break the server and kill the positive customer in service. The server is immediately sent for repair, and no customers are allowed during a repair. The server takes multiple working vacations after serving all the positive waiting customers. We obtain the equilibrium strategies and social benefit of positive customers under four different information situations. Numerical experiments are presented to show the effects of model parameters and information levels on the equilibrium joining behavior of positive customers.

Suggested Citation

  • Gopinath Panda & Veena Goswami, 2022. "Equilibrium Joining Strategies of Positive Customers in a Markovian Queue with Negative Arrivals and Working Vacations," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1439-1466, September.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:3:d:10.1007_s11009-021-09864-8
    DOI: 10.1007/s11009-021-09864-8
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    References listed on IDEAS

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    1. Wei Sun & Pengfei Guo & Naishuo Tian, 2010. "Equilibrium threshold strategies in observable queueing systems with setup/closedown times," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 18(3), pages 241-268, September.
    2. Refael Hassin & Moshe Haviv, 1997. "Equilibrium Threshold Strategies: The Case of Queues with Priorities," Operations Research, INFORMS, vol. 45(6), pages 966-973, December.
    3. Jie Liu & Jinting Wang, 2017. "Strategic joining rules in a single server Markovian queue with Bernoulli vacation," Operational Research, Springer, vol. 17(2), pages 413-434, July.
    4. Edelson, Noel M & Hildebrand, David K, 1975. "Congestion Tolls for Poisson Queuing Processes," Econometrica, Econometric Society, vol. 43(1), pages 81-92, January.
    5. Artalejo, J. R., 2000. "G-networks: A versatile approach for work removal in queueing networks," European Journal of Operational Research, Elsevier, vol. 126(2), pages 233-249, October.
    6. Naor, P, 1969. "The Regulation of Queue Size by Levying Tolls," Econometrica, Econometric Society, vol. 37(1), pages 15-24, January.
    7. Wei Sun & Shiyong Li, 2014. "Equilibrium and optimal behavior of customers in Markovian queues with multiple working vacations," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 694-715, July.
    8. Boudali, Olga & Economou, Antonis, 2012. "Optimal and equilibrium balking strategies in the single server Markovian queue with catastrophes," European Journal of Operational Research, Elsevier, vol. 218(3), pages 708-715.
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