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

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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.

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Acknowledgements

We would like to thank the anonymous referees for their valuable suggestions which helped to improve the manuscript.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Central Florida, Orlando, USA

    Gopinath Panda

  2. School of Computer Applications, Kalinga Institute of Industrial Technology, Bhubaneswar, 751024, India

    Veena Goswami

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  1. Gopinath Panda
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  2. Veena Goswami
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Correspondence to Veena Goswami.

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Panda, G., Goswami, V. Equilibrium Joining Strategies of Positive Customers in a Markovian Queue with Negative Arrivals and Working Vacations. Methodol Comput Appl Probab 24, 1439–1466 (2022). https://doi.org/10.1007/s11009-021-09864-8

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  • DOI: https://doi.org/10.1007/s11009-021-09864-8

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