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Customer equilibrium and optimal strategies in Markovian queues in series

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  • Apostolos Burnetas

Abstract

We consider series of M/M/m queues with strategic customer behavior. Customers arrive to the first queue and decide whether to enter the system or balk and, if they enter, up to which queue to proceed before departing. Each customer makes an independent decision, with the objective of maximizing her total net benefit, which is equal to the value of service minus a cost due to expected delay. We formulate the customer decision as a game and identify the unique symmetric Nash equilibrium strategy, which is expressed in a backward recursive form. We also analyze the problem of maximizing the total customer welfare and establish the relationship between the equilibrium and the welfare maximizing strategies. Copyright Springer Science+Business Media, LLC 2013

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  • Apostolos Burnetas, 2013. "Customer equilibrium and optimal strategies in Markovian queues in series," Annals of Operations Research, Springer, vol. 208(1), pages 515-529, September.
    • Handle: RePEc:spr:annopr:v:208:y:2013:i:1:p:515-529:10.1007/s10479-011-1010-4
    DOI: 10.1007/s10479-011-1010-4
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    Cited by:

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    3. Panayides, Michalis & Knight, Vince & Harper, Paul, 2023. "A game theoretic model of the behavioural gaming that takes place at the EMS - ED interface," European Journal of Operational Research, Elsevier, vol. 305(3), pages 1236-1258.
    4. Olivier Brun & Balakrishna Prabhu, 2016. "Worst-case analysis of non-cooperative load balancing," Annals of Operations Research, Springer, vol. 239(2), pages 471-495, April.
    5. Shu Zhang & Jeffrey W. Ohlmann & Barrett W. Thomas, 2018. "Dynamic Orienteering on a Network of Queues," Transportation Science, INFORMS, vol. 52(3), pages 691-706, June.
    6. Zhang, Shu & Ohlmann, Jeffrey W. & Thomas, Barrett W., 2014. "A priori orienteering with time windows and stochastic wait times at customers," European Journal of Operational Research, Elsevier, vol. 239(1), pages 70-79.

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