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Strategic Equilibrium for a Pair of Competing Servers with Convex Cost and Balking

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  • Duane Christ

    (RUTCOR, Rutgers, the State University of New Jersey, 640 Bartholomew Road, Piscataway, New Jersey 08854-8003)

  • Benjamin Avi-Itzhak

    (RUTCOR, Rutgers, the State University of New Jersey, 640 Bartholomew Road, Piscataway, New Jersey 08854-8003)

Abstract

A two-person game is formulated for a queuing situation involving a pair of exponential servers competing for arriving customers. The servers have identical characteristics except for their service rates. Each server is free to select its own service rate. The objective of each server is to select a service rate that will maximize its own profit. Arrivals are Poisson. The probability that an arriving customer enters the queue is allowed to depend on the queue length at the time of arrival. The proportion of arrivals to a given server is shown to be strictly concave in the server's own service rate and decreasing in the other service rate. Furthermore, we show that when the cost function is convex and increasing, there exists a unique pure strategy Nash equilibrium point for the resulting game.

Suggested Citation

  • Duane Christ & Benjamin Avi-Itzhak, 2002. "Strategic Equilibrium for a Pair of Competing Servers with Convex Cost and Balking," Management Science, INFORMS, vol. 48(6), pages 813-820, June.
    • Handle: RePEc:inm:ormnsc:v:48:y:2002:i:6:p:813-820
    DOI: 10.1287/mnsc.48.6.813.191
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    References listed on IDEAS

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    Cited by:

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    2. Benjamin Legros, 2022. "The principal-agent problem for service rate event-dependency," Post-Print hal-03605421, HAL.
    3. Mandjes, Michel & Timmer, Judith, 2007. "A duopoly model with heterogeneous congestion-sensitive customers," European Journal of Operational Research, Elsevier, vol. 176(1), pages 445-467, January.
    4. Gérard P. Cachon & Fuqiang Zhang, 2007. "Obtaining Fast Service in a Queueing System via Performance-Based Allocation of Demand," Management Science, INFORMS, vol. 53(3), pages 408-420, March.
    5. Gad Allon & Awi Federgruen, 2008. "Service Competition with General Queueing Facilities," Operations Research, INFORMS, vol. 56(4), pages 827-849, August.
    6. Benjamin Legros, 2021. "Agents’ Self‐Routing for Blended Operations to Balance Inbound and Outbound Services," Production and Operations Management, Production and Operations Management Society, vol. 30(10), pages 3599-3614, October.
    7. Wang, Haiyan & Olsen, Tava Lennon & Liu, Guiqing, 2018. "Service capacity competition with peak arrivals and delay sensitive customers," Omega, Elsevier, vol. 77(C), pages 80-95.
    8. Menezes, Mozart B.C. & Kim, Seokjin & Huang, Rongbing, 2015. "Return-on-investment (ROI) criteria for network design," European Journal of Operational Research, Elsevier, vol. 245(1), pages 100-108.

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