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A Note on Convexity of the Expected Delay Cost in Single-Server Queues

Author

Listed:
  • Kristin Fridgeirsdottir

    (Decision Sciences, London Business School, Regent’s Park, London, NW1 4SA United Kingdom)

  • Sam Chiu

    (Department of Management Science and Engineering, Stanford University, Stanford, California 94305)

Abstract

In this note, we show that the expected delay cost for a G/G/ 1 queue is not necessarily convex in the arrival rate as sometimes claimed in the literature. We can prove, however, that the total expected delay cost rate is convex in the arrival rate. This cost rate is often of interest when designing queueing systems.

Suggested Citation

  • Kristin Fridgeirsdottir & Sam Chiu, 2005. "A Note on Convexity of the Expected Delay Cost in Single-Server Queues," Operations Research, INFORMS, vol. 53(3), pages 568-570, June.
    • Handle: RePEc:inm:oropre:v:53:y:2005:i:3:p:568-570
    DOI: 10.1287/opre.1040.0173
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    References listed on IDEAS

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    1. Shaler Stidham, 1992. "Pricing and Capacity Decisions for a Service Facility: Stability and Multiple Local Optima," Management Science, INFORMS, vol. 38(8), pages 1121-1139, August.
    2. Sanjeev Dewan & Haim Mendelson, 1990. "User Delay Costs and Internal Pricing for a Service Facility," Management Science, INFORMS, vol. 36(12), pages 1502-1517, December.
    3. Richard R. Weber, 1983. "Technical Note—A Note on Waiting Times in Single Server Queues," Operations Research, INFORMS, vol. 31(5), pages 950-951, October.
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    Cited by:

    1. Legros, Benjamin, 2022. "The principal-agent problem for service rate event-dependency," European Journal of Operational Research, Elsevier, vol. 297(3), pages 949-963.
    2. S. Bhulai & A.C. Brooms, 2008. "Approximate Expected Delay Costs for Call and Contact Centre models under Light Traffic Regimes," Birkbeck Working Papers in Economics and Finance 0805, Birkbeck, Department of Economics, Mathematics & Statistics.
    3. Benjamin Legros, 2022. "The principal-agent problem for service rate event-dependency," Post-Print hal-03605421, HAL.
    4. van Eekelen, Wouter, 2023. "Distributionally robust views on queues and related stochastic models," Other publications TiSEM 9b99fc05-9d68-48eb-ae8c-9, Tilburg University, School of Economics and Management.

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    Keywords

    mathematics:convexity; queues:optimization;

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