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Proofs of conjectures on the competition between observable and unobservable servers

Author

Listed:
  • Bara Kim

    (Korea University)

  • Jeongsim Kim

    (Chungbuk National University)

  • Yan Su

    (Nanjing University of Posts and Telecommunications)

  • Chia-Li Wang

    (National Dong Hwa University)

Abstract

The impact of information about the quality of service on marketing can be demonstrated by a competition between an observable queue and an unobservable queue. An illustration was given by an earlier paper of Hassin (Manag Sci 42:618–623, 1996), which considers two gas stations located one after the other on a main road. A driver who needs to fill the gas can see the queue length upon arriving at the first station, but not the second one. The driver decides which station to enter based only on this partial information for minimizing the expected waiting time. Via extensive numerical experiments, Hassin showed that the first server enjoys a larger market share, which led him to making a number of challenging conjectures. In this paper, we prove that all the numerical observations and conjectures are true so that the advantage of being the first server is assured.

Suggested Citation

  • Bara Kim & Jeongsim Kim & Yan Su & Chia-Li Wang, 2023. "Proofs of conjectures on the competition between observable and unobservable servers," Queueing Systems: Theory and Applications, Springer, vol. 104(3), pages 211-238, August.
    • Handle: RePEc:spr:queues:v:104:y:2023:i:3:d:10.1007_s11134-023-09887-7
    DOI: 10.1007/s11134-023-09887-7
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    References listed on IDEAS

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    1. Refael Hassin, 1996. "On the Advantage of Being the First Server," Management Science, INFORMS, vol. 42(4), pages 618-623, April.
    2. Edelson, Noel M & Hildebrand, David K, 1975. "Congestion Tolls for Poisson Queuing Processes," Econometrica, Econometric Society, vol. 43(1), pages 81-92, January.
    3. Naor, P, 1969. "The Regulation of Queue Size by Levying Tolls," Econometrica, Econometric Society, vol. 37(1), pages 15-24, January.
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