Proofs of conjectures on the competition between observable and unobservable servers

Bara Kim, Jeongsim Kim, Yan Su, Chia Li Wang

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)211-238
Number of pages28
JournalQueueing Systems
Issue number3-4
Publication statusPublished - 2023 Aug

Bibliographical note

Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.


  • Censored Markov chain
  • Equilibrium strategy
  • Matrix analytic method

ASJC Scopus subject areas

  • Statistics and Probability
  • Computer Science Applications
  • Management Science and Operations Research
  • Computational Theory and Mathematics


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