Strategic behavior in queues with arrival rate uncertainty

Refael Hassin, Moshe Haviv, Binyamin Oz*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

This paper shows how to account for arrival rate uncertainty in the analysis of queueing models with strategic customer behavior. We consider a general queueing model with a Poisson arrival process whose rate is random, and realized once for the entire process. We show that the distribution of the arrival rate at arrival instants is the size-biased counterpart of the original distribution. In particular, the ASTA (arrivals see time averages) property does not hold but rather a rate-biased version of it which we define and coin by the term RASTA (Rate-biased ASTA). We show that the RASTA phenomenon plays a crucial role in the analysis of strategic behavior of customers who evaluate the consequences of the actions they take upon arrival. By studying such a system with a single server and strategic customers who decide whether to join or balk without observing the queue, we exemplify the importance of RASTA in deriving the equilibrium behavior.

Original languageAmerican English
Article number1
Pages (from-to)217-224
Number of pages8
JournalEuropean Journal of Operational Research
Volume309
Issue number1
DOIs
StatePublished - 16 Aug 2023

Bibliographical note

Publisher Copyright:
© 2023 Elsevier B.V.

Keywords

  • Applied probability
  • Nash equilibrium
  • Parameter uncertainty
  • Size-biased distribution
  • Unobservable queues

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