Abstract
We examine a system with two heterogeneous servers. An arriving customer first observes the queue length at the slower server and decides whether to join it or join the unobservable queue of the faster server. Customers arrive to the system and decide which queue to join according to the reward, waiting cost, and service rates. Once a customer chooses a queue, she cannot change her decision. We analyze a special case of this model where there is no waiting space except for the customer in service. The probability for entering the observable queue (if the server idle) is denoted by p, and this is the strategy of the customers. We analyze and characterize the Nash equilibria and the socially-optimal probabilities of the system, and the relation between the two as function of the model’s parameters. We also examine throughput maximization.
This research was supported by the Israel Science Foundation (grant No. 355/15).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Altman, E., Jiménez, T., Núñez-Queija, R., Yechiali, U.: Optimal routing among \(\cdot \)/M/1 queues with partial information. Stoch. Models 20(2), 149–171 (2004)
Hassin, R.: On the advantage of being the first server. Manage. Sci. 42(4), 618–623 (1996)
Hassin, R.: Rational Queueing. Chapman & Hall, CRC Press, Boca Raton (2006)
Hassin, R., Haviv, M.: To Queue or Not to Queue: Equilibrium Behavior in Queueing Systems. Kluwer Academic Publishers, Norwell (2003)
Hassin, R., Roet-Green, R.: Cascade equilibrium strategies in a two-server queueing system with inspection cost. Eur. J. Oper. Res. 267, 1014–1026 (2018)
Singh, S.P., Delasay, M., Scheller-Wolf, A.: Evaluating the First-Mover’s Advantage in Announcing Real-Time Delay Information. Available at SSRN-id3081583 (2019)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Hassin, R., Milo, J.H.P. (2019). On Rational Behavior in a Loss System with One Observable Queue and One Unobservable Queue. In: Phung-Duc, T., Kasahara, S., Wittevrongel, S. (eds) Queueing Theory and Network Applications. QTNA 2019. Lecture Notes in Computer Science(), vol 11688. Springer, Cham. https://doi.org/10.1007/978-3-030-27181-7_11
Download citation
DOI: https://doi.org/10.1007/978-3-030-27181-7_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-27180-0
Online ISBN: 978-3-030-27181-7
eBook Packages: Computer ScienceComputer Science (R0)