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Ticket queues with regular and strategic customers

Author

Listed:
  • Gabi Hanukov

    (Bar-Ilan University
    Tel Aviv University)

  • Shoshana Anily

    (Tel Aviv University)

  • Uri Yechiali

    (Tel Aviv University)

Abstract

We study a Markovian single-server ticket queue where, upon arrival, each customer can draw a number from a take-a-number machine, while the number of the customer currently being served is displayed on a panel. The difference between the above two numbers is called the “virtual queue length.” We consider a nonhomogeneous population of customers comprised of two types: “regular” and “strategic.” Upon arrival, a regular customer, regardless of the value of the virtual queue length, draws a number from the machine, joins the queue and waits in the system until being served. A strategic customer, depending on the virtual queue length, may either join, leave, or go to “orbit” for a random duration. If, upon return from orbit, a strategic customer realizes that s/he missed her/his turn, s/he balks. Otherwise, s/he joins the queue and waits to be served. We analyze this intricate stochastic system, calculate its steady-state probabilities, derive the sojourn time’s Laplace–Stieltjes transform of a regular and of a strategic customer and calculate the system’s performance measures. Finally, an economic analysis is performed to determine the optimal mean orbiting time of strategic customers for two types of objective functions. Numerical examples are presented.

Suggested Citation

  • Gabi Hanukov & Shoshana Anily & Uri Yechiali, 2020. "Ticket queues with regular and strategic customers," Queueing Systems: Theory and Applications, Springer, vol. 95(1), pages 145-171, June.
    • Handle: RePEc:spr:queues:v:95:y:2020:i:1:d:10.1007_s11134-020-09647-x
    DOI: 10.1007/s11134-020-09647-x
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    References listed on IDEAS

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    1. Yonatan Levy & Uri Yechiali, 1975. "Utilization of Idle Time in an M/G/1 Queueing System," Management Science, INFORMS, vol. 22(2), pages 202-211, October.
    2. Yoav Kerner & Eliran Sherzer & Mor Ann Yanco, 2017. "On non-equilibria threshold strategies in ticket queues," Queueing Systems: Theory and Applications, Springer, vol. 86(3), pages 419-431, August.
    3. I. Adiri & U. Yechiali, 1974. "Optimal Priority-Purchasing and Pricing Decisions in Nonmonopoly and Monopoly Queues," Operations Research, INFORMS, vol. 22(5), pages 1051-1066, October.
    4. Hanukov, Gabi & Avinadav, Tal & Chernonog, Tatyana & Spiegel, Uriel & Yechiali, Uri, 2018. "Improving efficiency in service systems by performing and storing “preliminary services”," International Journal of Production Economics, Elsevier, vol. 197(C), pages 174-185.
    5. Susan H. Xu & Long Gao & Jihong Ou, 2007. "Service Performance Analysis and Improvement for a Ticket Queue with Balking Customers," Management Science, INFORMS, vol. 53(6), pages 971-990, June.
    6. Otis B. Jennings & Jamol Pender, 2016. "Comparisons of ticket and standard queues," Queueing Systems: Theory and Applications, Springer, vol. 84(1), pages 145-202, October.
    7. Uri Yechiali, 1972. "Customers' Optimal Joining Rules for the GI/M/s Queue," Management Science, INFORMS, vol. 18(7), pages 434-443, March.
    8. George C. Mytalas & Michael A. Zazanis, 2015. "An MX/G/1 queueing system with disasters and repairs under a multiple adapted vacation policy," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(3), pages 171-189, April.
    9. Naor, P, 1969. "The Regulation of Queue Size by Levying Tolls," Econometrica, Econometric Society, vol. 37(1), pages 15-24, January.
    10. Kaan Kuzu & Long Gao & Susan H. Xu, 2019. "To Wait or Not to Wait: The Theory and Practice of Ticket Queues," Manufacturing & Service Operations Management, INFORMS, vol. 21(4), pages 853-874, October.
    11. Ding Ding & Jihong Ou & James Ang, 2015. "Analysis of ticket queues with reneging customers," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(2), pages 231-246, February.
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    Cited by:

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    3. Hanukov, Gabi, 2022. "A service system where junior servers approach a senior server on behalf of customers," International Journal of Production Economics, Elsevier, vol. 244(C).

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