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The Israeli queue with a capacitated server: modeling and approximations

Author

Listed:
  • Nir Perel

    (Afeka Tel-Aviv Academic College of Engineering)

  • Efrat Perel

    (Afeka Tel-Aviv Academic College of Engineering)

  • Mor Kaspi

    (Tel Aviv University)

Abstract

The Israeli Queue is a batch service polling system where a single server attends to multiple queues based on seniority. Each arriving customer belongs to one of several classes. Upon arrival, a customer either joins an existing queue for their class or initiates a new queue if they are the first of their class to arrive. Customers from the class with the most senior member are served together as a batch, with the service time remaining constant regardless of the batch size. This service model is found in applications like advanced elevator systems and on-demand shared mobility, where passengers heading to the same destination can share a ride. However, in many real-world scenarios, the vehicle capacities are small and constraining, which calls for a deeper exploration of the Israeli queue with a capacitated server (IQCS). In this paper, we formally define the IQCS and address the challenges of creating a mathematically tractable model to represent it. To approximate the IQCS, we develop a quasi-birth-death process and derive approximations for key performance measures. To validate our approach, we implement a simulation model and use it to compare the IQCS, the approximate model, and the original Israeli Queue. Our results across various scenarios demonstrate the accuracy of the approximate model. Nonetheless, the presence of a remaining gap underscores the ongoing challenge of precisely and efficiently modeling the IQCS, posing an open question for the research community.

Suggested Citation

  • Nir Perel & Efrat Perel & Mor Kaspi, 2025. "The Israeli queue with a capacitated server: modeling and approximations," Annals of Operations Research, Springer, vol. 344(1), pages 267-285, January.
  • Handle: RePEc:spr:annopr:v:344:y:2025:i:1:d:10.1007_s10479-024-06298-6
    DOI: 10.1007/s10479-024-06298-6
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    References listed on IDEAS

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    1. John Lees-Miller, 2016. "Minimising average passenger waiting time in personal rapid transit systems," Annals of Operations Research, Springer, vol. 236(2), pages 405-424, January.
    2. Sai Mali Ananthanarayanan & Charles C. Branas & Adam N. Elmachtoub & Clifford S. Stein & Yeqing Zhou, 2022. "Queuing safely for elevator systems amidst a pandemic," Production and Operations Management, Production and Operations Management Society, vol. 31(5), pages 2306-2323, May.
    3. Kahraman, Aykut & Gosavi, Abhijit, 2011. "On the distribution of the number stranded in bulk-arrival, bulk-service queues of the M/G/1 form," European Journal of Operational Research, Elsevier, vol. 212(2), pages 352-360, July.
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    5. John D. Lees-Miller, 2016. "Minimising average passenger waiting time in personal rapid transit systems," Annals of Operations Research, Springer, vol. 236(2), pages 405-424, January.
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