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Strategic behaviour in a tandem queue with alternating server

Author

Listed:
  • Nimrod Dvir

    (Tel-Aviv University)

  • Refael Hassin

    (Tel-Aviv University)

  • Uri Yechiali

    (Tel-Aviv University)

Abstract

This paper considers an unobservable two-site tandem queueing system attended by an alternating server. We study the strategic customer behaviour under two threshold-based operating policies, applied by a profit-maximizing server, while customers’ strategic behaviour and server’s switching costs are taken into account. Under the Exact-N policy, in each cycle the server first completes service of N customers in the first stage ( $$Q_1$$ Q 1 ), then switches to the second stage ( $$Q_2$$ Q 2 ) and then serves those N customers before switching back to $$Q_1$$ Q 1 to start a new cycle. This policy leads to a mixture of Follow-the-Crowd and Avoid-the-Crowd customer behaviour. In contrast, under the N-Limited policy, the server switches from $$Q_1$$ Q 1 to $$Q_2$$ Q 2 also when the first queue is emptied, making this regime work-conserving and leading only to Avoid-the-Crowd behaviour. Performance measures are obtained using matrix geometric methods for both policies and any threshold N, while for sequential service ( $$N=1$$ N = 1 ) explicit expressions are derived. It is shown that the system’s stability condition is independent of N, and of the switching policy. Optimal performances in equilibrium, under each of these switching policies, are analysed and compared through a numerical study.

Suggested Citation

  • Nimrod Dvir & Refael Hassin & Uri Yechiali, 2020. "Strategic behaviour in a tandem queue with alternating server," Queueing Systems: Theory and Applications, Springer, vol. 96(3), pages 205-244, December.
  • Handle: RePEc:spr:queues:v:96:y:2020:i:3:d:10.1007_s11134-020-09665-9
    DOI: 10.1007/s11134-020-09665-9
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    References listed on IDEAS

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    1. Uri Yechiali, 1971. "On Optimal Balking Rules and Toll Charges in the GI / M /1 Queuing Process," Operations Research, INFORMS, vol. 19(2), pages 349-370, April.
    2. Gad Allon & Achal Bassamboo, 2011. "The Impact of Delaying the Delay Announcements," Operations Research, INFORMS, vol. 59(5), pages 1198-1210, October.
    3. U. Yechiali & P. Naor, 1971. "Queuing Problems with Heterogeneous Arrivals and Service," Operations Research, INFORMS, vol. 19(3), pages 722-734, June.
    4. Bountali, Olga & Economou, Antonis, 2017. "Equilibrium joining strategies in batch service queueing systems," European Journal of Operational Research, Elsevier, vol. 260(3), pages 1142-1151.
    5. Edelson, Noel M & Hildebrand, David K, 1975. "Congestion Tolls for Poisson Queuing Processes," Econometrica, Econometric Society, vol. 43(1), pages 81-92, January.
    6. Miguel Taube-Netto, 1977. "Two Queues in Tandem Attended by a Single Server," Operations Research, INFORMS, vol. 25(1), pages 140-147, February.
    7. Naor, P, 1969. "The Regulation of Queue Size by Levying Tolls," Econometrica, Econometric Society, vol. 37(1), pages 15-24, January.
    8. Kostia Avrachenkov & Efrat Perel & Uri Yechiali, 2016. "Finite-buffer polling systems with threshold-based switching policy," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 541-571, October.
    9. Olga Bountali & Antonis Economou, 2019. "Strategic customer behavior in a two-stage batch processing system," Queueing Systems: Theory and Applications, Springer, vol. 93(1), pages 3-29, October.
    10. Kanta, Spyridoula & D'Auria, Bernardo, 2011. "Equilibrium strategies in a tandem queue under various levels of information," DES - Working Papers. Statistics and Econometrics. WS ws113325, Universidad Carlos III de Madrid. Departamento de Estadística.
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