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Dynamic Control of a Multiclass Queue with Thin Arrival Streams

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  • Barış Ata

    (Kellogg School of Management, Northwestern University, Evanston, Illinois 60208)

Abstract

As a model of make-to-order production, we consider an admission control problem for a multiclass, single-server queue. The production system serves multiple demand streams, each having a rigid due-date lead time. To meet the due-date constraints, a system manager may reject orders when a backlog of work is judged to be excessive, thereby incurring lost revenues. The system manager strives to minimize long-run average lost revenues by dynamically making admission control and sequencing decisions. Under heavy-traffic conditions the scheduling problem is approximated by a Brownian control problem, which is solved explicitly. Interpreting this solution in the context of the original queueing system, a nested threshold policy is proposed. A simulation experiment is performed to demonstrate the effectiveness of this policy.

Suggested Citation

  • Barış Ata, 2006. "Dynamic Control of a Multiclass Queue with Thin Arrival Streams," Operations Research, INFORMS, vol. 54(5), pages 876-892, October.
    • Handle: RePEc:inm:oropre:v:54:y:2006:i:5:p:876-892
    DOI: 10.1287/opre.1060.0308
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    References listed on IDEAS

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    Cited by:

    1. Ghosh, Arka P. & Weerasinghe, Ananda P., 2010. "Optimal buffer size and dynamic rate control for a queueing system with impatient customers in heavy traffic," Stochastic Processes and their Applications, Elsevier, vol. 120(11), pages 2103-2141, November.
    2. Baris Ata & Deishin Lee & Mustafa Hayri Tongarlak, 2024. "A diffusion model of dynamic participant inflow management," Queueing Systems: Theory and Applications, Springer, vol. 108(3), pages 383-414, December.
    3. Philipp Afèche & Barış Ata, 2013. "Bayesian Dynamic Pricing in Queueing Systems with Unknown Delay Cost Characteristics," Manufacturing & Service Operations Management, INFORMS, vol. 15(2), pages 292-304, May.
    4. Ryan Palmer & Martin Utley, 2020. "On the modelling and performance measurement of service networks with heterogeneous customers," Annals of Operations Research, Springer, vol. 293(1), pages 237-268, October.
    5. A. Baykal Hafızoğlu & Esma S. Gel & Pınar Keskinocak, 2016. "Price and Lead Time Quotation for Contract and Spot Customers," Operations Research, INFORMS, vol. 64(2), pages 406-415, April.
    6. Ananda Weerasinghe, 2014. "Diffusion Approximations for G / M / n + GI Queues with State-Dependent Service Rates," Mathematics of Operations Research, INFORMS, vol. 39(1), pages 207-228, February.
    7. Sabri Çelik & Costis Maglaras, 2008. "Dynamic Pricing and Lead-Time Quotation for a Multiclass Make-to-Order Queue," Management Science, INFORMS, vol. 54(6), pages 1132-1146, June.
    8. Mustafa Akan & Barı ş Ata & Tava Olsen, 2012. "Congestion-Based Lead-Time Quotation for Heterogenous Customers with Convex-Concave Delay Costs: Optimality of a Cost-Balancing Policy Based on Convex Hull Functions," Operations Research, INFORMS, vol. 60(6), pages 1505-1519, December.
    9. Melanie Rubino & Barış Ata, 2009. "Dynamic Control of a Make-to-Order, Parallel-Server System with Cancellations," Operations Research, INFORMS, vol. 57(1), pages 94-108, February.
    10. Barιş Ata & Deishin Lee & Erkut Sönmez, 2019. "Dynamic Volunteer Staffing in Multicrop Gleaning Operations," Operations Research, INFORMS, vol. 67(2), pages 295-314, March.
    11. Lee, Chihoon & Weerasinghe, Ananda, 2011. "Convergence of a queueing system in heavy traffic with general patience-time distributions," Stochastic Processes and their Applications, Elsevier, vol. 121(11), pages 2507-2552, November.
    12. Shuangchi He & Dacheng Yao & Hanqin Zhang, 2017. "Optimal Ordering Policy for Inventory Systems with Quantity-Dependent Setup Costs," Mathematics of Operations Research, INFORMS, vol. 42(4), pages 979-1006, November.
    13. Amir A. Alwan & Baris Ata & Yuwei Zhou, 2024. "A queueing model of dynamic pricing and dispatch control for ride-hailing systems incorporating travel times," Queueing Systems: Theory and Applications, Springer, vol. 106(1), pages 1-66, February.

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