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A conservation law for a wide class of queueing disciplines

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  • Leonard Kleinrock

Abstract

A large class of queueing disciplines is defined for Poisson arrival statistics. For this class, a Conservation Law is proven which constrains the allowed variation in the average waiting times. Specifically, defining ρp as the product of the average arrival rate and the average service time for customers from the pth priority group (where the priority system is any queue discipline included in the defined class) and Wp as their average waiting time (in queue), the Conservation Law states that Σ ρp Wp is invariant over the set of queue disciplines in the class.

Suggested Citation

  • Leonard Kleinrock, 1965. "A conservation law for a wide class of queueing disciplines," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 12(2), pages 181-192, June.
    • Handle: RePEc:wly:navlog:v:12:y:1965:i:2:p:181-192
    DOI: 10.1002/nav.3800120206
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    Cited by:

    1. José Niño-Mora, 2006. "Restless Bandit Marginal Productivity Indices, Diminishing Returns, and Optimal Control of Make-to-Order/Make-to-Stock M/G/1 Queues," Mathematics of Operations Research, INFORMS, vol. 31(1), pages 50-84, February.
    2. Huiyin Ouyang & Nilay Taník Argon & Serhan Ziya, 2022. "Assigning Priorities (or Not) in Service Systems with Nonlinear Waiting Costs," Management Science, INFORMS, vol. 68(2), pages 1233-1255, February.
    3. Li, Na & Stanford, David A., 2016. "Multi-server accumulating priority queues with heterogeneous servers," European Journal of Operational Research, Elsevier, vol. 252(3), pages 866-878.
    4. Hideaki Takagi & Tetsuya Takine & Onno J. Boxma, 1992. "Distribution of the workload in multiclass queueing systems with server vacations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(1), pages 41-52, February.
    5. Erica L. Plambeck & Qiong Wang, 2013. "Implications of Hyperbolic Discounting for Optimal Pricing and Scheduling of Unpleasant Services That Generate Future Benefits," Management Science, INFORMS, vol. 59(8), pages 1927-1946, August.
    6. Veeraruna Kavitha & Jayakrishnan Nair & Raman Kumar Sinha, 2019. "Pseudo conservation for partially fluid, partially lossy queueing systems," Annals of Operations Research, Springer, vol. 277(2), pages 255-292, June.
    7. Stephanie Carew & Mahesh Nagarajan & Steven Shechter & Jugpal Arneja & Erik Skarsgard, 2021. "Dynamic Capacity Allocation for Elective Surgeries: Reducing Urgency-Weighted Wait Times," Manufacturing & Service Operations Management, INFORMS, vol. 23(2), pages 407-424, March.

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