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A Dynamic Priority Queue with General Concave Priority Functions

Author

Listed:
  • A. Netterman

    (Israel Institute of Technology, Haifa, Israel)

  • I. Adiri

    (Israel Institute of Technology, Haifa, Israel)

Abstract

This paper analyzes mathematically a queueing model where a single server dispenses service to several, m , non-preemptive priority classes. It is assumed that the arrival process of customers who belong to the k class ( k customers) is Poisson, and their service times are independent, identical, arbitrarily distributed random variables. The priority degree of a customer at a certain moment is not only a function of his class, but is also a general concave function of the time he has already spent in the system. (The discipline is termed “dynamic-priority.”) Upon departure the server selects for service, from the customers present, the one with the highest instantaneous priority degree, breaking ties by the FIFO rule. An implicit function as well as upper and lower bounds on the expected waiting time of k customer are found. The effectiveness of the bounds is demonstrated by a numerical example.

Suggested Citation

  • A. Netterman & I. Adiri, 1979. "A Dynamic Priority Queue with General Concave Priority Functions," Operations Research, INFORMS, vol. 27(6), pages 1088-1100, December.
    • Handle: RePEc:inm:oropre:v:27:y:1979:i:6:p:1088-1100
    DOI: 10.1287/opre.27.6.1088
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    Cited by:

    1. Emy Mariam George & Lillykutty Jacob, 2022. "Medical QoS provisioning for multi-class data in coexisting wireless body area networks," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 79(1), pages 151-161, January.
    2. Na Li & David A. Stanford & Peter Taylor & Ilze Ziedins, 2017. "Nonlinear Accumulating Priority Queues with Equivalent Linear Proxies," Operations Research, INFORMS, vol. 65(6), pages 1712-1721, December.
    3. Val Andrei Fajardo & Steve Drekic, 2017. "Waiting Time Distributions in the Preemptive Accumulating Priority Queue," Methodology and Computing in Applied Probability, Springer, vol. 19(1), pages 255-284, March.
    4. Moshe Haviv & Liron Ravner, 2016. "Strategic bidding in an accumulating priority queue: equilibrium analysis," Annals of Operations Research, Springer, vol. 244(2), pages 505-523, September.

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