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Priority Assignment in Waiting Line Problems

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  • Alan Cobham

    (Operations Evaluation Group, United States Navy)

Abstract

There are several commonly occurring situations in which the position of a unit or member of a waiting line is determined by a priority assigned to the unit rather than by its time of arrival in the line. An example is the line formed by messages awaiting transmission over a crowded communication channel in which urgent messages may take precedence over routine ones. With the passage of time a given unit may move forward in the line owing to the servicing of units at the front of the line or may move back owing to the arrival of units holding higher priorities. Though it does not provide a complete description of this process, the average elapsed time between the arrival in the line of a unit of a given priority and its admission to the facility for servicing is useful in evaluating the procedure by which priority assignments are made. Expressions for this quantity are derived for two cases---the single-channel system in which the unit servicing times are arbitrarily distributed (Eq. 3) and the multiple-channel system in which the servicing times are exponentially distributed (Eq. 6). In both cases it is assumed that arrivals occur at random. Operations Research , ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.

Suggested Citation

  • Alan Cobham, 1954. "Priority Assignment in Waiting Line Problems," Operations Research, INFORMS, vol. 2(1), pages 70-76, February.
    • Handle: RePEc:inm:oropre:v:2:y:1954:i:1:p:70-76
    DOI: 10.1287/opre.2.1.70
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    Cited by:

    1. Zaki, Ahmed S. & Cheng, Hsing Kenneth & Parker, Barnett R., 1997. "A Simulation Model for the Analysis and Management of An Emergency Service System," Socio-Economic Planning Sciences, Elsevier, vol. 31(3), pages 173-189, September.
    2. van Vianen, L.A. & Gabor, A.F. & van Ommeren, J.C.W., 2014. "A simple derivation of the waiting time distributions in a non-preemptive M/M/c queue with priorities," ERIM Report Series Research in Management ERS-2014-016-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    3. Divya Velayudhan Nair & Achyutha Krishnamoorthy & Agassi Melikov & Sevinj Aliyeva, 2021. "MMAP/(PH,PH)/1 Queue with Priority Loss through Feedback," Mathematics, MDPI, vol. 9(15), pages 1-26, July.
    4. Thomas Kittsteiner & Benny Moldovanu, 2005. "Priority Auctions and Queue Disciplines That Depend on Processing Time," Management Science, INFORMS, vol. 51(2), pages 236-248, February.
    5. Haviv, Moshe & van der Wal, Jan, 2008. "Mean sojourn times for phase-type discriminatory processor sharing systems," European Journal of Operational Research, Elsevier, vol. 189(2), pages 375-386, September.
    6. Hideaki Takagi, 2016. "Waiting time in the M/M/ $$ m $$ m LCFS nonpreemptive priority queue with impatient customers," Annals of Operations Research, Springer, vol. 247(1), pages 257-289, December.
    7. Sanjiv Kapoor & Junghwan Shin, 2020. "Price of Anarchy in Networks with Heterogeneous Latency Functions," Mathematics of Operations Research, INFORMS, vol. 45(2), pages 755-773, May.
    8. Daniel Jaramillo-Ramirez & Manuel Perez, 2021. "Spectrum Demand Forecasting for IoT Services," Future Internet, MDPI, vol. 13(9), pages 1-24, September.
    9. Josef Zuk & David Kirszenblat, 2024. "Explicit results for the distributions of queue lengths for a non-preemptive two-level priority queue," Annals of Operations Research, Springer, vol. 341(2), pages 1223-1246, October.
    10. Andrei Sleptchenko & M. Eric Johnson, 2015. "Maintaining Secure and Reliable Distributed Control Systems," INFORMS Journal on Computing, INFORMS, vol. 27(1), pages 103-117, February.
    11. Nilay Tan{i}k Argon & Serhan Ziya, 2009. "Priority Assignment Under Imperfect Information on Customer Type Identities," Manufacturing & Service Operations Management, INFORMS, vol. 11(4), pages 674-693, June.
    12. 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.
    13. Mor Harchol-Balter & Takayuki Osogami & Alan Scheller-Wolf & Adam Wierman, 2005. "Multi-Server Queueing Systems with Multiple Priority Classes," Queueing Systems: Theory and Applications, Springer, vol. 51(3), pages 331-360, December.
    14. Soroush Saghafian & Wallace J. Hopp & Mark P. Van Oyen & Jeffrey S. Desmond & Steven L. Kronick, 2014. "Complexity-Augmented Triage: A Tool for Improving Patient Safety and Operational Efficiency," Manufacturing & Service Operations Management, INFORMS, vol. 16(3), pages 329-345, July.
    15. Phan, Trang Hoai & Stachuletz, Rainer, 2022. "Bribery - Export Nexus under the Firm’s Growth Obstacles," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 132144, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    16. Jori Selen & Brian Fralix, 2017. "Time-dependent analysis of an M / M / c preemptive priority system with two priority classes," Queueing Systems: Theory and Applications, Springer, vol. 87(3), pages 379-415, December.
    17. Tsiligianni, Christiana & Tsiligiannis, Aristeides & Tsiliyannis, Christos, 2023. "A stochastic inventory model of COVID-19 and robust, real-time identification of carriers at large and infection rate via asymptotic laws," European Journal of Operational Research, Elsevier, vol. 304(1), pages 42-56.
    18. G. M. Koole & B. F. Nielsen & T. B. Nielsen, 2012. "First in Line Waiting Times as a Tool for Analysing Queueing Systems," Operations Research, INFORMS, vol. 60(5), pages 1258-1266, October.

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