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The Queue M / G /1 with the Shortest Remaining Processing Time Discipline

Author

Listed:
  • Linus E. Schrage

    (Cornell University, Ithaca, New York)

  • Louis W. Miller

    (The Rand Corporation, Santa Monica, California)

Abstract

A priority queuing model in which the processing times of jobs are known upon arrival and preemption without loss of time or processing already accomplished is studied. Priority is assigned to jobs according to the length of processing remaining with highest priority going to the job with least processing left. A preemption will occur whenever the processing time of a newly arriving job is less than the remaining processing time of the job then in service. The Laplace-Stieltjes transforms of the waiting time and time-in-system distributions are obtained and comparisons with other queuing disciplines are made.

Suggested Citation

  • Linus E. Schrage & Louis W. Miller, 1966. "The Queue M / G /1 with the Shortest Remaining Processing Time Discipline," Operations Research, INFORMS, vol. 14(4), pages 670-684, August.
    • Handle: RePEc:inm:oropre:v:14:y:1966:i:4:p:670-684
    DOI: 10.1287/opre.14.4.670
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    Citations

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    Cited by:

    1. Douglas G. Down & H. Christian Gromoll & Amber L. Puha, 2009. "Fluid Limits for Shortest Remaining Processing Time Queues," Mathematics of Operations Research, INFORMS, vol. 34(4), pages 880-911, November.
    2. Łukasz Kruk & Ewa Sokołowska, 2016. "Fluid Limits for Multiple-Input Shortest Remaining Processing Time Queues," Mathematics of Operations Research, INFORMS, vol. 41(3), pages 1055-1092, August.
    3. 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.
    4. Łukasz Kruk & Robert Gieroba, 2022. "Local edge minimality of SRPT networks with shared resources," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 96(3), pages 459-492, December.
    5. Hyytiä, Esa & Penttinen, Aleksi & Aalto, Samuli, 2012. "Size- and state-aware dispatching problem with queue-specific job sizes," European Journal of Operational Research, Elsevier, vol. 217(2), pages 357-370.
    6. Predrag Jelenković & Xiaozhu Kang & Jian Tan, 2009. "Heavy-tailed limits for medium size jobs and comparison scheduling," Annals of Operations Research, Springer, vol. 170(1), pages 133-159, September.
    7. Jouini, Oualid & Pot, Auke & Koole, Ger & Dallery, Yves, 2010. "Online scheduling policies for multiclass call centers with impatient customers," European Journal of Operational Research, Elsevier, vol. 207(1), pages 258-268, November.
    8. Yonatan Shadmi, 2022. "Fluid limits for shortest job first with aging," Queueing Systems: Theory and Applications, Springer, vol. 101(1), pages 93-112, June.
    9. Jinting Wang & Zhongbin Wang & Yunan Liu, 2020. "Reducing Delay in Retrial Queues by Simultaneously Differentiating Service and Retrial Rates," Operations Research, INFORMS, vol. 68(6), pages 1648-1667, November.
    10. Jing Dong & Rouba Ibrahim, 2021. "SRPT Scheduling Discipline in Many-Server Queues with Impatient Customers," Management Science, INFORMS, vol. 67(12), pages 7708-7718, December.
    11. Sunil Kumar & Ramandeep S. Randhawa, 2010. "Exploiting Market Size in Service Systems," Manufacturing & Service Operations Management, INFORMS, vol. 12(3), pages 511-526, September.
    12. Mor Harchol-Balter, 2021. "Open problems in queueing theory inspired by datacenter computing," Queueing Systems: Theory and Applications, Springer, vol. 97(1), pages 3-37, February.
    13. Łukasz Kruk, 2022. "Heavy traffic analysis for single-server SRPT and LRPT queues via EDF diffusion limits," Annals of Operations Research, Springer, vol. 310(2), pages 411-429, March.

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