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Queuing with Preemptive Priorities or with Breakdown

Author

Listed:
  • Harrison White

    (Operations Research Office, The Johns Hopkins University, Bethesda, Maryland)

  • Lee S. Christie

    (Operations Research Office, The Johns Hopkins University, Bethesda, Maryland)

Abstract

Preemptive priority is defined and contrasted with head-of-the line priority Poisson arrivals at a single server are assumed throughout, and only steady-state solutions are found. The effect on service-time statistics of preempted items re-entering service according to various rules is considered. A formula for the joint probability distribution of queue lengths of two preemptive priority classes is derived assuming negative exponential service statistics. Moments of this queue length distribution are found by a generating function approach. For any number of preemptive priority classes, expected times-in-system are found for a general service time distribution for each class, and for negative exponential service, with the same rate for each class, the generating functions of the delay distributions are also obtained. The similarity of queuing with breakdown to queuing with preemptive priority is pointed out, and two models of breakdown effects are worked out.

Suggested Citation

  • Harrison White & Lee S. Christie, 1958. "Queuing with Preemptive Priorities or with Breakdown," Operations Research, INFORMS, vol. 6(1), pages 79-95, February.
    • Handle: RePEc:inm:oropre:v:6:y:1958:i:1:p:79-95
    DOI: 10.1287/opre.6.1.79
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    Cited by:

    1. Sheng Zhu & Jinting Wang & Bin Liu, 2020. "Equilibrium joining strategies in the Mn/G/1 queue with server breakdowns and repairs," Operational Research, Springer, vol. 20(4), pages 2163-2187, December.
    2. Herwig Bruneel & Dieter Fiems & Joris Walraevens & Sabine Wittevrongel, 2014. "Queueing models for the analysis of communication systems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 421-448, July.
    3. I. Atencia, 2015. "A discrete-time queueing system with server breakdowns and changes in the repair times," Annals of Operations Research, Springer, vol. 235(1), pages 37-49, December.
    4. A. Krishnamoorthy & S. Jaya & B. Lakshmy, 2015. "Queues with interruption in random environment," Annals of Operations Research, Springer, vol. 233(1), pages 201-219, October.
    5. P. Vijaya Laxmi & E. Girija Bhavani, 2024. "Strategic behavior of customers in a second optional service queue with service interruptions," OPSEARCH, Springer;Operational Research Society of India, vol. 61(2), pages 762-784, June.
    6. Atencia-Mc.Killop, Ivan & Galán-García, José L. & Aguilera-Venegas, Gabriel & Rodríguez-Cielos, Pedro & Galán-García, MÁngeles, 2018. "A Geo[X]/G[X]/1 retrial queueing system with removal work and total renewal discipline," Applied Mathematics and Computation, Elsevier, vol. 319(C), pages 245-253.
    7. B. Krishna Kumar & R. Rukmani & A. Thanikachalam & V. Kanakasabapathi, 2018. "Performance analysis of retrial queue with server subject to two types of breakdowns and repairs," Operational Research, Springer, vol. 18(2), pages 521-559, July.
    8. Pedram Sahba & Bariş Balciog̃lu & Dragan Banjevic, 2013. "Analysis of the finite‐source multiclass priority queue with an unreliable server and setup time," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(4), pages 331-342, June.
    9. Baykal-Gürsoy, M. & Xiao, W. & Ozbay, K., 2009. "Modeling traffic flow interrupted by incidents," European Journal of Operational Research, Elsevier, vol. 195(1), pages 127-138, May.
    10. Fiems, Dieter & Maertens, Tom & Bruneel, Herwig, 2008. "Queueing systems with different types of server interruptions," European Journal of Operational Research, Elsevier, vol. 188(3), pages 838-845, August.
    11. Zamani, Shokufeh & Arkat, Jamal & Niaki, Seyed Taghi Akhavan, 2022. "Service interruption and customer withdrawal in the congested facility location problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 165(C).
    12. 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.
    13. Sauer Cornelia & Daduna Hans, 2003. "Availability Formulas and Performance Measures for Separable Degradable Networks," Stochastics and Quality Control, De Gruyter, vol. 18(2), pages 165-194, January.
    14. Madhu Jain & Sandeep Kaur & Parminder Singh, 2021. "Supplementary variable technique (SVT) for non-Markovian single server queue with service interruption (QSI)," Operational Research, Springer, vol. 21(4), pages 2203-2246, December.
    15. Pedram Sahba & Barış Balcıog̃lu & Dragan Banjevic, 2022. "The impact of disruption characteristics on the performance of a server," Annals of Operations Research, Springer, vol. 317(1), pages 239-252, October.

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