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Two Queues Under Preemptive Priority with Poisson Arrival and Service Rates

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  • Frederick F. Stephan

    (Princeton University, Princeton, New Jersey)

Abstract

This paper extends the work of White and Christie, reported in O perations R esearch , vol 6, pp 79-95 (January-February, 1958), on preemptive priority queuing. A random walk procedure yields recursive relations between the state probabilities in the steady state. Recursive relations for the moments of the length of the lower priority queue follow. Combined with the use of moment generating functions, this approach provides moments of the waiting time for elements of the lower priority class that arrive when the system is in a given state, i.e., the two queues are of given lengths. The moments of waiting time and time in the system are also obtained recursively for the steady state. Routines for computing and checking are provided.

Suggested Citation

  • Frederick F. Stephan, 1958. "Two Queues Under Preemptive Priority with Poisson Arrival and Service Rates," Operations Research, INFORMS, vol. 6(3), pages 399-418, June.
    • Handle: RePEc:inm:oropre:v:6:y:1958:i:3:p:399-418
    DOI: 10.1287/opre.6.3.399
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    Cited by:

    1. Sachin Jayaswal & Navneet Vidyarthi, 2017. "Facility location under service level constraints for heterogeneous customers," Annals of Operations Research, Springer, vol. 253(1), pages 275-305, June.
    2. Jayaswal, Sachin & Vidyarthi, Navneet, 2013. "Capacitated Multiple Allocation Hub Location with Service Level Constraints for Multiple Consignment Classes," IIMA Working Papers WP2013-11-02, Indian Institute of Management Ahmedabad, Research and Publication Department.
    3. Jayaswal, Sachin & Vidyarthi, Navneet, 2023. "Multiple allocation hub location with service level constraints for two shipment classes," European Journal of Operational Research, Elsevier, vol. 309(2), pages 634-655.
    4. Jayaswal, Sachin & Jewkes, Elizabeth & Ray, Saibal, 2011. "Product differentiation and operations strategy in a capacitated environment," European Journal of Operational Research, Elsevier, vol. 210(3), pages 716-728, May.

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