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The MAP/(PH/PH)/1 queue with self-generation of priorities and non-preemptive service

Author

Listed:
  • Krishnamoorthy, A.
  • Babu, S.
  • Narayanan, Viswanath C.

Abstract

Customers arriving according to a Markovian arrival process are served at a single server facility. Waiting customers generate priority at a constant rate [gamma]; such a customer waits in a waiting space of capacity 1 if this waiting space is not already occupied by a priority generated customer; else it leaves the system. A customer in service will be completely served before the priority generated customer is taken for service (non-preemptive service discipline). Only one priority generated customer can wait at a time and a customer generating into priority at that time will have to leave the system in search of emergency service elsewhere. The service times of ordinary and priority generated customers follow PH-distributions. The matrix analytic method is used to compute the steady state distribution. Performance measures such as the probability of n consecutive services of priority generated customers, the probability of the same for ordinary customers, and the mean waiting time of a tagged customer are found by approximating them by their corresponding values in a truncated system. All these results are supported numerically.

Suggested Citation

  • Krishnamoorthy, A. & Babu, S. & Narayanan, Viswanath C., 2009. "The MAP/(PH/PH)/1 queue with self-generation of priorities and non-preemptive service," European Journal of Operational Research, Elsevier, vol. 195(1), pages 174-185, May.
    • Handle: RePEc:eee:ejores:v:195:y:2009:i:1:p:174-185
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    References listed on IDEAS

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    Cited by:

    1. Jie Zhou & Jun Li, 2017. "An M/E k /1 queues with emergency non-preemptive priority of a diagnostic resource," Operational Research, Springer, vol. 17(1), pages 1-16, April.
    2. Zhu, Juanxiu & Hu, Lu & Jiang, Yangsheng & Khattak, Afaq, 2017. "Circulation network design for urban rail transit station using a PH(n)/PH(n)/C/C queuing network model," European Journal of Operational Research, Elsevier, vol. 260(3), pages 1043-1068.
    3. Baumann, Hendrik & Sandmann, Werner, 2017. "Multi-server tandem queue with Markovian arrival process, phase-type service times, and finite buffers," European Journal of Operational Research, Elsevier, vol. 256(1), pages 187-195.
    4. Hu, Lu & Jiang, Yangsheng & Zhu, Juanxiu & Chen, Yanru, 2015. "A PH/PH(n)/C/C state-dependent queuing model for metro station corridor width design," European Journal of Operational Research, Elsevier, vol. 240(1), pages 109-126.
    5. Gwiggner, Claus & Nagaoka, Sakae, 2014. "Data and queueing analysis of a Japanese air-traffic flow," European Journal of Operational Research, Elsevier, vol. 235(1), pages 265-275.
    6. Przemysław Korytkowski & Tomasz Wiśniewski, 2011. "Performance analysis of commercial offset printing under dynamic priority rules," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 21(1), pages 53-64.

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