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Analysis of the adaptive MMAP[K]/PH[K]/1 queue: A multi-type queue with adaptive arrivals and general impatience

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  • Van Houdt, Benny

Abstract

In this paper we introduce the adaptive MMAP[K] arrival process and analyze the adaptive MMAP[K]/PH[K]/1 queue. In such a queueing system, customers of K different types with Markovian inter-arrival times and possibly correlated customer types, are fed to a single server queue that makes use of r thresholds. Service times are phase-type and depend on the type of customer in service. Type k customers are accepted with some probability ai,k if the current workload is between threshold i−1 and i. The manner in which the arrival process changes its state after generating a type k customer also depends on whether the customer is accepted or rejected.

Suggested Citation

  • Van Houdt, Benny, 2012. "Analysis of the adaptive MMAP[K]/PH[K]/1 queue: A multi-type queue with adaptive arrivals and general impatience," European Journal of Operational Research, Elsevier, vol. 220(3), pages 695-704.
    • Handle: RePEc:eee:ejores:v:220:y:2012:i:3:p:695-704
    DOI: 10.1016/j.ejor.2012.02.029
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    References listed on IDEAS

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    1. Silva Soares, Ana da & Latouche, Guy, 2009. "Fluid queues with level dependent evolution," European Journal of Operational Research, Elsevier, vol. 196(3), pages 1041-1048, August.
    2. Wang, Qinan, 2004. "Modeling and analysis of high risk patient queues," European Journal of Operational Research, Elsevier, vol. 155(2), pages 502-515, June.
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    Cited by:

    1. Yutaka Sakuma & Onno Boxma & Tuan Phung-Duc, 2021. "An M/PH/1 queue with workload-dependent processing speed and vacations," Queueing Systems: Theory and Applications, Springer, vol. 98(3), pages 373-405, August.
    2. Horváth, Gábor, 2015. "Efficient analysis of the MMAP[K]/PH[K]/1 priority queue," European Journal of Operational Research, Elsevier, vol. 246(1), pages 128-139.
    3. Ni, Guanqun & Xu, Yinfeng & Dong, Yucheng, 2013. "Price and speed decisions in customer-intensive services with two classes of customers," European Journal of Operational Research, Elsevier, vol. 228(2), pages 427-436.
    4. Casale, Giuliano & Sansottera, Andrea & Cremonesi, Paolo, 2016. "Compact Markov-modulated models for multiclass trace fitting," European Journal of Operational Research, Elsevier, vol. 255(3), pages 822-833.
    5. Qi-Ming He & Hao Zhang & Qingqing Ye, 2018. "An M/PH/K queue with constant impatient time," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 87(1), pages 139-168, February.
    6. Ivo Adan & Brett Hathaway & Vidyadhar G. Kulkarni, 2019. "On first-come, first-served queues with two classes of impatient customers," Queueing Systems: Theory and Applications, Springer, vol. 91(1), pages 113-142, February.
    7. O’Reilly, Małgorzata M., 2014. "Multi-stage stochastic fluid models for congestion control," European Journal of Operational Research, Elsevier, vol. 238(2), pages 514-526.
    8. Peter Buchholz & Jan Kriege, 2017. "Fitting correlated arrival and service times and related queueing performance," Queueing Systems: Theory and Applications, Springer, vol. 85(3), pages 337-359, April.

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