IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v220y2012i3p695-704.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221712001610
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2012.02.029?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Michael Samudra & Carla Van Riet & Erik Demeulemeester & Brecht Cardoen & Nancy Vansteenkiste & Frank E. Rademakers, 2016. "Scheduling operating rooms: achievements, challenges and pitfalls," Journal of Scheduling, Springer, vol. 19(5), pages 493-525, October.
    2. Sumi Kim & Seongmoon Kim, 2015. "Differentiated waiting time management according to patient class in an emergency care center using an open Jackson network integrated with pooling and prioritizing," Annals of Operations Research, Springer, vol. 230(1), pages 35-55, July.
    3. O. Boxma & A. Löpker & D. Perry, 2016. "On a make-to-stock production/mountain modeln with hysteretic control," Annals of Operations Research, Springer, vol. 241(1), pages 53-82, June.
    4. Zarrinpoor, Naeme & Fallahnezhad, Mohammad Saber & Pishvaee, Mir Saman, 2018. "The design of a reliable and robust hierarchical health service network using an accelerated Benders decomposition algorithm," European Journal of Operational Research, Elsevier, vol. 265(3), pages 1013-1032.
    5. 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.
    6. Samuelson, Aviva & Haigh, Andrew & O'Reilly, Małgorzata M. & Bean, Nigel G., 2017. "Stochastic model for maintenance in continuously deteriorating systems," European Journal of Operational Research, Elsevier, vol. 259(3), pages 1169-1179.
    7. Soroush Saghafian & Wallace J. Hopp & Mark P. Van Oyen & Jeffrey S. Desmond & Steven L. Kronick, 2014. "Complexity-Augmented Triage: A Tool for Improving Patient Safety and Operational Efficiency," Manufacturing & Service Operations Management, INFORMS, vol. 16(3), pages 329-345, July.
    8. 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.
    9. 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.
    10. Artur Nagapetyan & Alexander Drozd & Dmitry Subbotovsky, 2023. "How to Determine the Optimal Number of Cardiologists in a Region?," Mathematics, MDPI, vol. 11(21), pages 1-23, October.
    11. Carmen, Raïsa & Van Nieuwenhuyse, Inneke & Van Houdt, Benny, 2018. "Inpatient boarding in emergency departments: Impact on patient delays and system capacity," European Journal of Operational Research, Elsevier, vol. 271(3), pages 953-967.
    12. Gábor Horváth & Miklós Telek, 2017. "Matrix-analytic solution of infinite, finite and level-dependent second-order fluid models," Queueing Systems: Theory and Applications, Springer, vol. 87(3), pages 325-343, December.
    13. Salah Al-Deen Almousa & Gábor Horváth & Miklós Telek, 2022. "Transient analysis of piecewise homogeneous Markov fluid models," Annals of Operations Research, Springer, vol. 310(2), pages 333-353, March.
    14. Mohammadi, M. & Dehbari, S. & Vahdani, Behnam, 2014. "Design of a bi-objective reliable healthcare network with finite capacity queue under service covering uncertainty," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 72(C), pages 15-41.
    15. D’Auria, Bernardo & Adan, Ivo J.B.F. & Bekker, René & Kulkarni, Vidyadhar, 2022. "An M/M/c queue with queueing-time dependent service rates," European Journal of Operational Research, Elsevier, vol. 299(2), pages 566-579.
    16. Fournier, Derrick L. & Zaric, Gregory S., 2013. "Simulating neonatal intensive care capacity in British Columbia," Socio-Economic Planning Sciences, Elsevier, vol. 47(2), pages 131-141.
    17. 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.
    18. 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.
    19. Zahiri, B. & Tavakkoli-Moghaddam, R. & Mohammadi, M. & Jula, P., 2014. "Multi-objective design of an organ transplant network under uncertainty," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 72(C), pages 101-124.
    20. Mehmet Akif Yazici & Nail Akar, 2017. "The finite/infinite horizon ruin problem with multi-threshold premiums: a Markov fluid queue approach," Annals of Operations Research, Springer, vol. 252(1), pages 85-99, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:220:y:2012:i:3:p:695-704. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.