IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v195y2009i1p174-185.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(08)00170-7
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. I. D. S. Taylor & J. G. C. Templeton, 1980. "Waiting Time In a Multi-Server Cutoff-Priority Queue, and Its Application to an Urban Ambulance Service," Operations Research, INFORMS, vol. 28(5), pages 1168-1188, October.
    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.
    3. Jeffrey Diamond & Attahiru Alfa, 1999. "Matrix analytic methods for a multi-server retrial queue with buffer," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 7(2), pages 249-266, December.
    4. Ety Zohar & Avishai Mandelbaum & Nahum Shimkin, 2002. "Adaptive Behavior of Impatient Customers in Tele-Queues: Theory and Empirical Support," Management Science, INFORMS, vol. 48(4), pages 566-583, April.
    5. Stephen C. Graves, 1982. "The Application of Queueing Theory to Continuous Perishable Inventory Systems," Management Science, INFORMS, vol. 28(4), pages 400-406, April.
    6. David Perry, 1999. "Analysis of a Sampling Control Scheme for a Perishable Inventory System," Operations Research, INFORMS, vol. 47(6), pages 966-973, December.
    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.

    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. Onno Boxma & David Perry & Shelley Zacks, 2015. "A Fluid EOQ Model of Perishable Items with Intermittent High and Low Demand Rates," Mathematics of Operations Research, INFORMS, vol. 40(2), pages 390-402, February.
    2. De Munck, Thomas & Chevalier, Philippe & Tancrez, Jean-Sébastien, 2023. "Managing priorities on on-demand service platforms with waiting time differentiation," International Journal of Production Economics, Elsevier, vol. 266(C).
    3. Ravichandran, N., 1995. "Stochastic analysis of a continuous review perishable inventory system with positive lead time and Poisson demand," European Journal of Operational Research, Elsevier, vol. 84(2), pages 444-457, July.
    4. Marcos Singer & Patricio Donoso & Natalia Jadue, 2004. "Evaluacion De Las Oportunidades De Mejoramiento De La Logistica Directa De Emergencia," Abante, Escuela de Administracion. Pontificia Universidad Católica de Chile., vol. 7(2), pages 179-209.
    5. Diwakar Gupta & Lei Wang, 2008. "Revenue Management for a Primary-Care Clinic in the Presence of Patient Choice," Operations Research, INFORMS, vol. 56(3), pages 576-592, June.
    6. Pengfei Guo & Paul Zipkin, 2007. "Analysis and Comparison of Queues with Different Levels of Delay Information," Management Science, INFORMS, vol. 53(6), pages 962-970, June.
    7. 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.
    8. Jouini, Oualid & Dallery, Yves & Aksin, Zeynep, 2009. "Queueing models for full-flexible multi-class call centers with real-time anticipated delays," International Journal of Production Economics, Elsevier, vol. 120(2), pages 389-399, August.
    9. Pengfei Guo & Refael Hassin, 2011. "Strategic Behavior and Social Optimization in Markovian Vacation Queues," Operations Research, INFORMS, vol. 59(4), pages 986-997, August.
    10. Marcos Singer & Patricio Donoso & Alan Scheller-Wolf, 2008. "Una Introducción A La Teoría De Colas Aplicada A La Gestión De Servicios," Abante, Escuela de Administracion. Pontificia Universidad Católica de Chile., vol. 11(2), pages 93-120.
    11. Oualid Jouini & Zeynep Akşin & Yves Dallery, 2011. "Call Centers with Delay Information: Models and Insights," Manufacturing & Service Operations Management, INFORMS, vol. 13(4), pages 534-548, October.
    12. 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.
    13. Lawrence Brown & Noah Gans & Avishai Mandelbaum & Anat Sakov & Haipeng Shen & Sergey Zeltyn & Linda Zhao & Novemer, "undated". "Statistical Analysis of a Telephone Call Center: A Queueing-Science Perspective," Center for Financial Institutions Working Papers 03-12, Wharton School Center for Financial Institutions, University of Pennsylvania.
    14. Li Xiao & Susan H. Xu & David D. Yao & Hanqin Zhang, 2022. "Optimal staffing for ticket queues," Queueing Systems: Theory and Applications, Springer, vol. 102(1), pages 309-351, October.
    15. Soovin Yoon & Laura A. Albert, 2018. "An expected coverage model with a cutoff priority queue," Health Care Management Science, Springer, vol. 21(4), pages 517-533, December.
    16. Zeynep Akşin & Barış Ata & Seyed Morteza Emadi & Che-Lin Su, 2013. "Structural Estimation of Callers' Delay Sensitivity in Call Centers," Management Science, INFORMS, vol. 59(12), pages 2727-2746, December.
    17. 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.
    18. J. E. Reed & Amy R. Ward, 2008. "Approximating the GI/GI/1+GI Queue with a Nonlinear Drift Diffusion: Hazard Rate Scaling in Heavy Traffic," Mathematics of Operations Research, INFORMS, vol. 33(3), pages 606-644, August.
    19. Yoon, Soovin & Albert, Laura A., 2021. "Dynamic dispatch policies for emergency response with multiple types of vehicles," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 152(C).
    20. 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.

    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:195:y:2009:i:1:p:174-185. 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.