IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v162y2008i1p143-15810.1007-s10479-008-0313-6.html
   My bibliography  Save this article

Consecutive customer losses in oscillating GI X /M//n systems with state dependent services rates

Author

Listed:
  • António Pacheco
  • Helena Ribeiro

Abstract

We address the probability that k or more Consecutive Customer Losses take place during a busy period of a queue, the so-called k-CCL probability, for oscillating GI X /M//n systems with state dependent services rates, also denoted as GI X /M(m)−M(m)//n systems, in which the service rates oscillate between two forms according to the evolution of the number of customers in the system. We derive an efficient algorithm to compute k-CCL probabilities in these systems starting with an arbitrary number of customers in the system that involves solving a linear system of equations. The results derived are illustrated for specific sets of parameters. Copyright Springer Science+Business Media, LLC 2008

Suggested Citation

  • António Pacheco & Helena Ribeiro, 2008. "Consecutive customer losses in oscillating GI X /M//n systems with state dependent services rates," Annals of Operations Research, Springer, vol. 162(1), pages 143-158, September.
    • Handle: RePEc:spr:annopr:v:162:y:2008:i:1:p:143-158:10.1007/s10479-008-0313-6
    DOI: 10.1007/s10479-008-0313-6
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-008-0313-6
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-008-0313-6?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. Doo Il Choi & Charles Knessl & Charles Tier, 1999. "A queueing system with queue length dependent service times, with applications to cell discarding in ATM networks," International Journal of Stochastic Analysis, Hindawi, vol. 12, pages 1-28, January.
    2. J. R. Artalejo & A. Economou, 2005. "Markovian Controllable Queueing Systems with Hysteretic Policies: Busy Period and Waiting Time Analysis," Methodology and Computing in Applied Probability, Springer, vol. 7(3), pages 353-378, September.
    3. Emil Bahary & Peter Kolesar, 1972. "Multilevel Bulk Service Queues," Operations Research, INFORMS, vol. 20(2), pages 406-420, April.
    4. Terrell J. Harris, 1971. "The Remaining Busy Period of a Finite Queue," Operations Research, INFORMS, vol. 19(1), pages 219-223, February.
    5. M. Yadin & P. Naor, 1967. "On queueing systems with variable service capacities," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 14(1), pages 43-53.
    6. F. V. Lu & R. F. Serfozo, 1984. "M / M /1 Queueing Decision Processes with Monotone Hysteretic Optimal Policies," Operations Research, INFORMS, vol. 32(5), pages 1116-1132, October.
    7. Mykola Bratiychuk & Andrzej Chydzinski, 2003. "On the ergodic distribution of oscillating queueing systems," International Journal of Stochastic Analysis, Hindawi, vol. 16, pages 1-16, January.
    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. Andrzej Chydzinski & Pawel Mrozowski, 2016. "Queues with Dropping Functions and General Arrival Processes," PLOS ONE, Public Library of Science, vol. 11(3), pages 1-23, March.
    2. Souvik Ghosh & A. D. Banik & Joris Walraevens & Herwig Bruneel, 2022. "A detailed note on the finite-buffer queueing system with correlated batch-arrivals and batch-size-/phase-dependent bulk-service," 4OR, Springer, vol. 20(2), pages 241-272, June.
    3. Pawel Mrozowski & Andrzej Chydzinski, 2018. "Queues with Dropping Functions and Autocorrelated Arrivals," Methodology and Computing in Applied Probability, Springer, vol. 20(1), pages 97-115, March.
    4. M. L. Chaudhry & A. D. Banik & A. Pacheco, 2017. "A simple analysis of the batch arrival queue with infinite-buffer and Markovian service process using roots method: $$ GI ^{[X]}/C$$ G I [ X ] / C - $$ MSP /1/\infty $$ M S P / 1 / ∞," Annals of Operations Research, Springer, vol. 252(1), pages 135-173, May.

    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. Fátima Ferreira & António Pacheco & Helena Ribeiro, 2017. "Moments of losses during busy-periods of regular and nonpreemptive oscillating $$M^X/G/1/n$$ M X / G / 1 / n systems," Annals of Operations Research, Springer, vol. 252(1), pages 191-211, May.
    2. Terekhov, Daria & Christopher Beck, J., 2009. "An extended queueing control model for facilities with front room and back room operations and mixed-skilled workers," European Journal of Operational Research, Elsevier, vol. 198(1), pages 223-231, October.
    3. Berman, Oded & Wang, Jiamin & Sapna, K. P., 2005. "Optimal management of cross-trained workers in services with negligible switching costs," European Journal of Operational Research, Elsevier, vol. 167(2), pages 349-369, December.
    4. J. R. Artalejo & A. Economou, 2005. "Markovian Controllable Queueing Systems with Hysteretic Policies: Busy Period and Waiting Time Analysis," Methodology and Computing in Applied Probability, Springer, vol. 7(3), pages 353-378, September.
    5. Fowler, John W. & Mönch, Lars, 2022. "A survey of scheduling with parallel batch (p-batch) processing," European Journal of Operational Research, Elsevier, vol. 298(1), pages 1-24.
    6. Alexander Zadorojniy & Guy Even & Adam Shwartz, 2009. "A Strongly Polynomial Algorithm for Controlled Queues," Mathematics of Operations Research, INFORMS, vol. 34(4), pages 992-1007, November.
    7. Kim, Eungab, 2005. "Optimal inventory replenishment policy for a queueing system with finite waiting room capacity," European Journal of Operational Research, Elsevier, vol. 161(1), pages 256-274, February.
    8. Niek Baer & Ahmad Al Hanbali & Richard J. Boucherie & Jan-Kees van Ommeren, 2022. "A successive censoring algorithm for a system of connected LDQBD-processes," Annals of Operations Research, Springer, vol. 310(2), pages 389-410, March.
    9. 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.
    10. Sunggon Kim & Jongwoo Kim & Eui Lee, 2006. "Stationary distribution of queue length in G / M / 1 queue with two-stage service policy," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(3), pages 467-480, December.
    11. Foreest, N. D. van & Wijngaard, J., 2010. "On the Optimal Policy for the Single-product Inventory Problem with Set-up Cost and a Restricted Production Capacity," Research Report 10005, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    12. Boronico, Jess S. & Siegel, Philip H., 1998. "Capacity planning for toll roadways incorporating consumer wait time costs," Transportation Research Part A: Policy and Practice, Elsevier, vol. 32(4), pages 297-310, May.
    13. repec:dgr:rugsom:10005 is not listed on IDEAS
    14. Kim, Eungab, 2004. "Stochastic vendor managed replenishment with demand dependent shipment," European Journal of Operational Research, Elsevier, vol. 152(3), pages 723-744, February.
    15. Tirdad, Ali & Grassmann, Winfried K. & Tavakoli, Javad, 2016. "Optimal policies of M(t)/M/c/c queues with two different levels of servers," European Journal of Operational Research, Elsevier, vol. 249(3), pages 1124-1130.
    16. Carri W. Chan & Mor Armony & Nicholas Bambos, 2016. "Maximum weight matching with hysteresis in overloaded queues with setups," Queueing Systems: Theory and Applications, Springer, vol. 82(3), pages 315-351, April.
    17. Nicky D. Van Foreest & Jacob Wijngaard, 2014. "On Optimal Policies for Production-Inventory Systems with Compound Poisson Demand and Setup Costs," Mathematics of Operations Research, INFORMS, vol. 39(2), pages 517-532, May.
    18. Mouloud Cherfaoui & Aicha Bareche, 2020. "An optimal approximation of the characteristics of the GI/M/1 queue with two-stage service policy," Operational Research, Springer, vol. 20(2), pages 959-983, June.
    19. Guy Even & Alexander Zadorojniy, 2012. "Strong polynomiality of the Gass-Saaty shadow-vertex pivoting rule for controlled random walks," Annals of Operations Research, Springer, vol. 201(1), pages 159-167, December.
    20. Nasuh Buyukkaramikli & J. Bertrand & Henny Ooijen, 2013. "Flexible hiring in a make to order system with parallel processing units," Annals of Operations Research, Springer, vol. 209(1), pages 159-178, October.
    21. M. Yu. Kitaev & Richard F. Serfozo, 1999. "M/M/1 Queues with Switching Costs and Hysteretic Optimal Control," Operations Research, INFORMS, vol. 47(2), pages 310-312, April.

    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:spr:annopr:v:162:y:2008:i:1:p:143-158:10.1007/s10479-008-0313-6. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.