IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v212y2011i2p352-360.html
   My bibliography  Save this article

On the distribution of the number stranded in bulk-arrival, bulk-service queues of the M/G/1 form

Author

Listed:
  • Kahraman, Aykut
  • Gosavi, Abhijit

Abstract

Bulk-arrival queues with single servers that provide bulk service are widespread in the real world, e.g., elevators in buildings, people-movers in amusement parks, air-cargo delivery planes, and automated guided vehicles. Much of the literature on this topic focusses on the development of the theory for waiting time and number in such queues. We develop the theory for the number stranded, i.e., the number of customers left behind after each service, in queues of the M/G/1 form, where there is single server, the arrival process is Poisson, the service is of a bulk nature, and the service time is a random variable. For the homogenous Poisson case, in our model the service time can have any given distribution. For the non-homogenous Poisson arrivals, due to a technicality, we assume that the service time is a discrete random variable. Our analysis is not only useful for performance analysis of bulk queues but also in designing server capacity when the aim is to reduce the frequency of stranding. Past attempts in the literature to study this problem have been hindered by the use of Laplace transforms, which pose severe numerical difficulties. Our approach is based on using a discrete-time Markov chain, which bypasses the need for Laplace transforms and is numerically tractable. We perform an extensive numerical analysis of our models to demonstrate their usefulness. To the best of our knowledge, this is the first attempt in the literature to study this problem in a comprehensive manner providing numerical solutions.

Suggested Citation

  • Kahraman, Aykut & Gosavi, Abhijit, 2011. "On the distribution of the number stranded in bulk-arrival, bulk-service queues of the M/G/1 form," European Journal of Operational Research, Elsevier, vol. 212(2), pages 352-360, July.
  • Handle: RePEc:eee:ejores:v:212:y:2011:i:2:p:352-360
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(11)00141-X
    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. Artalejo, Jesus R. & Economou, Antonis & Gómez-Corral, Antonio, 2008. "Algorithmic analysis of the Geo/Geo/c retrial queue," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1042-1056, September.
    2. Artalejo, J.R. & Economou, A. & Lopez-Herrero, M.J., 2007. "Algorithmic approximations for the busy period distribution of the M/M/c retrial queue," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1687-1702, February.
    3. Mejia-Tellez, Juan & Worthington, David, 1994. "Practical methods for queue length behaviour for bulk service queues of the form M/G0,C/1 and M(t)/G0,C/1," European Journal of Operational Research, Elsevier, vol. 73(1), pages 103-113, February.
    4. Chen, Shih-Pin, 2005. "Parametric nonlinear programming approach to fuzzy queues with bulk service," European Journal of Operational Research, Elsevier, vol. 163(2), pages 434-444, June.
    5. Armero, Carmen & Conesa, David, 2004. "Statistical performance of a multiclass bulk production queueing system," European Journal of Operational Research, Elsevier, vol. 158(3), pages 649-661, November.
    6. Thomas L. Saaty, 1960. "Time-Dependent Solution of the Many-Server Poisson Queue," Operations Research, INFORMS, vol. 8(6), pages 755-772, December.
    7. Ulrich W. Thonemann & Margaret L. Brandeau, 1996. "Designing A Single-Vehicle Automated Guided Vehicle System with Multiple Load Capacity," Transportation Science, INFORMS, vol. 30(4), pages 351-363, November.
    8. Ke, Jau-Chuan & Wang, Kuo-Hsiung, 2002. "A recursive method for the N policy G/M/1 queueing system with finite capacity," European Journal of Operational Research, Elsevier, vol. 142(3), pages 577-594, November.
    9. A. G. Pakes, 1969. "Some Conditions for Ergodicity and Recurrence of Markov Chains," Operations Research, INFORMS, vol. 17(6), pages 1058-1061, December.
    10. Teghem, J., 1986. "Control of the service process in a queueing system," European Journal of Operational Research, Elsevier, vol. 23(2), pages 141-158, February.
    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. Schwarz, Justus Arne & Selinka, Gregor & Stolletz, Raik, 2016. "Performance analysis of time-dependent queueing systems: Survey and classification," Omega, Elsevier, vol. 63(C), pages 170-189.
    2. Xiaohan Wu & Anyue Chen, 2023. "Further results of Markovian bulk-arrival and bulk-service queues with general-state-dependent control," Queueing Systems: Theory and Applications, Springer, vol. 104(1), pages 19-52, June.
    3. Justus Arne Schwarz & Martin Epp, 2016. "Performance evaluation of a transportation-type bulk queue with generally distributed inter-arrival times," International Journal of Production Research, Taylor & Francis Journals, vol. 54(20), pages 6251-6264, October.
    4. Xu, Jianjun & Serrano, Alejandro & Lin, Bing, 2017. "Optimal production and rationing policy of two-stage tandem production system," International Journal of Production Economics, Elsevier, vol. 185(C), pages 100-112.

    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. Dong-Yuh Yang & Po-Kai Chang, 2015. "A parametric programming solution to the -policy queue with fuzzy parameters," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(4), pages 590-598, March.
    2. Jeongsim Kim & Bara Kim, 2016. "A survey of retrial queueing systems," Annals of Operations Research, Springer, vol. 247(1), pages 3-36, December.
    3. Haque, Lani & Armstrong, Michael J., 2007. "A survey of the machine interference problem," European Journal of Operational Research, Elsevier, vol. 179(2), pages 469-482, June.
    4. Öner-Közen, Miray & Minner, Stefan, 2017. "Impact of priority sequencing decisions on on-time probability and expected tardiness of orders in make-to-order production systems with external due-dates," European Journal of Operational Research, Elsevier, vol. 263(2), pages 524-539.
    5. Jain, Apurva, 2007. "Value of capacity pooling in supply chains with heterogeneous customers," European Journal of Operational Research, Elsevier, vol. 177(1), pages 239-260, February.
    6. M. A. C. Almeida & F. R. B. Cruz & F. L. P. Oliveira & G. Souza, 2020. "Bias correction for estimation of performance measures of a Markovian queue," Operational Research, Springer, vol. 20(2), pages 943-958, June.
    7. Zhang, Zhe G. & Tian, Naishuo, 2004. "An analysis of queueing systems with multi-task servers," European Journal of Operational Research, Elsevier, vol. 156(2), pages 375-389, July.
    8. Wei Li & Attahiru Sule Alfa, 2000. "Optimal policies for M/M/m queue with two different kinds of (N, T)‐policies," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(3), pages 240-258, April.
    9. Benjamin Legros, 2022. "The principal-agent problem for service rate event-dependency," Post-Print hal-03605421, HAL.
    10. R. Sudhesh & A. Mohammed Shapique, 2022. "Transient analysis of power management in wireless sensor network with start-up times and threshold policy," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 80(1), pages 1-16, May.
    11. Baumann, Hendrik & Sandmann, Werner, 2014. "On finite long run costs and rewards in infinite Markov chains," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 41-46.
    12. Falin, G.I., 2010. "A single-server batch arrival queue with returning customers," European Journal of Operational Research, Elsevier, vol. 201(3), pages 786-790, March.
    13. R.E. Lillo, 2001. "Optimal control of an M/G/1 queue with impatient priority customers," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(3), pages 201-209, April.
    14. Shweta Upadhyaya, 2020. "Investigating a general service retrial queue with damaging and licensed units: an application in local area networks," OPSEARCH, Springer;Operational Research Society of India, vol. 57(3), pages 716-745, September.
    15. Artalejo, Jesus R. & Economou, Antonis & Gómez-Corral, Antonio, 2008. "Algorithmic analysis of the Geo/Geo/c retrial queue," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1042-1056, September.
    16. T. Deepak, 2015. "On a retrial queueing model with single/batch service and search of customers from the orbit," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 493-520, July.
    17. Weng, Z. Kevin, 1996. "Manufacturing lead times, system utilization rates and lead-time-related demand," European Journal of Operational Research, Elsevier, vol. 89(2), pages 259-268, March.
    18. Seyed Khodadadi & Fariborz Jolai, 2012. "A fuzzy based threshold policy for a single server retrial queue with vacations," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 20(2), pages 281-297, June.
    19. 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.
    20. Ioannis Dimitriou, 2013. "A preemptive resume priority retrial queue with state dependent arrivals, unreliable server and negative customers," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(3), pages 542-571, October.

    More about this item

    Keywords

    Queueing Bulk queues Downside risk;

    Statistics

    Access and download statistics

    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:212:y:2011:i:2:p:352-360. 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.