IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v34y1987i4p579-591.html
   My bibliography  Save this article

The N‐seasons S‐servers loss system

Author

Listed:
  • Antony Svoronos
  • Linda Green

Abstract

We consider a class of loss systems with exponential service times and a Poisson arrival process with a rate that varies periodically among N levels called seasons. For two special cases, we derive transient and steady‐state solutions and provide simple proofs that losses are minimized when the arrival rates for all seasons are equal. In the general case, we describe a straightforward procedure to derive the steady‐state probabilities. We also prove that when S=1, the server is generally busier during the high arrival rate seasons.

Suggested Citation

  • Antony Svoronos & Linda Green, 1987. "The N‐seasons S‐servers loss system," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(4), pages 579-591, August.
    • Handle: RePEc:wly:navres:v:34:y:1987:i:4:p:579-591
    DOI: 10.1002/1520-6750(198708)34:43.0.CO;2-K
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/1520-6750(198708)34:43.0.CO;2-K
    Download Restriction: no
    File URL: https://libkey.io/10.1002/1520-6750(198708)34:43.0.CO;2-K?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
    ---><---

    References listed on IDEAS

    as
    1. Shun-Chen Niu, 1980. "A Single Server Queueing Loss Model with Heterogeneous Arrival and Service," Operations Research, INFORMS, vol. 28(3-part-i), pages 584-593, June.
    2. Ronald W. Wolff, 1982. "Poisson Arrivals See Time Averages," Operations Research, INFORMS, vol. 30(2), pages 223-231, April.
    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. Søren Asmussen & Colm O'cinneide, 2002. "On the Tail of the Waiting Time in a Markov-Modulated M/G/1 Queue," Operations Research, INFORMS, vol. 50(3), pages 559-565, June.

    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. Tetsuji Hirayama, 2003. "Mean sojourn times in multiclass feedback queues with gated disciplines," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(7), pages 719-741, October.
    2. Ananth V. Iyer & Apurva Jain, 2003. "The Logistics Impact of a Mixture of Order-Streams in a Manufacturer-Retailer System," Management Science, INFORMS, vol. 49(7), pages 890-906, July.
    3. Yanting Chen & Jingui Xie & Taozeng Zhu, 2023. "Overflow in systems with two servers: the negative consequences," Flexible Services and Manufacturing Journal, Springer, vol. 35(3), pages 838-863, September.
    4. Mohan L. Chaudhry & James J. Kim, 2016. "Analytically elegant and computationally efficient results in terms of roots for the $$GI^{X}/M/c$$ G I X / M / c queueing system," Queueing Systems: Theory and Applications, Springer, vol. 82(1), pages 237-257, February.
    5. Mohebbi, E., 2008. "A note on a production control model for a facility with limited storage capacity in a random environment," European Journal of Operational Research, Elsevier, vol. 190(2), pages 562-570, October.
    6. Hassin, Refael & Haviv, Moshe & Oz, Binyamin, 2023. "Strategic behavior in queues with arrival rate uncertainty," European Journal of Operational Research, Elsevier, vol. 309(1), pages 217-224.
    7. Huseyin C. Ozmutlu, 2009. "Markovian analysis for automatic new topic identification in search engine transaction logs," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(6), pages 737-768, November.
    8. Chester Chambers & Panagiotis Kouvelis, 2006. "Modeling and Managing the Percentage of Satisfied Customers in Hidden and Revealed Waiting Line Systems," Production and Operations Management, Production and Operations Management Society, vol. 15(1), pages 103-116, March.
    9. Zsolt Saffer & Sergey Andreev & Yevgeni Koucheryavy, 2016. "$$M/D^{[y]}/1$$ M / D [ y ] / 1 Periodically gated vacation model and its application to IEEE 802.16 network," Annals of Operations Research, Springer, vol. 239(2), pages 497-520, April.
    10. Qiao‐Chu He & Ying‐Ju Chen & Rhonda Righter, 2020. "Learning with Projection Effects in Service Operations Systems," Production and Operations Management, Production and Operations Management Society, vol. 29(1), pages 90-100, January.
    11. Kim, Young Joo & Hwang, Hark, 2009. "Incremental discount policy of cell-phone carrier with connection success rate constraint," European Journal of Operational Research, Elsevier, vol. 196(2), pages 682-687, July.
    12. Josh Reed & Bo Zhang, 2017. "Managing capacity and inventory jointly for multi-server make-to-stock queues," Queueing Systems: Theory and Applications, Springer, vol. 86(1), pages 61-94, June.
    13. Lee, Doo Ho & Kim, Bo Keun, 2015. "A note on the sojourn time distribution of an M/G/1 queue with a single working vacation and vacation interruption," Operations Research Perspectives, Elsevier, vol. 2(C), pages 57-61.
    14. Carri W. Chan & Jing Dong & Linda V. Green, 2017. "Queues with Time-Varying Arrivals and Inspections with Applications to Hospital Discharge Policies," Operations Research, INFORMS, vol. 65(2), pages 469-495, April.
    15. Hum, Sin-Hoon & Parlar, Mahmut & Zhou, Yun, 2018. "Measurement and optimization of responsiveness in supply chain networks with queueing structures," European Journal of Operational Research, Elsevier, vol. 264(1), pages 106-118.
    16. Johansen, Søren Glud, 2021. "The Markov model for base-stock control of an inventory system with Poisson demand, non-crossing lead times and lost sales," International Journal of Production Economics, Elsevier, vol. 231(C).
    17. Mohebbi, Esmail & Posner, Morton J. M., 1999. "A lost-sales continuous-review inventory system with emergency ordering," International Journal of Production Economics, Elsevier, vol. 58(1), pages 93-112, January.
    18. Vyacheslav M. Abramov, 2018. "Conservative and Semiconservative Random Walks: Recurrence and Transience," Journal of Theoretical Probability, Springer, vol. 31(3), pages 1900-1922, September.
    19. Johansen, Soren Glud, 2005. "Base-stock policies for the lost sales inventory system with Poisson demand and Erlangian lead times," International Journal of Production Economics, Elsevier, vol. 93(1), pages 429-437, January.
    20. Karsten, Frank & Basten, Rob J.I., 2014. "Pooling of spare parts between multiple users: How to share the benefits?," European Journal of Operational Research, Elsevier, vol. 233(1), pages 94-104.

    More about this item

    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:wly:navres:v:34:y:1987:i:4:p:579-591. 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    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.