IDEAS home Printed from https://ideas.repec.org/a/bpj/ecqcon/v18y2003i2p165-194n2.html
   My bibliography  Save this article

Availability Formulas and Performance Measures for Separable Degradable Networks

Author

Listed:
  • Sauer Cornelia

    (University of Hamburg, Department of Mathematics, Center of Mathematical Statistics and Stochastic Processes. sauer@math.uni-hamburg.de)

  • Daduna Hans

    (University of Hamburg, Department of Mathematics, Center of Mathematical Statistics and Stochastic Processes. daduna@math.uni-hamburg.de)

Abstract

We derive explicit formulas for availability and performance measures in complex degradable stochastic networks. The networks consist of interacting service systems (queues) where servers are unreliable and may break down. The breakdown and repair mechanisms are of rather general structure, and may show complex dependencies among the nodes of the networks. The degradable network models investigated incorporate the breakdowns of the servers and their repairs as well as the behavior of the service mechanisms and the customers' routing into the overall Markovian system description. The service rates may depend on the local loads of the service centers, and furthermore working and repair periods are globally determined by state dependent intensities. Three different rules are applied to handle the customers' routing connected with nodes in repair status. These rules originate from communication and production theory where they are used to resolve blocking situations.

Suggested Citation

  • Sauer Cornelia & Daduna Hans, 2003. "Availability Formulas and Performance Measures for Separable Degradable Networks," Stochastics and Quality Control, De Gruyter, vol. 18(2), pages 165-194, January.
    • Handle: RePEc:bpj:ecqcon:v:18:y:2003:i:2:p:165-194:n:2
    DOI: 10.1515/EQC.2003.165
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/EQC.2003.165
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.1515/EQC.2003.165?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. Harrison White & Lee S. Christie, 1958. "Queuing with Preemptive Priorities or with Breakdown," Operations Research, INFORMS, vol. 6(1), pages 79-95, February.
    2. Daduna, Hans & Szekli, Ryszard, 1996. "A queueing theoretical proof of increasing property of Polya frequency functions," Statistics & Probability Letters, Elsevier, vol. 26(3), pages 233-242, February.
    3. Benjamin Melamed, 1982. "Sojourn Times in Queueing Networks," Mathematics of Operations Research, INFORMS, vol. 7(2), pages 223-244, May.
    4. James R. Jackson, 1963. "Jobshop-Like Queueing Systems," Management Science, INFORMS, vol. 10(1), pages 131-142, October.
    5. K. Thiruvengadam, 1963. "Queuing with Breakdowns," Operations Research, INFORMS, vol. 11(1), pages 62-71, February.
    6. James R. Jackson, 1957. "Networks of Waiting Lines," Operations Research, INFORMS, vol. 5(4), pages 518-521, August.
    7. I. L. Mitrany & B. Avi-Itzhak, 1968. "A Many-Server Queue with Service Interruptions," Operations Research, INFORMS, vol. 16(3), pages 628-638, June.
    Full references (including those not matched with items on IDEAS)

    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. B. Krishna Kumar & R. Rukmani & A. Thanikachalam & V. Kanakasabapathi, 2018. "Performance analysis of retrial queue with server subject to two types of breakdowns and repairs," Operational Research, Springer, vol. 18(2), pages 521-559, July.
    2. Sheng Zhu & Jinting Wang & Bin Liu, 2020. "Equilibrium joining strategies in the Mn/G/1 queue with server breakdowns and repairs," Operational Research, Springer, vol. 20(4), pages 2163-2187, December.
    3. Madhu Jain & Sandeep Kaur & Parminder Singh, 2021. "Supplementary variable technique (SVT) for non-Markovian single server queue with service interruption (QSI)," Operational Research, Springer, vol. 21(4), pages 2203-2246, December.
    4. Francisco Castro & Hamid Nazerzadeh & Chiwei Yan, 2020. "Matching queues with reneging: a product form solution," Queueing Systems: Theory and Applications, Springer, vol. 96(3), pages 359-385, December.
    5. Flötteröd, G. & Osorio, C., 2017. "Stochastic network link transmission model," Transportation Research Part B: Methodological, Elsevier, vol. 102(C), pages 180-209.
    6. Papadopoulos, H. T. & Heavey, C., 1996. "Queueing theory in manufacturing systems analysis and design: A classification of models for production and transfer lines," European Journal of Operational Research, Elsevier, vol. 92(1), pages 1-27, July.
    7. Morabito, Reinaldo & de Souza, Mauricio C. & Vazquez, Mariana, 2014. "Approximate decomposition methods for the analysis of multicommodity flow routing in generalized queuing networks," European Journal of Operational Research, Elsevier, vol. 232(3), pages 618-629.
    8. 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.
    9. John S. Hollywood, 2005. "An approximate planning model for distributed computing networks," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(6), pages 590-605, September.
    10. Fiems, Dieter & Maertens, Tom & Bruneel, Herwig, 2008. "Queueing systems with different types of server interruptions," European Journal of Operational Research, Elsevier, vol. 188(3), pages 838-845, August.
    11. Kurt M. Bretthauer, 2000. "Optimal service and arrival rates in Jackson queueing networks," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(1), pages 1-17, February.
    12. Haskose, A. & Kingsman, B. G. & Worthington, D, 2004. "Performance analysis of make-to-order manufacturing systems under different workload control regimes," International Journal of Production Economics, Elsevier, vol. 90(2), pages 169-186, July.
    13. Pedram Sahba & Bariş Balciog̃lu & Dragan Banjevic, 2013. "Analysis of the finite‐source multiclass priority queue with an unreliable server and setup time," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(4), pages 331-342, June.
    14. Nico Dijk & Barteld Schilstra, 2022. "On two product form modifications for finite overflow systems," Annals of Operations Research, Springer, vol. 310(2), pages 519-549, March.
    15. Miaomiao Yu & Yinghui Tang, 2022. "Analysis of a renewal batch arrival queue with a fault-tolerant server using shift operator method," Operational Research, Springer, vol. 22(3), pages 2831-2858, July.
    16. Osorio, Carolina & Wang, Carter, 2017. "On the analytical approximation of joint aggregate queue-length distributions for traffic networks: A stationary finite capacity Markovian network approach," Transportation Research Part B: Methodological, Elsevier, vol. 95(C), pages 305-339.
    17. D Worthington, 2009. "Reflections on queue modelling from the last 50 years," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(1), pages 83-92, May.
    18. Bretthauer, Kurt M., 1996. "Capacity planning in manufacturing and computer networks," European Journal of Operational Research, Elsevier, vol. 91(2), pages 386-394, June.
    19. Osorio, Carolina & Bierlaire, Michel, 2009. "An analytic finite capacity queueing network model capturing the propagation of congestion and blocking," European Journal of Operational Research, Elsevier, vol. 196(3), pages 996-1007, August.
    20. Hoseinpour, Pooya & Ahmadi-Javid, Amir, 2016. "A profit-maximization location-capacity model for designing a service system with risk of service interruptions," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 96(C), pages 113-134.

    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:bpj:ecqcon:v:18:y:2003:i:2:p:165-194:n:2. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.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.