IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v26y1996i3p233-242.html
   My bibliography  Save this article

A queueing theoretical proof of increasing property of Polya frequency functions

Author

Listed:
  • Daduna, Hans
  • Szekli, Ryszard

Abstract

Let X1,...,Xn be independent random variables with PF2 densities and [phi] an increasing function. Then E([phi](X1,...,Xn) [Sigma]i=1n X1 = s) is increasing in s, almost surely (Efron, 1965). We put this theorem into the context of queueing theory and provide an elementary proof for non-negative random variables.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:26:y:1996:i:3:p:233-242
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0167-7152(95)00015-1
    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. J. George Shanthikumar & David D. Yao, 1987. "Stochastic Monotonicity of the Queue Lengths in Closed Queueing Networks," Operations Research, INFORMS, vol. 35(4), pages 583-588, August.
    2. James R. Jackson, 1957. "Networks of Waiting Lines," Operations Research, INFORMS, vol. 5(4), pages 518-521, August.
    3. Shanthikumar, J. George & Yao, David D., 1986. "The preservation of likelihood ratio ordering under convolution," Stochastic Processes and their Applications, Elsevier, vol. 23(2), pages 259-267, December.
    4. Rajan Suri, 1985. "A Concept of Monotonicity and Its Characterization for Closed Queueing Networks," Operations Research, INFORMS, vol. 33(3), pages 606-624, June.
    5. Block, Henry W. & Savits, Thomas H. & Shaked, Moshe, 1985. "A concept of negative dependence using stochastic ordering," Statistics & Probability Letters, Elsevier, vol. 3(2), pages 81-86, 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. Bogso, Antoine Marie, 2015. "MRL order, log-concavity and an application to peacocks," Stochastic Processes and their Applications, Elsevier, vol. 125(4), pages 1282-1306.
    2. Franco Pellerey & Jorge Navarro, 2022. "Stochastic monotonicity of dependent variables given their sum," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 543-561, June.
    3. 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.

    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. Dijk, N.M. van, 1989. "The importance of bias-terms for error bounds and comparison results," Serie Research Memoranda 0036, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    2. Saumard, Adrien & Wellner, Jon A., 2018. "Efron’s monotonicity property for measures on R2," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 212-224.
    3. Franco Pellerey & Jorge Navarro, 2022. "Stochastic monotonicity of dependent variables given their sum," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 543-561, June.
    4. Ward Whitt & Wei You, 2022. "New decomposition approximations for queueing networks," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 365-367, April.
    5. 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.
    6. Wu, Kan & McGinnis, Leon, 2012. "Performance evaluation for general queueing networks in manufacturing systems: Characterizing the trade-off between queue time and utilization," European Journal of Operational Research, Elsevier, vol. 221(2), pages 328-339.
    7. Flötteröd, G. & Osorio, C., 2017. "Stochastic network link transmission model," Transportation Research Part B: Methodological, Elsevier, vol. 102(C), pages 180-209.
    8. 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.
    9. Shaked, Moshe & George Shanthikumar, J., 1995. "Hazard rate ordering of k-out-of-n systems," Statistics & Probability Letters, Elsevier, vol. 23(1), pages 1-8, April.
    10. 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.
    11. 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.
    12. Hu, Taizhong & Zhu, Zegang, 2001. "An analytic proof of the preservation of the up-shifted likelihood ratio order under convolutions," Stochastic Processes and their Applications, Elsevier, vol. 95(1), pages 55-61, September.
    13. Li, Yongli & Gao, Xin & Xu, Zhiwei & Zhou, Xuanrui, 2018. "Network-based queuing model for simulating passenger throughput at an airport security checkpoint," Journal of Air Transport Management, Elsevier, vol. 66(C), pages 13-24.
    14. Gordon H. Lewis & Ashok Srinivasan & Eswaran Subrahmanian, 1998. "Staffing and Allocation of Workers in an Administrative Office," Management Science, INFORMS, vol. 44(4), pages 548-570, April.
    15. Ward Whitt & Wei You, 2020. "Heavy-traffic limits for stationary network flows," Queueing Systems: Theory and Applications, Springer, vol. 95(1), pages 53-68, June.
    16. 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.
    17. Cai, Jun & Wei, Wei, 2012. "On the invariant properties of notions of positive dependence and copulas under increasing transformations," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 43-49.
    18. Bäuerle, Nicole & Glauner, Alexander, 2018. "Optimal risk allocation in reinsurance networks," Insurance: Mathematics and Economics, Elsevier, vol. 82(C), pages 37-47.
    19. Yasushi Masuda & Seungjin Whang, 1999. "Dynamic Pricing for Network Service: Equilibrium and Stability," Management Science, INFORMS, vol. 45(6), pages 857-869, June.
    20. 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.

    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:stapro:v:26:y:1996:i:3:p:233-242. 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/wps/find/journaldescription.cws_home/622892/description#description .

    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.