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The Pareto Distribution as a Queue Service Discipline

Author

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  • Carl M. Harris

    (Western Electric Co., Inc., Princeton, New Jersey)

Abstract

A queuing system is described in which service times are conditioned upon a random parameter μ, such that the conditional service distribution is exponential and μ has a gamma density. It is shown that the resultant unconditional distribution of service times is Paretian. Several measures of effectiveness are discussed and the question of statistical estimation of service parameters is also explored.

Suggested Citation

  • Carl M. Harris, 1968. "The Pareto Distribution as a Queue Service Discipline," Operations Research, INFORMS, vol. 16(2), pages 307-313, April.
    • Handle: RePEc:inm:oropre:v:16:y:1968:i:2:p:307-313
    DOI: 10.1287/opre.16.2.307
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    Cited by:

    1. Malinovskii, Vsevolod K. & Kosova, Ksenia O., 2014. "Simulation analysis of ruin capital in Sparre Andersen’s model of risk," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 184-193.
    2. D. Kern, 1983. "Minimum variance unbiased estimation in the Pareto distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 30(1), pages 15-19, December.
    3. Wangxue Chen & Rui Yang & Dongsen Yao & Chunxian Long, 2021. "Pareto parameters estimation using moving extremes ranked set sampling," Statistical Papers, Springer, vol. 62(3), pages 1195-1211, June.
    4. Zeinab Amin, 2008. "Bayesian inference for the Pareto lifetime model under progressive censoring with binomial removals," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(11), pages 1203-1217.
    5. Gorbunova, A.V. & Lebedev, A.V., 2023. "Nonlinear approximation of characteristics of a fork–join queueing system with Pareto service as a model of parallel structure of data processing," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 214(C), pages 409-428.
    6. Axel Gandy & Luitgard A. M. Veraart, 2017. "A Bayesian Methodology for Systemic Risk Assessment in Financial Networks," Management Science, INFORMS, vol. 63(12), pages 4428-4446, December.
    7. Bercher, J.-F. & Vignat, C., 2008. "A new look at q-exponential distributions via excess statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(22), pages 5422-5432.
    8. Muhammad Ahsan Ul Haq & G. G. Hamedani & M. Elgarhy & Pedro Luiz Ramos, 2020. "Marshall-Olkin Power Lomax Distribution: Properties and Estimation Based on Complete and Censored Samples," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 9(1), pages 1-48, January.
    9. Kasteridis, Panagiotis & Rice, Nigel & Santos, Rita, 2022. "Heterogeneity in end of life health care expenditure trajectory profiles," Journal of Economic Behavior & Organization, Elsevier, vol. 204(C), pages 221-251.
    10. Brill, P.H. & Huang, M.L. & Hlynka, M., 2020. "On the service time in a workload-barrier M/G/1 queue with accepted and blocked customers," European Journal of Operational Research, Elsevier, vol. 283(1), pages 235-243.
    11. Thomas G. Koch, 2017. "The Shifting Shape of Risk: Endogenous Market Failure for Insurance," Risks, MDPI, vol. 5(1), pages 1-13, January.
    12. Alan Washburn, 2006. "A sequential Bayesian generalization of the Jelinski–Moranda software reliability model," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(4), pages 354-362, June.
    13. Sanaa Al-Marzouki & Farrukh Jamal & Christophe Chesneau & Mohammed Elgarhy, 2019. "Type II Topp Leone Power Lomax Distribution with Applications," Mathematics, MDPI, vol. 8(1), pages 1-26, December.
    14. Elfessi, Abdulaziz & Chun Jin, 1996. "On robust estimation of the common scale parameter of several Pareto distributions," Statistics & Probability Letters, Elsevier, vol. 29(4), pages 345-352, September.
    15. Amal S. Hassan & Marwa Abd-Allah, 2019. "On the Inverse Power Lomax Distribution," Annals of Data Science, Springer, vol. 6(2), pages 259-278, June.
    16. Li, Baibing, 2013. "A model of pedestrians’ intended waiting times for street crossings at signalized intersections," Transportation Research Part B: Methodological, Elsevier, vol. 51(C), pages 17-28.
    17. Badiollah Asrabadi, 1990. "Estimation in the pareto distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 37(1), pages 199-205, December.
    18. Saralees Nadarajah & Samuel Kotz, 2003. "Reliability for Pareto models," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 191-204.
    19. Majdah Badr & Muhammad Ijaz, 2021. "The Exponentiated Exponential Burr XII distribution: Theory and application to lifetime and simulated data," PLOS ONE, Public Library of Science, vol. 16(3), pages 1-20, March.
    20. Thomas G. Koch, 2014. "Bankruptcy, Medical Insurance, And A Law With Unintended Consequences," Health Economics, John Wiley & Sons, Ltd., vol. 23(11), pages 1326-1339, November.
    21. Constantinos Petropoulos, 2017. "Estimation of the order restricted scale parameters for two populations from the Lomax distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(4), pages 483-502, May.

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