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Geometric Distribution in Some Two-Dimensional Queuing Systems

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  • Richard V. Evans

    (University of California, Los Angeles, California)

Abstract

The state of the system is a two dimensional random variable N = ( N 1 , N 2 ) with N 1 ≧ 0, 1 ≦ N 2 ≦ m . Transitions require negative exponential times. The vector P n of probabilities of being in states for which N 1 = n satisfy the general condition λ IP n −1 + BP n + CP n +1 = 0. Two arguments are given showing P n = RP n −1 and an iterative scheme for finding R is constructed.

Suggested Citation

  • Richard V. Evans, 1967. "Geometric Distribution in Some Two-Dimensional Queuing Systems," Operations Research, INFORMS, vol. 15(5), pages 830-846, October.
    • Handle: RePEc:inm:oropre:v:15:y:1967:i:5:p:830-846
    DOI: 10.1287/opre.15.5.830
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    Cited by:

    1. Fadiloglu, Mehmet Murat & Yeralan, Sencer, 2001. "A general theory on spectral properties of state-homogeneous finite-state quasi-birth-death processes," European Journal of Operational Research, Elsevier, vol. 128(2), pages 402-417, January.
    2. Yacov Satin & Rostislav Razumchik & Alexander Zeifman & Ilya Usov, 2024. "On One Approach to Obtaining Estimates of the Rate of Convergence to the Limiting Regime of Markov Chains," Mathematics, MDPI, vol. 12(17), pages 1-12, September.
    3. Baoxian Chang & Qingqing Ye & Jun Lv & Tao Jiang, 2019. "Mathematical modelling of a tollbooth system with two parallel skill-based servers and two vehicle types," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 479-501, October.

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