罗斯猜想

罗斯猜想是排队理论的猜想，若一个排队队伍中，顾客不是随机到达的最简单模型来排队，此猜想提供顾客平均等待时间下界。这是美国南加州大学教授谢尔顿·M·罗斯在1978年提出的猜想，1981年由波兰罗可洛大学（英语：University of Wrocław）的Tomasz Rolski教授证明^[1]。用罗斯猜想可得到其下界，而在有限的缓冲队列下，下界不成立。^[2]

下界

罗斯猜想是指一个队伍，其到达几率是依考克斯过程（英语：doubly stochastic Poisson process）^[3]，或是非静态的卜瓦松过程^[1]^[4]，其平均等待时间会大于等于

{\frac {\lambda \operatorname {E} (S^{2})}{2\{1-\lambda \operatorname {E} (S)\}}}

其中

S为服务时间

λ是平均到达率^[1]

参考资料

^ ^1.0 ^1.1 ^1.2 Rolski, Tomasz, Queues with non-stationary input stream: Ross's conjecture, Advances in Applied Probability, 1981, 13 (3): 603–618, JSTOR 1426787, MR 0615953, doi:10.2307/1426787 .
^ Heyman, D. P., On Ross's conjectures about queues with non-stationary Poisson arrivals, Journal of Applied Probability, 1982, 19 (1): 245–249, JSTOR 3213936, MR 0644439, doi:10.2307/3213936 .
^ Huang, J., A Study on Queuing Theory and Teletraffic Models (Part 1 of 3), Ph.D Dissertation, 1991, (1), doi:10.13140/RG.2.1.1259.6329 .
^ Ross, Sheldon M., Average delay in queues with non-stationary Poisson arrivals, Journal of Applied Probability, 1978, 15 (3): 602–609, JSTOR 3213122, MR 0483101, doi:10.2307/3213122 .

[rolski-1] 1.0 ^1.1 ^1.2 Rolski, Tomasz, Queues with non-stationary input stream: Ross's conjecture, Advances in Applied Probability, 1981, 13 (3): 603–618, JSTOR 1426787, MR 0615953, doi:10.2307/1426787 .

[2] Heyman, D. P., On Ross's conjectures about queues with non-stationary Poisson arrivals, Journal of Applied Probability, 1982, 19 (1): 245–249, JSTOR 3213936, MR 0644439, doi:10.2307/3213936 .

[3] Huang, J., A Study on Queuing Theory and Teletraffic Models (Part 1 of 3), Ph.D Dissertation, 1991, (1), doi:10.13140/RG.2.1.1259.6329 .

[ross-4] Ross, Sheldon M., Average delay in queues with non-stationary Poisson arrivals, Journal of Applied Probability, 1978, 15 (3): 602–609, JSTOR 3213122, MR 0483101, doi:10.2307/3213122 .

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