查看“︁罗斯猜想”︁的源代码

{{Cleanup-jargon|time=2024-08-26T09:15:01+00:00}}
'''罗斯猜想'''（{{lang-en|Ross's conjecture}}）是[[排队理论]]的[[猜想]]，若一個排队队伍中，顾客不是随机到达的最简单模型來排队，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[[謝爾登·M·羅斯]]在1978年提出的猜想，1981年由波兰[[弗罗茨瓦夫大学]]的托马什·罗尔斯基（Tomasz Rolski）教授证明<ref name="rolski">{{citation
 | last = Rolski | first = Tomasz
 | doi = 10.2307/1426787
 | issue = 3
 | journal = Advances in Applied Probability
 | jstor = 1426787
 | mr = 615953
 | pages = 603–618
 | title = Queues with non-stationary input stream: Ross's conjecture
 | volume = 13
 | year = 1981}}.</ref>。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。<ref>{{citation
 | last = Heyman | first = D. P.
 | issue = 1
 | journal = Journal of Applied Probability
 | jstor = 3213936
 | mr = 644439
 | pages = 245–249
 | title = On Ross's conjectures about queues with non-stationary Poisson arrivals
 | volume = 19
 | year = 1982
 | doi = 10.2307/3213936}}.</ref>

==下界==
罗斯猜想是指一個隊伍，其到達機率是依{{le|考克斯过程|doubly stochastic Poisson process}}<ref>{{citation
 | last = Huang | first = J.
 | issue = 1
 | journal = Ph.D Dissertation
 | title = A Study on Queuing Theory and Teletraffic Models (Part 1 of 3)
 | year = 1991
 | doi = 10.13140/RG.2.1.1259.6329 }}.</ref>，或是非靜態的[[卜瓦松過程]]<ref name="rolski"/><ref name="ross">{{citation
 | last = Ross | first = Sheldon M.
 | issue = 3
 | journal = Journal of Applied Probability
 | jstor = 3213122
 | mr = 0483101
 | pages = 602–609
 | title = Average delay in queues with non-stationary Poisson arrivals
 | volume = 15
 | year = 1978
 | doi = 10.2307/3213122}}.</ref>，其平均等待時間會大於等於
::<math>\frac{\lambda \operatorname E (S^2)}{2 \{1-\lambda \operatorname E (S) \}}</math>

其中
:''S''為服務時間
:λ是平均到達率<ref name="rolski" />

==參考資料==
{{reflist}}

{{數學小作品}}

[[Category:概率不等式]]
[[Category:等候理論]]