非对称长队列模型II:边际概率和条件概率

Applied mathematics research express : AMRX Pub Date : 2014-03-25 DOI:10.1093/AMRX/ABU002

C. Knessl, Haishen Yao

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摘要

队列，0 < ν < 1。设(N1, N2)为两个并行队列中的顾客数，设p(m, n) = Prob[N1 = m, N2 = n]为稳态下的联合队列长度分布。两个到达率分别为λ1和λ2，指数服务器的工作速率为μ， ρ1 = λ1/μ， ρ2 = λ2/μ。如果N1 > N2 (N1 < N2)，服务器工作在第一(第二)队列上，如果N1 = N2，服务器工作在第一(第二)队列上，速率为μν，速率为μ(1−ν)。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On the Nonsymmetric Longer Queue Model II: Marginal and Conditional Probabilities

queue, with 0 < ν < 1. We let (N1, N2) be the numbers of customers in the two parallel queues, and let p(m, n) = Prob[N1 = m, N2 = n] be the joint queue length distribution in the steady state. The two arrival rates are λ1 and λ2, the exponential server works at rate μ, and ρ1 = λ1/μ, ρ2 = λ2/μ. If N1 > N2 (N1 < N2), the server works on the first (second) queue, but if N1 = N2, the server works at rate μν on the first queue and rate μ(1 − ν)

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Applied mathematics research express : AMRX

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