NEW FRONTIERS IN APPLIED PROBABILITY A Festschrift for SØREN ASMUSSEN Edited by P. GLYNN, T. MIKOSCH and T. ROLSKI Part 4. Simulation EXACT SIMULATION OF THE STATIONARY DISTRIBUTION OF THE FIFO M/G/c QUEUE
NEW FRONTIERS IN APPLIED PROBABILITY A Festschrift for SØREN ASMUSSEN Edited by P. GLYNN, T. MIKOSCH and T. ROLSKI Part 4. Simulation EXACT SIMULATION OF THE STATIONARY DISTRIBUTION OF THE FIFO M/G/c QUEUE
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应用概率的新领域 SØREN ASMUSSEN 的 Festschrift 由 P. GLYNN、T. MIKOSCH 和 T. ROLSKI 编辑 第 4 部分：模拟 FIFO M/G/c 队列的平稳分布的精确模拟
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发表时间：
2011
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通讯作者：
K. Sigman
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作者：
K. Sigman
本文提出了一种精确的模拟算法，计算了ρ = λ/μ < 1的M/G/c排队系统中顾客延迟D的平稳分布.假设服务时间分布G（x）= P（S ≤ x），x ≥ 0（平均值0 < E（S）= 1/μ < ∞），以及相应的平衡分布Ge（x）= μ μ ≤ x 0 P（S > y）dy，使得它们的样本可以被模拟.我们进一步假设G具有有限的二阶矩。我们的方法涉及的一般方法支配耦合从过去（DCFTP），我们使用的单服务器M/G/1队列下的处理器共享纪律作为上限。我们的算法产生整个Kiefer-Wolfowitz工作量过程的平稳分布，其第一个坐标是D。本文还对模拟广义杰克逊网络平稳性的方法进行了扩展。
We present an exact simulation algorithm for the stationary distribution of the customer delay D for first-in–first-out (FIFO) M/G/c queues in which ρ = λ/μ < 1. We assume that the service time distribution G(x) = P(S ≤ x), x ≥ 0 (with mean 0 < E(S) = 1/μ < ∞), and its corresponding equilibrium distribution Ge(x) = μ ∫ x 0 P(S > y) dy are such that samples of them can be simulated. We further assume that G has a finite second moment. Our method involves the general method of dominated coupling from the past (DCFTP) and we use the single-server M/G/1 queue operating under the processor sharing discipline as an upper bound. Our algorithm yields the stationary distribution of the entire Kiefer–Wolfowitz workload process, the first coordinate of which is D. Extensions of the method to handle simulating generalized Jackson networks in stationarity are also remarked upon.