Presidential Young Investigator Award: Stability, Moments and Regenerative Simulation of Queueing Networks

戈德法布 具有一定总类的各种不同的分类系统 作为输入的点过程可以被建模为再生的 流程. Harris递归马尔可夫链（HRMI）理论 和过程将被用作主要工具。 这些结果给出 为发展一个广泛的 排队论 随着再生能源的发展， 模拟，这是认为，这样的理论将至少 严格证明模拟大规模和 复杂的网络（无法分析研究）， 可能，通过利用固有的再生 结构，将导致更好的模拟方法。 许多问题仍然没有答案，立即研究计划 （1）求解排队的矩问题。 的 主要目的是获得充分必要条件 在输入点过程中，使稳定的分布- 状态系统量具有有限矩。 解决这个 问题应该导致这些近似和界限 （非常棘手）稳态数量，并应给予 使用模拟来估计它们的严格条件。 (2)将现有理论的大部分推广到允许 反馈 研究表明，（在合理的 条件），即使到达开放的旅游网络， 允许他们重复到达给定车站的路径，和/或 返回到以前参加的站，然后队列是 如果输入为HRMI，则为再生。 (3)得出一般结果 (with HRMI）更合理。 假设这样的一般结果成立， 网络的每个节点在被隔离时可以被建模， 当这些网络的问题出现在 framework.

Goldfarb A variety of queueing systems having a certain general class of point process as input can be modeled as regenerative processes. The theory of Harris recurrent Markov (HRMI) chains and processes will be used as the main tool. These results give a significant contribution towards the development of a broad theory of queues. Together with the development of regenerative simulation, it is felt that such a theory will at least rigorously justify the standard practice of simulating large and complicated networks (that cannot be studied analytically) and possibly, by taking advantage of the inherent regenerative structure, will lead to better simulation methods. Many questions remain unanswered, immediate research plans are as follows: (1) Solve moment problems for the queues. The main objective is to obtain necessary and sufficient conditions on the input point process so that the distribution of steady- state system quantities have finite moments. Solving this problem should lead to approximations and bounds for these (extremely intractable) steady-state quantities and should give rigorous conditions for using simulation to estimate them. (2) Generalize much of the present theory to systems that allow feedback. The research should show that (under reasonable conditions) even if arrivals to an open queueing network have paths allowing them to repeatedly attend a given station and/or return to previously attended stations, then the queue is regenerative if the input is HRMI. (3) Make the general result (with HRMI) more plausible. Assuming such general results hold, each node of the network when isolated could be modeled so that the moment problems for these networks would fall in the framework.//