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首页> 外文期刊>ACM Transactions on Modeling and Computer Simulation >Gradient Estimation for a Class of Systems with Bulk Services: A Problem in Public Transportation
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Gradient Estimation for a Class of Systems with Bulk Services: A Problem in Public Transportation

机译：一类具有批量服务的系统的梯度估计：公共交通中的一个问题

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摘要

This article presents a comparison of different gradient estimators for the sensitivity of waiting times in a bulk server system. Inspired by a transportation network, our model is that of a bursty arrival process that waits at a "platform" until the server is available (representing a train or bus ready for departure). At the departure epochs, all waiting passengers leave at once. The departure process is assumed to be a renewal process and, based on a limiting result, the interdeparture times are approximated by truncated normal random variables. The interarrival times are assumed to be identically and independently distributed (i.i.d.), with a general distribution of bounded density. We are interested in calculating the sensitivities of the total cumulative waiting time of all passengers with respect to the interdeparture times. For this general model where neither the interarrival times nor the interdeparture times are exponential, there is no analytical formula available. However, the estimation of such sensitivities is an important problem for flow control in such networks. We establish a Smoothed Perturbation Analysis (SPA), a Measure-Valued Differentiation (MVD), and a Score Function (SF) estimator, including numerical experiments.
机译：本文针对大容量服务器系统中等待时间的敏感性，对不同的梯度估计量进行了比较。受运输网络的启发，我们的模型是一个突发性到达过程，该过程在“平台”等待直到服务器可用（代表准备出发的火车或公共汽车）。在出发时刻，所有等待的乘客立即离开。出发过程被假定为更新过程，并且基于限制结果，出发时间由截断的正常随机变量近似。假设到达间隔时间是相同且独立分布的（i.i.d.），且具有有限密度的一般分布。我们有兴趣计算所有乘客的总累积等待时间对出发时间的敏感度。对于到达时间或离开时间都不是指数的一般模型，没有可用的解析公式。然而，对于这种网络中的流量控制，这种灵敏度的估计是重要的问题。我们建立了平滑扰动分析（SPA），量值微分（MVD）和分数函数（SF）估计量，包括数值实验。

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