A fast cross-entropy method for estimating buffer overflows in queueing networks

• 成果类型: Article
• 署名作者: de Boer, PT; Kroese, DP; Rubinstein, RY
• 署名单位: University of Twente; University of Queensland; Technion Israel Institute of Technology
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.1030.0139
• 发表日期: 2004
• 页码: 883-895
• 关键词: importance sampling; Rare events; cross-entropy; queueing networks; simulation

摘要

In this paper, we propose a fast adaptive importance sampling method for the efficient simulation of buffer overflow probabilities in queueing networks. The method comprises three stages. First, we estimate the minimum cross-entropy tilting parameter for a small buffer level; next, we use this as a starting value for the estimation of the optimal tilting parameter for the actual (large) buffer level. Finally, the tilting parameter just found is used to estimate the overflow probability of interest. We study various properties of the method in more detail for the M/M/1 queue and conjecture that similar properties also hold for quite general queueing networks. Numerical results support this conjecture and demonstrate the high efficiency of the proposed algorithm.