Revisiting Stochastic Loss Networks: Structures and Approximations

• 成果类型: Article
• 署名作者: Jung, Kyomin; Lu, Yingdong; Shah, Devavrat; Sharma, Mayank; Squillante, Mark S.
• 署名单位: Seoul National University (SNU); International Business Machines (IBM); IBM USA; Massachusetts Institute of Technology (MIT); International Business Machines (IBM); IBM USA
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2018.0949
• 发表日期: 2019
• 页码: 890-918
• 关键词: blocking probabilities; optimization; models

摘要

We consider fundamental properties of stochastic loss networks, seeking to improve on the so-called Erlang fixed-point approximation. We propose a family of mathematical approximations for estimating the stationary loss probabilities and show that they always converge exponentially fast, provide asymptotically exact results, and yield greater accuracy than the Erlang fixed-point approximation. We further derive structural properties of the inverse of the classical Erlang loss function that characterize the region of capacities that ensures a workload is served within a set of loss probabilities. We then exploit these results to efficiently solve a general class of stochastic optimization problems involving loss networks. Computational experiments investigate various issues of both theoretical and practical interest, and demonstrate the benefits of our approach.