A Uniformization Approach for the Dynamic Control of Queueing Systems with Abandonments

• 成果类型: Article
• 署名作者: Legros, Benjamin; Jouini, Oualid; Koole, Ger
• 署名单位: Universite Paris Saclay; Vrije Universiteit Amsterdam
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2017.1652
• 发表日期: 2018
• 页码: 200-209
• 关键词: CUSTOMERS

摘要

We consider queueing systems with general abandonment. Abandonment times are approximated by a particular Cox distribution with all phase exponential rates being the same. We prove that this distribution arbitrarily closely approximates any nonnegative distribution. By explicitly modeling the waiting time of the first customer in line, we obtain a natural bounded jump Markov process allowing for uniformization. This approach is useful to solve, via dynamic programming, various optimization problems where the objectives and/or constraints involve the distributions of the performance measures, not only their expected values. It is also useful for the performance analysis of queueing systems with general abandonment times.