A Uniformization Approach for the Dynamic Control of Queueing Systems with Abandonments
提出一种均匀化方法，用特定Cox分布近似一般放弃时间，将排队系统转化为有界跳跃马尔可夫过程，从而通过动态规划求解涉及性能指标分布的优化问题。
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.