Optimization of Jump Stochastic Systems: Undiscounted Criteria and Applications

这笔资金用于研究和开发一种分析和优化跳跃随机系统的新方法。这种方法是基于将均衡化技术与最近发现的连续时间系统跳跃之间改变动作的控制策略与离散时间系统的随机策略之间的关系结合起来的。该方法的应用将为多目标连续时间跳跃随机系统的优化提供新的结果。这些结果将包括对最优策略的结构及其计算算法的描述。除了多目标问题的结果外，预计这种新方法将显著简化单准则问题的分析，并将为它们开发新的计算算法。跳跃随机过程建模了生产、服务和电信系统的广泛类别。如果成功，这个项目将提高对这类系统建模和分析的能力，并为它们设计有效的控制算法。通过将连续时间问题简化为更简单的离散时间问题，它将极大地简化和推广现有方法。除了基本方法的发展，这个项目还将把这些方法应用于几个特殊的问题，包括随机需求制造系统的交换策略的优化，更换和预防性维护程序的设计，以及有限带宽电信系统的呼叫准入。

This grant provides funding for the research and development of a new approach to the analysis and optimization of jump stochastic systems. This approach is based on combining the uniformization techniqueswith the recently discovered relationship between control strategies that change actions between jumps in continuous time systems and randomized strategies in discrete time systems. The utilization of this approach will lead to the development of new results for optimization of continuous time jump stochastic systems with multiple objectives. These results will include the description of the structure of optimal strategies and the algorithms for their computation. In addition to the results for problems with multiple objectives, it is expected that this new approach will significantly simplify the analysis of one-criterion problems and will develop new computational algorithms for them.Jump stochastic processes model broad classes of production, service, and telecommunication systems. If successful, this project will improve the abilities to model and analyze broad classes of such system and to design efficient control algorithms for them. It will significantly simplify and generalize the existing methods by reducing continuous time problems to much simpler discrete time problems. In addition to the development of fundamental methods, this project will apply these methods to several particular problemsincluding optimization of switching policies for manufacturing systems with stochastic demand, design of replacement and preventive maintenance procedures, and call admission to telecommunication systems with limited bandwidth.