Optimization of Jump Stochastic Systems: Undiscounted Criteria and Applications

这笔赠款为研究和开发一种新的方法来分析和优化跳跃随机系统提供资金。 这种方法的基础上相结合的uniforization technologies与最近发现的控制策略之间的关系，改变连续时间系统的跳跃和离散时间系统的随机策略之间的行动。 该方法的应用将为连续时间跳变随机系统的多目标优化提供新的结果。 这些结果将包括最优策略的结构和计算算法的描述。 除了多个目标的问题的结果，预计这种新的方法将大大简化一个标准问题的分析，并将开发新的计算算法them.Jump随机过程模型广泛的生产，服务和电信系统类。 如果成功，该项目将提高建模和分析广泛类别的此类系统的能力，并为它们设计有效的控制算法。 它将大大简化和推广现有的方法，减少连续时间问题更简单的离散时间问题。除了基本方法的发展，这个项目将这些方法应用到几个特定的problemsincluding随机需求的制造系统的切换策略的优化，更换和预防性维护程序的设计，和呼叫接纳有限带宽的电信系统。

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.