Research Initiation Award: Resource Allocation in Queueing and Inventory Systems

众所周知，由于机器故障、维护和许多其他因素，制造系统中的随机性是一种常见现象。最近的研究表明，跳跃扩散是这些解析难解系统的良好近似。本研究的目的是对生产系统和计算机通信网络中出现的多类跳跃扩散网络中的随机资源分配问题进行建模和分析。随机强度模型允许用强度调度和漂移控制来描述资源分配问题。在此框架下，离散排队网络模型和流体网络模型中的调度问题就变成了特例。本研究将利用状态空间分解定义分配规则，并在所定义的控制集上找到充分的最优性条件，从而表征、计算和搜索最优分配规则的启发式。通过仿真得到直观的调度控制规则；并利用离散时间近似对推测结果进行验证。

It is well understood that randomness in manufacturing systems is a common occurrence due to machine breakdowns, maintenance and many other factors. Recent studies show that jump diffusions are good approximations for these analytically intractable systems. The objective of this research is to model and analyze the stochastic resource allocation problem in multiple class jump diffusion networks which arise in production systems and computer communication networks. A stochastic intensity model allows resource allocation problems to be described in terms of intensity scheduling and drift control. With such a framework, schedulings in discrete queueing network model and fluid network model turn out to be special cases. This research will characterize, compute, and search for heuristics of the optimal allocation rule by defining allocation rules using state space decomposition and finding sufficient optomality condition on the defined control sets. Intuitive scheduling control rules will be obtained by simulation; and the conjectured results will be verified using discrete time approximation.