Study on congestion and optimal control for fluid networks of queues

本研究旨在阐明具有大量顾客的排队网络的拥塞机制，并为其优化设计和运行提供理论基础。为此，我们通过在多维非负正交上反映扩散和随机游走过程来描述网络系统，并研究了其平稳分布的尾部渐近性。特别地，我们得到了二维反射过程的尾部渐近性，并将其解应用于优化设计和操作。

This research aims to elucidate congestion mechanism of queueing networks with large numbers of customers and to establish theoretical basics for their optimal design and operations. For this, we described the network systems by reflecting processes(of diffusion and random walk) on multidimensional nonnegative orthants, and studied the tail asymptotics of their stationary distributions. In particular, we have obtained those tail asymptotics for the two dimensional reflecting processes, and apply the solutions to the optimal design and operations.