Study on congestion and optimal control for fluid networks of queues

本研究的目的在于阐明具有大量用户的嵌入式网络的拥塞机理，并为其优化设计和运营奠定理论基础。为此，我们用多维非负正射上的反射过程（扩散和随机行走）描述网络系统，并研究了它们的平稳分布的尾渐近性。特别地，我们得到了二维反射过程的尾渐近性，并将其应用于最优设计和操作。

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.