Discipline: 
Mathematics
Status: 
Available
Level: 
PhD Project
Level: 
Masters Project

Standard queueing network models such as the celebrated Jackson and BCMP networks exhibit mathematically elegant product form solutions of the stationary distribution. This means that the problem of evaluating the probabilistic behavior of the network at steady state is typically tractable. As opposed to that, queueing networks with finite buffers, overflow mechanisms and multi-class structure are typically not solved explicitly. Nevertheless, many approximation schemes can be employed. In this project we shall handle networks with finite buffers and overflows. Our goal is to devise rigorous approximation schemes for such networks which are based on the first order fluid dynamics of the network and second order diffusion approximations.