I have been working on queueing theory and applied probability. My current research interest is a martingale approach for asymptotiic analysis of stochastic networks including queues and multidimensional reflecting processes. I am working on two subjects for them. One is tail asymptotics of their multidimensional stationary distributions. Another is their diffusion approximations, using semi-martingale reflecting Brownian motion on orthants. I am particularly interested in how boundary reflecting behavior affect the tail asymptotics and the diffusion approximations, and represent them in terms of modeling primitives. There is a big jump between 2-dimensional and 3-dimensional reflecting processes, which corresponds with 2-node and 3-node queueing networks. I am currently challenging to fill this gap.
I was originally interested in single node queues with a general class of stationary inputs. I then worked on Palm culculas, characterizations of insensitivity, product form queueing networks, and Markov modulated queueing models. These are more or less exact analysis, but require stronger conditions to get something to be specific. I felt their limitations, and got into theoretical study on asymptotic behavior.
I was graduated at Tokyo Institute of Technology, and joined Science University of Tokyo as a lecturer. I had been a professor at the same department since 1989.
|Updated, April 2, 2017||