Keigo Yamada

We consider open queueing networks in which arrival and service rates are dependent on the state (i.e., queue length) of the network. They are modeled as multidimensional birth and death processes. If a heavy traffic condition is sastisfied on the behavior of arrival and service rates when the queue length becomes very large, it is shown that a properly normalized sequence of queue length converges in law to a reflecting diffusion process.

Optimization of sensor selection has been studied to monitor complex and large-scale systems with data-driven linear reduced-order modeling. An algorithm for greedy sensor selection is presented under the assumption of correlated noise in the sensor signals. A noise model is given using truncated modes in reduced-order modeling, and sensor positions that are optimal for generalized least squares estimation are selected. The determinant of the covariance matrix of the estimation error is minimize

Optimization approaches that determine sensitive sensor nodes in a large-scale, linear time-invariant, and discrete-time dynamical system are examined under the assumption of independent and identically distributed measurement noise. This study offers two novel selection algorithms, namely an approximate convex relaxation method with the Newton method and a gradient greedy method, and confirms the performance of the selection methods, including a convex relaxation method with semidefinite progra

For a sequence of storage processes with general release rate functions which contain, as a special case, queueing processes, we show that under appropriate conditions suitably normalized storage processes converge to a Bessel process with negative drift in the sense of law.

For a sequence of stochastic differential equations of the the type: a stabilty theorem is presented under appropritate convergence mode of [d] and m application to stochastic control problems is also briefly discussed.

We consider a storage process $X(t)$ having a compound Poisson process as input and general release rules, and a nonnegative additive functional $Z(t) = \int^t_0 f(X(s)) ds$. Under the situation that the input rate is equal to the maximal output rate, it is shown for a suitable class of functions of $f$ that an appropriate normalization of the process $Z(t)$ converges weakly to a process which is represented as a constant times the local time of a Bessel process at zero.