Let Z = {Z(t), t ≥ 0} be a semimartingale reflecting Brownian motion that lives in the three-dimensional non-negative orthant. A 2002 paper by El Kharroubi, Ben Tahar and Yaacoubi gave sufficient conditions for positive recurrence of Z. Recently Bramson, Dai and Harrison have shown that...

We consider two locations in tandem of an inventory model, so-called the buffer and the store. The content levels in both locations are controlled simultaneously by transferring inventory from the buffer location to the store location. Under a certain cost function that takes into account the...

In this note we develop a framework for computing upper and lower bounds of an exponential form for a class of stochastic recursive equations with uniformly recurrent Markov modulated inputs. These bounds generalize Kingman's bounds for queues with renewal inputs. Copyright Springer-Verlag...