Two-sided reflected Markov-modulated Brownian motion with applications to fluid queues and dividend payouts

In this paper we consider the first passage process of a spectrally negative Markov additive process (MAP). The law of this process is uniquely characterized by a certain matrix function, which plays a crucial role in fluctuation theory. We show how to identify this matrix using the theory of...

In this paper we consider the two-sided reflection of a Markov modulated Brownian motion by analyzing the spectral properties of the matrix polynomial associated with the generator of the free process. We show how to compute for the general case the Laplace transform of the stationary...

We analyze the behavior of closed product-form queueing networks when the number of customers grows to infinity and remains proportionate on each route (or class). First, we focus on the stationary behavior and prove the conjecture that the stationary distribution at non-bottleneck queues...

We analyze from an economical point of view a tandem network with two nodes. We look at different situations, that is, when customers upon their arrival are no informed, partially informed or totally informed about the state of the system. For each case, we look for the strategy that optimizes...