In this paper, we extend the work of Chen and Zhang (2000b) and establish a new sufficient condition for the existence of the (conventional) diffusion approximation for multiclass queueing networks under priority service disciplines. This sufficient condition relates to the weak stability of the fluid networks and the stability of the high priority classes of the fluid networks that correspond ...

The theory of neuronal firing in Stein’s model is outlined as well as the corresponding theory for a diffusion approximation which has the same first two infinitesimal moments. The diffusion approximation is derived from the discontinuous model in the limit of large input frequencies and small postsynaptic potential amplitudes. A comparison of the calculated mean interspike intervals is made fo...

In this paper we show how to derive the mean and variance of the transilluminated signal obtained in models of light propagation in tissue, based both on a stochastic Monte Carlo method and on a deterministic diffusion approximation. The theoretical treatment of the Monte Carlo model applies only to integrated intensity measurements, whereas the diffusion approximation gives an estimator for th...

In this paper we consider large state space continuous time Markov chains arising in the field of systems biology. For a class of such models, namely, for density dependent families of Markov chains that model the interaction of large groups of identical objects, Kurtz has proposed two kinds of approximations. One is based on ordinary differential equations and provides a deterministic approxim...

The article presents a diffusion approximation model applied to investigate the behavior of priority queues. We discusses the use of the diffusion approximation in transient analysis of queueing models in the case of a single station and of a queueing network presenting the solutions. We emphasize the numerical aspect of the solution and analyze the errors. In classical queuing theory, the anal...

We discuss and compare three different, but related, approximations to the stochastic dynamics of populations, all of them having as limit the same deterministic dynamics. The diffusion approximation (van Kampen (1981a); Arnold (1997)), linearized diffusion approximation (Kurtz (1971)) and the Poisson approximation (Aparicio & Solari (2001a); Solari & Natiello (2003b)) are briefly revisited and...