In this note, the sequence of the interarrivals of a stationary Markovian Arrival process is shown to be ρ-mixing with a geometric rate of convergence when the driving process is ρ-mixing. This provides an answer to an issue raised in the recent paper [4] on the geometric convergence of the autocorrelation function of the stationary Markovian Arrival process. keywords: Markov renewal process AM...

— We define a notion of Markov process indexed by curves drawn on a compact surface and taking its values in a compact Lie group. We call such a process a two-dimensional Markovian holonomy field. The prototype of this class of processes, and the only one to have been constructed before the present work, is the canonical process under the Yang-Mills measure, first defined by Ambar Sengupta [32]...

The advantages of using stochastic process algebra to specify performance models are well-documented. There remains, however, a reluctance in some quarters to use process algebras; this is particularly the case amongst queueing theorists. This paper demonstrates the use of a Markovian process algebra to represent a wide range of queueing models. Moreover, it shows that the most common interacti...

It is shown that all statistical properties of the generalized Langevin equation with Gaussian fluctuations are determined by a single, two-point correlation function. The resulting description corresponds with a stationary, Gaussian, non-Markovian process. Fokker-Planck-like equations are discussed, and it is explained how they can lead one to the erroneous conclusion that the process is nonst...