TRAFFIC GENERATED BY A SEMI-MARKOV ADDITIVE PROCESS

摘要

We consider a semi-Markov additive process A(·)-that is, a Markov additive process for which the sojourn times in the various states have general (rather than exponential) distributions. Letting the Levy processes X_i(·), which describe the evolution of A(·) while the background process is in state i, be increasing, it is shown how double transforms of the type ∫~∞_0 e~(-qt) E[e~(-aA((t)) dt] can be computed. It turns out that these follow, for given nonnegative α and q, from a system of linear equations, which has a unique positive solution. Several extensions are considered as well.