- Traffic generated by a semi-Markov additive process
- Probability in the Engineering and Informational Sciences
- Volume | Issue number
- 25 | 01
- Pages (from-to)
- Document type
- Faculty of Science (FNWI)
- Korteweg-de Vries Institute for Mathematics (KdVI)
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 integral(infinity)(0) e(-qt) E[e(-alpha A(t)) dt] can be computed. It turns out that these follow, for given nonnegative alpha and q, from a system of linear equations, which has a unique positive solution. Several extensions are considered as well.
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