Note on Superposition of Renewal Processes

Suyono Suyono ( Jurusan Matematika, FMIPA, Universitas Negeri Jakarta, Jakarta)
J.A.M. van der Weide ( Department DIAM, Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology)

Jurnal Matematika & Sains
Vol 15, No 2 (2010)

In this paper we discuss distributional properties of superposition of renewal processes. Firstly, as a special case, we discuss probability distributions of a superposition of Poisson processes and its generalization, namely the sum of independent compound Poisson processes. In this case we have explicit expressions for their probability distributions. Secondly, we discuss the statistical moments of general superposition of renewal processes. We also discuss the statistical moments of the sum of independent renewal reward processes, a generalization of a supervision of renewal processes. The results are presented in the form of Laplace transforms. Finally we present the distributions of recurrence times of a superposition of renewal processes.