Levy, Joshua B.; Taqqu, Murad S. Renewal reward processes with heavy-tailed inter-renewal times and heavy-tailed rewards. (English) Zbl 0954.60071 Bernoulli 6, No. 1, 23-44 (2000). This paper studies a superposition \(W^*\) of renewal-reward processes having inter-renewal time and reward distributions with heavy tails of exponents \(\alpha\) and \(\beta\), respectively, where \(1< \alpha< 2\), \(0<\beta<2\). In the case \(\beta\leq\alpha\), \(W^*\) suitably normalized converges to Lévy stable motion with index \(\beta\); see the authors [Ann. Sci. Math. Qué. 11, 95-110 (1987; Zbl 0646.60091)]. The present work re-iterates this result and establishes a limit for the case \(\beta>\alpha\), which is also a self-similar, symmetric \(\beta\)-stable process with stationary increments; here, however, the increments are dependent. Reviewer: J.Preater (Keele) Cited in 2 ReviewsCited in 26 Documents MSC: 60K05 Renewal theory 60K30 Applications of queueing theory (congestion, allocation, storage, traffic, etc.) Keywords:computer networks; infinite variance; self-similar processes; stable processes; telecommunications Citations:Zbl 0646.60091 PDF BibTeX XML Cite \textit{J. B. Levy} and \textit{M. S. Taqqu}, Bernoulli 6, No. 1, 23--44 (2000; Zbl 0954.60071) Full Text: DOI Euclid OpenURL