Konstantopoulos, Takis; Last, Günter; Lin, Si-Jian On a class of Lévy stochastic networks. (English) Zbl 1061.90012 Queueing Syst. 46, No. 3-4, 409-437 (2004). Summary: We consider a Lévy stochastic network as a regulated multidimensional Lévy process. The reflection direction is constant on each boundary of the positive orthant and the corresponding reflection matrix corresponds to a single-class network. We use the representation of the Lévy process and Itô’s formula to arrive at some equations for the steady-state process; the latter is shown to exist, under natural stability conditions. We specialize first to the class of Lévy processes with non-negative jumps and then add the assumption of self-similarity. We show that the stationary distribution of the network corresponding the the latter process does not has product form (except in trivial cases). Finally, we derive asymptotic bounds for two-dimensional Lévy stochastic network. Cited in 12 Documents MSC: 90B15 Stochastic network models in operations research Keywords:Lévy process; Skorokhod reflection; stochastic network; Itô’s formula; Loynes’ scheme PDFBibTeX XMLCite \textit{T. Konstantopoulos} et al., Queueing Syst. 46, No. 3--4, 409--437 (2004; Zbl 1061.90012) Full Text: DOI