On a class of Levy stochastic networks
We consider a Levy stochastic network as a regulated multidimensional Levy 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 Levy process and Ito'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 Levy 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 Levy stochastic network.
stochastic network levy process ito's formula skorokhod reflection loynes' scheme