On positive harris recurrence of stochastic fluid networks

Abstract

The stochastic fluid networks we consider here are open multiclass fluid networks with Markov-modulated inflow rate. They are typically used as models for manufacturing and telecommunication systems. The main aim of this paper is to investigate the question of positive Harris recurrence of the joint process of buffer content and inflow rate. It will turn out that a Markovian server allocation exists under which the process is positive Harris recurrent if the usual traffic conditions are satisfied on average. Moreover, for special networks like single-server networks, re-entrant lines and Jackson networks it is possible to show that certain service disciplines induce positive Harris recurrent state processes. As a by-product we show that these stochastic fluid networks converge under appropriately defined scaling to solutions of deterministic fluid models.