Fluid Limit of Generalized Jackson Queueing Networks with Stationary and Ergodic Arrivals and Service Times
Résumé
We use a sample-path technique to derive asymptotics of generalized Jackson queueing networks in the fluid scale, namely when space and time are scaled by the same factor n. The analysis only presupposes the existence of long-run averages and is based on some monotonicity and concavity arguments for the fluid processes. The results provide a functional strong law of large numbers for stochastic Jackson queueing networks since they apply to their sample paths with probability one. The fluid processes are shown to be piece-wise linear and an explicit formulation of the different drifts is computed. A few applications of this fluid limit are given. In particular, a new computation of the constant (0) that appears in in the stability condition for such networks is given. In the context of rare event as described in , the fluid limit of the network is also derived explicitly.