Polling systems in the critical regime

We study polling systems with Poisson arrival streams and exhaustive servic e discipline in the critical load case rho =1. We show that the system may exhibit null-recurrence or transient behavior and give the corresponding co nditions in terms of the first two moments of the distribution of service a nd switching times. For models with two nodes we establish existence of mom ents of small orders for the return time to the origin of the corresponding embedded Markov chain in the case of null-recurrence. (C) 2001 Elsevier Sc ience B.V. All rights reserved.