Asymptotics of first passage times for random walk in an orthant

Abstract

We wish to describe how a chosen node in a network of queues overloads. The overloadednode may also drive other nodes into overload but the remaining "super" stable nodes areonly driven into a new steady state with stochastically larger queues. We model this networkof queues as a Markov additive chain with a boundary. The customers at the "super" stablenodes are described by a Markov chain while the other nodes are described by an additivechain.We use the existence of a harmonic function...