Long-Time Behavior of Non-Ergodic Infinite Jackosn Network

For the infinite Jackson network, assume that the net input rates are greater than the service rates for some nodes. Via solving the new throughput equation, the stochastic comparable processes are obtained by coupling method, and furthermore the limits for the queueing length in all nodes are also obtained. Despite the whole network is non-ergodic, it is possible to get the maximal ergodic subnetwork.