Ergodicity properties of rerouting strategies in queueing networks

In this paper we study ergodicity properties for simple Markovian models describing different rerouting policies for queueing systems with two Poisson arrival streams and two exponential servers. On their arrival, customers are either routed to their normal server or are rerouted to the alternate server. We model the extra work for rerouted customers by assuming that each rerouted customer generates several tasks for the alternate server. This model can become non-ergodic even when the total arrival rate is smaller than the total service rate in the system. We compare different strategies for rerouting customers on the basis of necessary and sufficient conditions for ergodicity. For this purpose we make use of Lyapunov functions.