Large deviations of multiclass M/G/1 queues

Consider a multiclass M/G/1 queue where queued customers are served in their order of arrival at a rate which depends on the customer class. We model this system using a chain with states represented by a tree. Since the service time distribution depends on the customer class, the stationary distribution is not of product form so there is no simple expression for the stationary distribution. Nevertheless, we can find a harmonic function on this chain which provides information about the asymptotics of this stationary distribution. The associated h-transformation produces a change of measure that increases the arrival rate of customers and decreases the departure rate thus making large deviations common. The Canadian Journal of Statistics 37: 327-346; 2009 (C) 2009 Statistical Society of Canada