A large deviations characterization of the fixed point of a ./G/1 queue

This paper characterizes the large deviations behaviour of the fixed point of a ./G/1 queue. Given a general service time distribution with mean 1 and any α<1, the large deviation rate function, I _α, of the fixed point with mean arrival rate α is derived. I_α is shown to be identical to the rate function of an exponential tilting of the service distribution. An implication of this result is that the fixed point has minimum relative entropy with respect to the service process over all processes satisfying the constraint that the mean arrival rate is α