EXPONENTS FOR THE TAILS OF DISTRIBUTIONS IN SOME POLLING MODELS

The tail asymptotics of the distribution of the waiting-time W in some polling models is investigated. When this is of the form P[W > x] sim ilar to alpha x(beta)e(-eta x) for some alpha, beta, eta, we show how to calculate the exponents beta and eta, and we establish the extent a nd form of their dependence on the distributions of the service-time a nd switchover-time. The exponents are expressed in terms of the fixed points and Lyapunov exponents of a dynamical system which we associate with the recursion which is used to calculate the moment generating f unctions of the waiting time.