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 > ϰ] ∼ αϰ^βe ^-ηϰ for some α,β,η, we show how to calculate the exponents β and η, and we establish the extent and form of their dependence on the distributions of the service-time and 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 functions of the waiting time. This revised version was published online in June 2006 with corrections to the Cover Date.