We obtain the moment structure of a general class of random variables generated by a Poisson process. We then apply these relationships to several applied probability models. Among these are queues, counter models and low density traffic flow.

A previous paper discussed explicit bounds in the exponential approximation for the distribution of the waiting time until a stationary reversible Markov chain first enters a 'rare' subset of states. In this paper Stein's method is used to get explicit (but complicated) bounds on the Poisson...

Let {C(t), t [greater-or-equal, slanted] 0} be a renewal reward process. We obtain the approximation Var C(t) = ct + d + o(1), and explicitly identify c and d.