TAIL PROBABILITIES FOR M G/INFINITY INPUT PROCESSES(I) - PRELIMINARY ASYMPTOTICS/

The infinite server model of Cox with arbitrary service time distribut ion appears to provide a large class of traffic models - Pareto and lo g-normal distributions have already been reported in the literature fo r several applications. Here we begin the analysis of the large buffer asymptotics for a multiplexer driven by this class of inputs. To do s o we rely on recent results by Duffield and O'Connell on overflow prob abilities for the general single server queue. In this paper we focus on the key step in this approach: The appropriate large deviations sca ling is shown to be related to the forward recurrence time of the serv ice time distribution, and a closed form expression is derived for the corresponding generalized limiting log-moment generating function ass ociated with the input process. Three different regimes are identified . In a companion paper we apply these results to obtain the large buff er asymptotics under a variety of service time distributions.