M. Parulekar et Am. Makowski, TAIL PROBABILITIES FOR M G/INFINITY INPUT PROCESSES(I) - PRELIMINARY ASYMPTOTICS/, Queuing systems, 27(3-4), 1997, pp. 271-296
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.