On a Reduced Load Equivalence under Heavy Tail Assumptions

Abstract

Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. AbstractWe propose a general framework for obtaining asymptotic distributional bounds on the stationary backlog W A1+A2;c in a bu er fed by a combined uid process A 1 +A 2 and drained at a constant r a t e c. The uid process A 1 is an independent on-o source with average and peak rates 1 and r 1 , respectively, and with distribution G for the activity periods. The uid process A 2 of average rate 2 is arbitrary but independent of A 1 . These bounds are used to identify subexponential distributions G and fairly general uid processes A 2 such that the asymptotic equivalence P

A note on queues with M/G/∞ input

“…Let t ? b be the optimizing argument for t in (1). In his proof of this theorem, particularly in the lower bound, Du eld [5] needed that t ?…”

“…Our proof consists of a lower bound and an upper bound. Starting point of both is the variational problem (1). The lower bound is derived by 'guessing' the  and performing the optimization over t-in the upper bound the value of t is 'guessed', and given this t the supremum over  is computed.…”

“…where the optimizing K can be interpreted as the most likely number of sessions that stay in the system during the complete trajectory to over ow. The above heuristic can be considered as a variant of the reduced load equivalence proven in [1].…”

When Are On–off Sources Sis?: Conditions and Applications

“…On the other hand, the rvsÎ andB being DFR, it follows from Lemma 2.2 that hÎ(2) ≤ h I (1) and hB(2) ≤ h B (1). Combining this observation with (15) we obtain (v).…”