On a Reduced Load Equivalence for Fluid Queues Under Subexponentiality

We propose a general framework for obtaining asymptotic distributional bounds on the stationary backlog WA1+A2;c in a bu er fed by a combined uid process A1 + A2 and drained at a constant rate c. The uid process A1 is an (independent) on-o source with average and peak rates 1 and r1, respectively, and with distribution G for the activity periods. The uid process A2 of average rate 2 is arbitrary but independent of A1. These bounds are used to identify subexponential distributions G and fairly general uid processes A2 such that the asymptotic equivalence P WA1+A2;c > x P WA1;c 2 > x (x ! 1) holds under the stability condition 1+ 2 < c and under the non-triviality condition c 2 < r1. The stationary backlog WA1;c 2 in these asymptotics results from feeding source A1 into a bu er drained at reduced rate c 2. This reduced load asymptotic equivalence extends to a larger class of distributions G a result obtained by Jelenkovic and Lazar [18] in the case when G belongs to the class of regular intermediate varying distributions. This work was performed in part while R. Agrawal was visiting INRIA during the Spring of 1997 and while A. M. Makowski was visiting INRIA during the academic year 1997/98. yThe work of this author was funded in part by the National Science Foundation under grant NCR-93-05018. zThe work of this author was supported partially through NSF Grant NSFD CDR-88-03012, NASA Grant NAGW77S, the Army Research Laboratory under Cooperative Agreement No. DAAL01-96-2-0002 and through the Maryland Procurement O ce under Grant No. MDA90497C3015. 0