Balanced job bound analysis of queueing networks

Abstract

The rule we used to terminate the Core algorithm was max ] L~k --L~-~ 1 ]/Nk < cutoff (over all ra, k ) where I is the iteration number. Since Fmk = L,~k/Nk, this rule requires that all the Fmk fractions change very little. The cutoff should be a function that increases with increasing population, since at very large populations, removing one job has very little effect, and the algorithm would otherwise terminate prematurely. The cutoff we used was cutoff = 1/(4000 + 16IN I) which is smaller than 0.00025 even for very small populations and decreases with increasing population, as desired.