The overflow distribution for constant holding time

An infinite trunk group split into a finite first-choice group and an overflow group is studied. The equilibrium distribution, at an arbitrary instant, of the number of busy trunks in the overflow is obtained for the case of Poisson input and constant holding time. Some numerical comparisons of variances and distributions for exponential and constant holding time are given. The variance of the overflow was found to be always the greater for constant holding time, and in the case of one trunk in the first-choice group this inequality is proven to be true analytically. In same cases studied, the variances differ markedly — by as much as 50 percent. Implications of these results for the traffic engineering of overflow groups with nonexponential holding time are discussed.