Lower bounds for two call control problems

Abstract

We present lower bounds for two call control scheduling problems. For the problem of scheduling infinite-duration calls deterministically without pre-emption on a linear array of processors, in which the goal is to use as many edges as possible, we show a 2Φ + 1 ≈ 4.2 lower bound on the competitive ratio (where Φ is the golden ratio). For the problem of scheduling infinite-duration calls on an edge of capacity 1 with randomization but no pre-emption, such that calls have bandwidth between $\text{1}\text{B}$ and 1, we show a $\text{(log B)}\text{2}$ lower bound.