Energy-efficient windows scheduling

A server repeatedly transmits data items (pages) possibly with different speeds on a set of channels. The objective is to minimize energy consumption of the schedule. We adopt the common model that sending at speed s for t time units consumes t center dot s(alpha) energy for a constant alpha >= 2. An individual window length is associated with each page. This length is a strict upper bound on the time between two consecutive broadcasts for that page. We present an easy to implement algorithm for the single channel case that obtains an approximation ratio of 3 center dot 4(alpha). For the multi-channel case with identical channels an extension of this algorithm computes an 8(alpha)-approximation. Both algorithms run in low-order polynomial time. As our main tool for the analysis, we show that it suffices to consider periodic schedules as their energy density (total energy consumption per time unit) differs from the one of general schedules at most by (1 + epsilon) for an arbitrary constant epsilon > 0.