Routing and Scheduling for Energy and Delay Minimization in the Powerdown Model

Energy conservation is drawing increasing attention in data networking. One school of thought believes that a dominant amount of energy saving comes from turning off network elements. The difficulty is that transitioning between the active and sleeping modes consumes considerable energy and time. This results in an obvious trade-off between saving energy and provisioning performance guarantees such as end-to-end delays. We study the following routing and scheduling problem in a network in which each network element either operates in the full-rate active mode or the zero-rate sleeping mode. For a given network and traffic matrix, routing determines the path along which each traffic stream traverses. For frame-based periodic scheduling, a schedule determines the active period per element within each frame and prioritizes packets within each active period. For a line topology, we present a schedule with close-to-minimum delay for a minimum active period per element. For an arbitrary topology, we partition the network into a collection of lines and utilize the near-optimal schedule along each line. Additional delay is incurred only when a path switches from one line to another. By minimizing the number of switchings via routing, we show a logarithmic approximation for both energy consumption and end-to-end delays. If routing is given as input, we present two schedules one of which has active period proportional to the traffic load per network element, and the other proportional to the maximum load over all elements. The end-to-end delay of the latter is much improved compared to the delay for the former. This demonstrates the trade-off between energy and delay.