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Routing for Energy Minimization in the Speed Scaling Model
| Citations: | 11 - 0 self |
BibTeX
@MISC{Andrews_routingfor,
author = {Matthew Andrews and Antonio Fernández Anta and U. Rey and Juan Carlos and Lisa Zhang and Wenbo Zhao},
title = {Routing for Energy Minimization in the Speed Scaling Model},
year = {}
}
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Abstract
Abstract—We study network optimization that considers energy minimization as an objective. Studies have shown that mechanisms such as speed scaling can significantly reduce the power consumption of telecommunication networks by matching the consumption of each network element to the amount of processing required for its carried traffic. Most existing research on speed scaling focuses on a single network element in isolation. We aim for a network-wide optimization. Specifically, we study a routing problem with the objective of provisioning guaranteed speed/bandwidth for a given demand matrix while minimizing energy consumption. Optimizing the routes critically relies on the characteristic of the energy curve f(s), which is how energy is consumed as a function of the processing speed s. If f is superadditive, we show that there is no bounded approximation in general for integral routing, i.e., each traffic demand follows a single path. This contrasts with the well-known logarithmic approximation for subadditive functions. However, for common energy curves such as polynomials f(s) = µs α, we are able to show a constant approximation via a simple scheme of randomized rounding. The scenario is quite different when ajnon-zero startup cost σ 0 if s = 0 appears in the energy curve, e.g. f(s) = σ + µs α if s> 0. For this case a constant approximation is no longer feasible. In fact, for any α> 1, we show an Ω(log 1 4 N) hardness result under a common complexity assumption. (Here N is the size of the network.) On the positive side we present O((σ/µ) 1/α) and O(K) approximations, where K is the number of demands. I.
Keyphrases
energy minimization speed scaling model speed scaling energy curve constant approximation energy consumption hardness result common complexity assumption bounded approximation processing speed single path single network element integral routing well-known logarithmic approximation telecommunication network subadditive function traffic demand randomized rounding common energy curve network element power consumption ajnon-zero startup cost network-wide optimization carried traffic demand matrix routing problem speed bandwidth simple scheme network optimization positive side
