Page 2 Lecture Notes in Computer Science 2865 Edited by G. Goos ...

On the Interaction of Bandwidth Constraints and Energy Efficiency 221Fraction of Infeasible Solutions10.90.80.70.60.50.40.30.20.10N=10N=20N=30N=500 0.5 1 1.5 2Offered Traffic LoadFig. 4. Percentage of infeasible solutions corresponding to the Fig. 3.consumption curve rises when the load is around than 0.6. A similar observationfrom the previous result is that the global energy consumption increases as thenumber of participating node decreases. Still, as the load increases, the global energyconsumption curve rise abruptly capturing an, almost exponential, increaseof energy consumption in order to produce a feasible solution. The first explanationis that the energy consumption rises quickly because we do not find twoparticular small amount energy transmissions to replace via the inverse-trianglerelaxation. Another reason is, of course, that the load cannot be accommodated.4 ConclusionsIn this paper we considered the problem of energy minimization in a bandwidthconstrained ad hoc wireless environment. The apparent tendency of energy minimizationto reduce transmission radii would appear to be in agreement withspatial reuse (which benefits from transmission radius reduction as well). Unfortunately,in a bandwidth constrained setting, it becomes immediately obviousthat minimization of energy results in longer paths, adding to the congestion anddiminishing the benefits of spatial reuse. The observation applies to large networkconfigurations, leaving potential for smaller network configurations (loadwiseand node-wise) to still benefit by the choice of the right path constructionheuristic. Two such heuristics are studied in this paper, and it appears that ascheme that attempts to reduce the load of relay nodes could result in improvedperformance for a modest sacrifice in energy consumption. The next step is to