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

220 T. Chu and I. Nikolaidis2.0E+101.8E+10Global Energy Consumption1.6E+101.4E+101.2E+101.0E+108.0E+096.0E+094.0E+092.0E+090.0E+00N=10N=20N=30N=500 0.5 1 1.5 2Offered Traffic LoadFig. 3. Simulation results for All Pairs Minimum Energy Pathsoverhearing traffic twice. Although the energy consumption is reduced, each nodeconsumes capacity because of overhearing the traffic (S will overhear the relayingtransmission of R, and R will receive and transmit, acting as relay, the traffic fromS, thus consuming its capacity). As the loss exponent intensifies, this scenariooccurs more often. Even if we attempt to reconstruct the particular constraintviolatedpath, there may not exist a route from the source to the destination.As a result, most of the overhearing traffic drains out the bandwidth capacityand results in the infeasible solution.Our conclusion from the Successive Minimum Energy Paths constructionis that using the shortest path algorithm with the transmission power as thecost matrix results in the minimum energy path construction for the particularsource-destination pair. However, the overall traffic demands grow due to theuse of relays and the capacity allocation becomes infeasible. The All Pairs MinimumEnergy Paths Construction creates all minimum energy paths without theknowledge of the traffic demands. The resulting energy cost is subsequently compromised(increased) in order to “fix” the capacity violations, using the inverseof the triangle relaxation.The simulation of All Pairs Minimum Energy paths uses the same inputparameters, and the result are also expressed with global energy consumptionand the probability of having infeasible solution shown in Fig. 3 and Fig. 4 respectively.A comparison of Fig. 2 and Fig. 4 suggests that All Pairs MinimumEnergy provides a better potential for spatial reuse (the load exceeds 1 and stillresults in feasible configurations). In fact, when the traffic load is equal to 1.3in the 50 nodes scenario, the number of infeasible solutions was 0. The energy