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

218 T. Chu and I. Nikolaidis1.8E+091.6E+09Global Energy Consumption1.4E+091.2E+091.0E+098.0E+086.0E+084.0E+082.0E+080.0E+00N=10N=20N=30N=500 0.5 1 1.5 2Offered Traffic LoadFig. 1. The global energy consumption for Successive Minimum Energy Paths Algorithmselecting the source-destination paths to admit in arbitrary node number.sum of all traffic load divide by the relative load ( ∑ T i,j /L). The simulation arefor N=10, 20, 30, and 50 nodes and, L=0.1 to 2 in 0.1 interval. The traffic loadis between 0 and 2 because we would like to show the spatial reuse feature of adhoc network (revealed when the load is larger than 1). The simulation resultsare shown in Fig. 1 and Fig. 2 for the first algorithm and in Fig. 3 and Fig. 4for the second algorithm.The results are expressed as a relation between global energy consumptionand the average traffic load. Our intuition would suggest that the more theload, the more the nodes that end up violating their respective constraints, thelonger the paths to avoid such congested nodes, hence, the more the energyrequired. This situation is partly what happens in Fig. 1. However, the graphshows that the energy consumption drops when the load is near 0.8. The figureis misleading in this respect because what is missing is the fact that several ofthe runs that correspond to the point at 0.8 and higher resulted in infeasiblescenarios. Fig. 2 demonstrates the ratio of infeasible solution corresponding tothe result generated from the successive minimum energy paths algorithm withunordered path construction. With 50 nodes, the number of infeasible solution isaround 90 A more definite result from our simulations suggests that the globalenergy decreases as the number of nodes increases with the same simulationarea. This is because and additional node provides an opportunity for paths tobe split along a longer path where the sum of energy required over the entire pathis lower than with fewer intermediate hops. Nevertheless, this cannot counter thefact that additional nodes produce a higher node density and a higher probability