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

On the Interaction of Bandwidth Constraints and Energy Efficiency 219Fraction of Infeasible Solutions10.90.80.70.60.50.40.30.20.10N=10N=20N=30N=500 0.5 1 1.5 2Relative loadFig. 2. Percentage of infeasible solution corresponding to Fig. 1.that the transmissions will congest other nodes, and hence it restricts paths frombeing available. The unavailability of a path therefore has a direct impact on theability of conserve energy by using it as a relay.Applying the Successive Minimum Energy Paths construction, we find thatit is highly unlikely to obtain the optimal solution (or even a solution when thetraffic demand is high) for this multiple source-destination demands and energyconsumption optimization problem. Our experiments were also run with differentorder for path construction, such as increasing traffic demands or decreasingtraffic demands for the source-destination pairs, but the results are similar tothe ones reported here. The Successive Minimum Energy Paths algorithm constructsone path at a time using the shortest path algorithm using the energycost matrix. Each path construction achieves the minimum energy consumptionrequirement of a particular path. However, in the Successive Minimum EnergyPaths algorithm, the bandwidth reservation is performed by ignoring the alreadyallocated source-destination pairs.Furthermore, we observe that in order to minimize the energy consumption,the path construction process will likely end up with a longer path. Assume Sis the source node and D is the destination node. An additional node R caneither act a relay transmission such that the path is from S to R and fromR to D or sitting there overhearing it. The distance between a node pair isdenoted d i,j , and the energy usage is (d i,j ) α , where α is corresponding to theloss exponent (2 ≤ α ≤ 4). Assume d S,D is equal to 5 units of distance; d S,R andd S,D are equal to 3 units. With the energy as the cost matrix, since (d S,D ) α ≥(d S,R ) α +(d R,D ) α , R will not act as an relay, and therefore D will increase the