Figure 1

Optimal flows that minimize energy dissipation in (one dimensional) linear topology. The numbers on each arc show the fraction of the total amount of data generated at each sensor node. For example, $f_{50}^{53}=0.23$ shows that $f_{50}^{53}=0.23\times \lambda \times s_5\times M_{\mathit{\text{rnd}}}$ packets, which is equal to 1,010 packets; furthermore, it also shows that $b_5^1=1,010$ packets. Nodes are placed on a line with 30 m separation and R_max = 150 m. Base station is node-0. The MIP model is solved with (a) N _P →∞, (b) N _P = 2, and (c) N _P = 1. Energy dissipations are indicated near the nodes.