Wireless network for connecting the devices and sensors to communicate and sense is quite attractive nowadays for a wide range of applications. The scaling of the wireless network to millions of nodes currently is impractical if the process is supplied by battery energy. The batteries need to be periodically replaced or recharged due to the limited battery size. One solution is harvesting ambient energy to power the network. In this thesis, we consider a battery-limited energy harvesting communication system with online power control. Assuming independent and identically distributed (i.i.d.) energy arrivals and the harvest-store-use architecture, it is shown that the greedy policy achieves the maximum throughput if and only if the battery capacity is below a certain positive threshold that admits a precise characterization. Simple lower and upper bounds on this threshold are established. The asymptotic relationship between the threshold and the mean of the energy arrival process is analyzed for several examples. Furthermore, value iteration method is applied for solving the Bellman equation to obtain the optimal power allocation policy. The optimal policy is analyzed for several examples. / Thesis / Master of Applied Science (MASc)