Abstract-Fast data collection is one of the most important research issues for Wireless Sensor Networks (WSNs). In this paper, a TMDA based energy consumption balancing algorithm is proposed for the general k-hop WSNs, where one data packet is collected in one cycle. The optimal k that achieves the longest network life is obtained through our theoretical analysis. Required time slots, maximum energy consumption and residual network energy are all thoroughly analyzed in this paper. Theoretical analysis and simulation results demonstrate the effectiveness of the proposed algorithm in terms of energy efficiency and time slot scheduling.Index Terms-Wireless Sensor Networks, TDMA, load balancing, lifetime, k-hop network.I. INTRODUCTION ireless sensor networks (WSNs) [1][2][3][4] consists of a set of small, battery-operated, energy constrained sensor nodes, whose main goal is twofold: to monitor their surroundings for local data and to forward the gathered data toward a sink node where further processing and analysis of raw data through multi-hop communication. This transmission of data from nodes to sink often correspond to a many-to-one fashion or a "funnel" type of communication called convergecast [3][4][5][6][7][8][9].Convergecast [3-9] is a typical many-to-one communication pattern in sensor network applications, which can be considered as the reverse operation of broadcast or multicast. Researchers are working hard to minimize the time to execute convergecast and at the same time maximizing the network lifetime. There is a great deal of work in this field.A: In the case of reducing convergecast time. TDMA is a MAC communication method with non-conflict-detection capability, small number of conflicts, low energy usage, nice real-time performance and high reliability. Relevant research can be referred to in [3][4][5][6][7][8][9]. Ref.[6] and [9] mainly discuss the TDMA scheduling scheme that requires the minimum time slot in convergecast in the linear sensor network, but they do not mention how to balance the energy consumption as well as how to improve the network life.B: As the energy of wireless sensor nodes is limited, how to minimize the level of energy consumption and balance energy consumption to improve the network lifetime is another important topic in WSN research. Ref.[10-11] mainly discussed the strategy that how to improve the network lifetime from the energy being balanced, while the premise of balancing energy consumption is to obtain accuracy the amount of data in network and the energy consumption. The traffic characteristics of data collection in network are mainly discussed in [12][13][14]. The energy consumption of the network can be used to guide network performance optimization. Although the energy balance strategy can effectively improve the network performance, the ultimate goal is to maximize the network lifetime with the least number of nodes. In other words, it is to improve the network utility: the network lifetime of a unit node. So, the optimization strategy of the basic network effi...