In a multi-hop wireless sensor network (WSN), the traffic load is not evenly distributed over the nodes. For example, the sensors which are one hop away from the sink relay the whole network traffic. This imbalanced traffic distribution can degrade the network lifetime and functionality. Here, an analysis is proposed to characterize the traffic load distribution over a randomly deployed linear WSN. The effect of the number of nodes and their distribution over the network is taken into account and the results are verified through computer simulation.