This paper provides a theoretical model for the computation of the probability density function of multi-hop broadcast latency when using probabilistic broadcasting schemes in Wireless Sensor Networks. In this paper, a novel probabilistic approach is presented for directed data transmission without route discovery. In our model, we require each message can reach the BS successfully with a certain success probability and nodes which are located nearer to the base station relay messages with a certain relay probability. The relationship between the number of intermediate nodes and relay probability is analyzed and the condition for relay probability to guarantee a certain success probability of messages is obtained. This approach is robust, adaptive to change of topology of the sensor network and energy efficient. Implementation of this approach is discussed. Simulation helps to illustrate the main results obtained by analysis and shows that this approach is very energy efficient.
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