Mathematical Model for Sink Mobility (MMSM) in Wireless Sensor Networks to Improve Network Lifetime

Sink node mobility is to uniformly distribute the load of the sink neighbors in order to balance the energy level and to delegate sink’s neighbor responsibility between the sensor nodes. In this paper, we present a mathematical model that works with existing routing protocol. Sink mobility is decided on the basis of definite-stay-value (\( {\text{D}} = \Delta *(1 - {\text{P}}(S|Pos)) \)), where \( {\text{P}}\left( {{\text{S}}|{\text{Pos}}} \right) \) is defined as closeness of sink node and sink site. Closeness means surrounding density or an area where density of sensors is very high. This model performs the SINK_TEST for the determination of sink site. We have formulated this problem with the help of prior probability and continuous Bayes’ theorem. This mathematical model is verified by experiments and gives adequate accuracy for the improvement of network lifetime in independent environment.