An Exact Model of the Neighbor Discovery Time for Schedule-Based Asynchronous Duty Cycling

In Wireless Sensor Networks, if two neighbor nodes operate under schedule-based asynchronous duty cycles, it is nontrivial to determine when they will discover each other, since the discovery opportunities may be distributed irregularly throughout the cycle, and also because nodes present random time offsets to each other. Moreover, the probability of message loss must be considered for useful estimations. This paper presents a method to find the expected neighbor discovery time when opportunities are distributed in arbitrary time slots, and subject to message loss. As a case study, the method was employed to solve a real problem in WSN design.