First Passage Time Analysis in Event-Driven Wireless Sensor Networks

In this paper, we establish a first passage time analysis for event-driven sensor networks with single hop. Our model can be regarded as a theoretical analysis for time cost of message transmission to sink node in an event-driven process in which Slotted ALOHA protocol is implemented. The first passage time Tn,lambda depends on the size n of activated nodes and their transmission rate lambda. Given n, we study the optimal lambda and give the approximation radic1n n/n, further more we give the estimate of the size n from the view point of sink node. So that we can adjust the transmission rate lambda to attain the optimal expected time cost Tmin (n). Numerical result indicates that given the size of active nodes n, the optimal time cost of the procedure increases nearly linearly with n increasing which implies that ALOHA protocol is efficient even in dense event-driven sensor networks.