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 T_n,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 T_min (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.