tailieunhanh - Emerging Communications for Wireless Sensor Networks Part 9

Tham khảo tài liệu 'emerging communications for wireless sensor networks part 9', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Energy-aware Selective Communications in Sensor Networks 153 Therefore the gain is given by G 21 p 1 p J p p 2 1 p V p Exponential Using 25 we find that ụ is the solution of ụ aW p 39 40 where W x y is the real-valued Lambert s W function which solves the equation yeti x for 1 y 0 and 1 e x 0 Corless et al. 1996 . Thus G 1 p- 1 W p . 41 Figure 4 compares the gain of the uniform and the exponential distributions as a function of p. The graphic remarks that under exponential distributions the difference between the selective and the non-selective forwarding scheme is much more significant. The better performance of the exponential distribution compared to the uniform may be attributed to the tailed shape. We may think that for a long-tailed distribution the selective transmitter may be highly selective saving energy for rare but extremely important messages. This intuition is corroborated by the Pareto distribution see Arroyo-Valles et al. 2009 for further details . Fig. 4. Gain of the uniform and exponential distributions as a function of p. Influence of idle times The above examples show that the gain of the optimal selective transmitter increases with p. By noting that p in 32 is a decreasing function of Pi and Ei the influence of idle times becomes clear as soon as the frequency of idle times or the idle energy expenses increases the gain of the selective transmission scheme reduces. 5. Network Optimization Optimal selective forwarding Since each message must travel through several nodes before arriving to destination the message transmission is completely successful if the message arrives to the sink node. In general an intermediate node in the path has no way to know if the message arrives to the sink unless 154 Emerging Communications for Wireless Sensor Networks the sink returns a confirmation message but it can possibly listen if the neighboring node in the path propagated the message it was requested to forward. If dk denotes the decision at node i