Nodes mobility in MANET will cause network topology changing dynamically for sure, which is, to a great extent, a random rapid and unpredictable change. In wireless link environment, the necessary procedure to ensure robustness, reliability and effectiveness of network is to realize dependable communications between nodes.
The Optimal Exploration for Route
The optimal exploring theory is on how to find a target already existed, which is called exploring target, in an optimal way (Dimitrakakis, 2006). The probabilities of distribution function of target location and moving path, detection function and constraint condition are main parameters of this theory (Groot, 1970). Detection function and target position function can help calculate probability of the target being found successfully in every distributive scheme correspondingly to each area of exploring space (Ohsumi, 1986). Therefore, the solution of optimal exploring problem is to find an optimal distributive scheme on exploring time to maximize possibility of searching the target successfully or minimize the expectation value of cost needed (Li, 2001).
For optimal exploring model being set up better, some terms should be defined first as follows (Zhu, 2005).
Assume X(t)∈Rn is the position of target node at t, and S(t)∈Rn is the position of reconstructing node at t. Joint probability density f(x, t, S) can be defined as:
f(
x, t, S) is the joint probability density of position of target node and exploring process. It is obvious that
f(
x, t, S) tends to initial probability density
f0(
x) when
t approaches to 0. The detection probability at
t can be acquired as (1) according to joint probability density.
(1)Where integral region D is the area target node lying in, in other words, D is the subset of exploring space Rn and the probability of target lying in it is greater than 0. In two dimensional conditions, joint probability density function satisfies(2), which includes information on target node moving model and detection model. f0(x, y) is an initial density function of target node position and satisfied(3).
(2) (3)Conditional probability density in unsuccessfully exploring case can be obtained by Bayes formula (Wang, & Zeng, 2007) once f(x, t, S) is known. Generally, it is easy to get f(x, t, S), and ρ(x t|S) can be got by(4).
(4)Probability of survival u(x, t, T, Z) (Xi’an University of Electronic Science and Technology, 2006) on the interval of time [t, T] can be defined as:
Having noted that f(x, t, Z) depends on current position while u(x, t, T, Z) lies on the initial one, and when t→T, there is always u(x, t, T, Z)→1. Denominator in (4) denotes possibility of failed exploration until t, thereby P[t;Z] can be defined as(5). In this way, P[t;Z] is successful exploring probability along path Z, which can be rewritten as(6).
(5) (6)Other useful information can be educed from these basic probability characteristic metric. T is the time taken to find the target node, as a positive random variable, the expectation can be calculated by (Shi, Deng, & Qi, 2007):