Changeset 2812

Timestamp:

10/30/09 20:11:17 (4 weeks ago)

Author:

jaein

Message:

 

Files:

• HydroWatch/Tim/doc/ipsn10/sec_adaptive.tex (modified) (1 diff)

HydroWatch/Tim/doc/ipsn10/sec_adaptive.tex

@@ -287 +287 @@
 The multi-hop variation of this problem is complicated by the fact that all nodes in the same routing tree must have identical report periods in order to allow a path back to sink to form. We address this issue by solving the optimization problem as a two step process. In the first step, we solve for the parameters $F_s(n,k)$ and $F_r(n,k)$, however unlike the single-hop case, all nodes in a tree are simultaneously optimized.  In the second step we constrain all nodes in a sub-tree\footnote{A section of the tree that shares a common single-hop node} to have a common report frequency $\hat{F}_r(k)$ defined as the mean of all $F_r(n,k)$ in that subtree. Given this constraint we then solve for a new set of $F_s(n,k)$ for each sub-tree.
 
-Finally, the other feature we add to the multi-hop protocol is an enforced load-balancing to ensure that nodes deeper in the tree aren't always disadvantaged by forwarding data from higher sample rate leaf nodes which aren't burdened with a forwarding cost. In order to achieve this, we introduce a parameter $\gamma(n)$ which is equal to the \emph{number of descendants + 1}. This parameter is illustrated in Figure~\ref{fig:tree}. By introducing this parameter the leaf nodes will be weighted in the optimization process to pull back on their sampling frequency, where we now define the multi-hop utility function as:
+Finally, the other feature we add to the multi-hop protocol is enforced load-balancing to ensure that nodes deeper in the tree aren't always disadvantaged by forwarding data from higher sample rate leaf nodes which aren't burdened with a forwarding cost. In order to achieve this, we introduce a parameter $\gamma(n)$ which is equal to the \emph{number of descendants + 1}. This parameter is illustrated in Figure~\ref{fig:tree}. By introducing this parameter the leaf nodes will be weighted in the optimization process to pull back on their sampling frequency, where we now define the multi-hop utility function as:
 \begin{align}
 \begin{array}{rl}