Changeset 2758

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Timestamp:
10/30/09 06:09:48 (4 weeks ago)
Author:
wark
Message:

removed Nbuff

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1 modified

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  • HydroWatch/Tim/doc/ipsn10/sec_adaptive.tex

    r2740 r2758  
    137137Given the protocols as described in Section~\ref{sec:schedule}, we can describe the key energy relationships in the system for node $n$ for an interval $k$ as: 
    138138\begin{align} 
    139         E_a(n, k+1) = E_a(n, k) - E_c(n, k) + E_h(n, k) - E_l(n, k) 
    140 \end{align} 
    141 where $E_a(n, k)$ is the stored energy for node $n$ at interval $k$, $E_c(n,k)$ is the consumed energy, $E_h(n,k)$ is the harvested energy and $E_l(n,k)$ is the energy lost in both the process of pushing and pulling energy from the available storage.   
     139        E_a(n, k+1) = E_a(n, k) - E_c(n, k) + E_h(n, k) %- E_l(n, k) 
     140\end{align} 
     141where $E_a(n, k)$ is the stored energy for node $n$ at interval $k$, $E_c(n,k)$ is the consumed energy, $E_h(n,k)$ is the harvested energy.  
     142%and $E_l(n,k)$ is the energy lost in both the process of pushing and pulling energy from the available storage.   
    142143 
    143144We define the energy consumed by a node for interval $k$ as the sum of the energy when the node is in the various states as shown in Figure~\ref{fig:schedule1} as: 
    … …  
    152153        E_{samp}(n,k) &= A_1(n) F_s(n,k) \nonumber \\  
    153154        E_{lr}(n,k) &= A_2(n) F_r(n,k)\nonumber \\ 
    154         E_{hr}(n,k) &= A_3(n) F_s(n,k) \nonumber \\ 
     155        E_{hr}(n,k) &= A_3(n) F_s(n,k) + A_4(n)\nonumber \\ 
    155156        E_{f}(n,k) &= \sum_c \left(E_{lr}(c,k) + E_{hr}(c,k) \right) \nonumber \\ 
    156157        E_{sleep} &\approx P_{sleep} T_{int} 
    157158\end{align} 
    158  
    159 Based on our models energy consumption we define each constant as: 
     159where $c \in $ children of node $n$. Based on our models energy consumption we define each constant as: 
    160160\begin{align}\label{equ:A} 
    161161        A_1(n) &= T_{int} N_s E_s\nonumber \\  
    162162        A_2(n) &= P_{lpl} T_{lres} T_{int}\nonumber \\ 
    163         A_3(n) &= \left(\frac{\tau}{N_b} + T_{tx}\right)P_{on}T_{int} 
     163        %A_3(n) &= \left(\frac{\tau}{N_b} + T_{tx}\right)P_{on}T_{int} 
     164        A_3(n) &= T_{tx}P_{on}T_{int} \nonumber \\  
     165        A_4(n) &= \tau \frac{T_{int}}{T_{data}} 
    164166\end{align} 
    165167where we define parameters as given in Table~\ref{table:param_opt}: 
    … …  
    181183$P_{\text{on}}$ & Power consumption with radio 100\% on. \\ 
    182184$T_{\text{lres}}$ & Time to send low res samp - includes delay time for nodes to get in sync. \\ 
    183 $\tau$ & Delay period to ensure all nodes in network are in sync. \\ 
     185$\tau$ & Delay period to ensure network routing state is updated and all nodes in network are in sync. \\ 
    184186$E_{\text{off}}$ & Standby energy consumption of node (radio off and no sensing) \\ 
    185 $N_{\text{b}}$ & Size (in sample sets) of sample buffer \\ 
     187%$N_{\text{b}}$ & Size (in sample sets) of sample buffer \\ 
     188$T_{\text{data}}$ & Pre-assigned period for streaming HR data \\ 
    186189\hline 
    187190\end{tabular} 
    … …  
    221224    \mbox{subject to:} & \left(A_1(n) + A_3(n)\right)F_s(n,k) + A_2(n) F_r(n,k)  \\ 
    222225      \vspace{2mm} 
    223      &  \le \frac{1}{N_k}\sum_{j=k}^{k+N_k -1} \left(\hat{E}_h(n,j) + \frac{E_a(n,j)}{N_{int}(j)} \right)\\\\ 
     226     &  \le \frac{1}{N_k}\sum_{j=k}^{k+N_k -1} \left(\hat{E}_h(n,j) + \frac{E_a(n,j)}{N_{int}(j)} - A_4(n)\right)\\\\ 
    224227     & F_s^{min} \le F_s(n,k) \le F_s^{max} \\ 
    225228     & F_r^{min} \le F_r(n,k) \le F_r^{max}