% $Id: results.tex,v 1.8 2005/03/01 10:06:58 gokhale Exp $

\section{Results and Discussion}
\label{sec:results}

This section describes results and analysis of our experiments
described in Section~\ref{sec:eval}. The results are presented along
different dimensions of WSN performance metrics.

\subsection{Aggregate Energy Consumption}
\label{sec:energy}

Aggregate Energy Consumption is defined as the total energy consumed
(in joules) in transmission and receiving, during the simulation. The
Sink Size is the total number of sink nodes in the wireless network. 
Assume that the total energy per node $i$ is $E_i$ and energy
consumption for this node is $E_{consumed_i}$, then the energy
depletion, $E_{depletion}$, is defined as

\begin{equation}
E_{depletion} = \sum_{i=1}^n (E_i - E_{consumed_i})/n 
\end{equation}
where $n$ is the network density.

Figures~\ref{fig:energy1} and~\ref{fig:energy2} show the variation of
aggregate energy consumption against sink size for various network
densities for DD and TTDD, respectively. On an 
average, the energy consumption increases by 17\% for a 60\% increase
in the sensor nodes deployed. It would appear that increasing the
total sensors per unit flat space under observation will increase the
redundancy of the network. This follows from the fact that since
there are more nodes per unit space, at least some nodes will always
be ``alive'' and would route the through traffic for that
space. However, from Figures~\ref{fig:energy1} and~\ref{fig:energy2},
we observe that the energy gets depleted faster for highly dense 
nodes. For example, for the same sink size (of 2) the energy depletion
is 36\% for a network density of 100, while it is 50\% for a network
density of 400. Thus, a highly dense network will not increase the
redundancy. This is because for such a network for the same time the
energy of a single node will deplete at a faster rate and hence the
nodes that are ``alive'' per unit flat space will be lesser.  

\begin{figure}[htb]
\centering
\includegraphics[width=3.2in]{eps/dd_energy_consumption.eps}
\bfcaption{Average Energy Consumption During Transmit/\-Receive for DD}
\label{fig:energy1}
\end{figure}

\begin{figure}[htb]
\centering
\includegraphics[width=3.2in]{eps/ttdd_energy_consumption.eps}
\bfcaption{Average Energy Consumption During Transmit/\-Receive for TTDD}
\label{fig:energy2}
\end{figure}

\subsection{Packet Delivery Fraction discussions} 
\label{sec:delivery}

Packet Delivery Fraction is defined as the fraction of number of
packets received at the sink to the number of packets being sent from
the source nodes. The fraction is averaged for all the sink-source
pairs for each network density in the simulation. The variation of
packet delivery fraction against sink 
size, for network densities of 100, 196, 289 and 400 for DD and TTDD,
respectively, is shown in
Figures~\ref{fig:delivery1} and~\ref{fig:delivery2}. 

\begin{figure}[htb]
\centering
\includegraphics[width=3.2in]{eps/dd_packet_delivery.eps}
\bfcaption{Packet Delivery Fraction versus Sink Size for DD}
\label{fig:delivery1}
\end{figure}

\begin{figure}[htb]
\centering
\includegraphics[width=3.2in]{eps/ttdd_packet_delivery.eps}
\bfcaption{Packet Delivery Fraction versus Sink Size for TTDD}
\label{fig:delivery2}
\end{figure}

We observe that the fraction variation is about 7\% on an average, for
increase in sink size from 2 to 16.   
This reduction is owing to an increase in the overall traffic since
the reports have to reach more observers. This allows us to
accommodate more sinks (an 800\% increase) at the cost of 7\% more
packets getting dropped. This might seem a reasonable tradeoff,
however, it must be noted that for the same sink size increase, the
energy consumption increased almost 100\%! A better energy
utilization, in particular, as the sink size 
is increased is thus crucial to increase network performance, since
this will mean more sinks could be tolerated at an acceptable energy
consumption level and delivery fraction values. 

\subsection{Normalized Routing Load discussions} 
\label{sec:norm}

Routing load (L) for a single
node is defined as the total number of routing packets that it
transmits in a network for the duration of simulation. We define
Normalized Routing Load ($L_n$) as 

\begin{equation}
L_n = (\sum_{i=0}^n L_i)/n 
\end{equation}
where $n$ is the total number of nodes in the network. 

%Andy: the whole para on pause time has been moved in the methodology
% s.t. pause time is explained before it is used in any of the sections
%this above para. about pause time has to be removed.
% DONE

Figures~\ref{fig:norm1} and~\ref{fig:norm2} show the variation of
normalized routing load against pause time for various network
densities for DD and TTDD, respectively. The sink size is kept
constant at 6 for this set of experiments. Observe that, for less
mobile sinks (indicated by higher pause times), the TTDD has more
normalized routing load than DD. This is expected since, TTDD has to
construct and maintain the grid which is very costly. Further, TTDD has a
localized flooding, where a small area of topology is flooded till a
dissemination point is located. The flooding area is thus another
factor which contributes the routing load. The flooding area is a
static configuration parameter, and thus once set it can not be
dynamically varied (in order to reduce the normalized routing load,
since lesser are will mean lesser flooding). Thus, TTDD has more
routing load than DD for the same pause time and sink size. 

\begin{figure}[htb]
\centering
\includegraphics[width=3.2in]{eps/dd_norm_routing_load.eps}
\bfcaption{Normalized Routing Load versus Pause (in seconds) for DD}
\label{fig:norm1}
\end{figure}

\begin{figure}[htb]
\centering
\includegraphics[width=3.2in]{eps/ttdd_norm_routing_load.eps}
\bfcaption{Normalized Routing Load versus Pause (in seconds) for TTDD}
\label{fig:norm2}
\end{figure}

\subsection{Average Delay discussions}
\label{sec:delay}
The average delay is defined as the latency
seen by the sink in obtaining reports of interests from the source,
averaged for all sink-source pairs. Figures~\ref{fig:delay1}
and~\ref{fig:delay2} show the variation against sink size for DD and
TTDD, respectively. As one would expect, with the increase in
sink size, more packets are transmitted for the same per unit sensing
area causing increased delays as seen by the
sink. Figures~\ref{fig:delay1} and~\ref{fig:delay2} confirm this 
behavior where the average delay increases steadily as sink size
increases. One important observation from the TTDD and DD delay
results is that the delay increases more rapidly for TTDD than for
DD. This is corroborated by the fact that other parameters being
constant, the routing overhead is more for TTDD than DD, which leads to
congestion and hence an increase in the delays. 

\begin{figure}[htb]
\centering
\includegraphics[width=3.2in]{eps/dd_avg_delay.eps}
\bfcaption{Average Delay (in seconds) versus Sink Size for DD}
\label{fig:delay1}
\end{figure}

\begin{figure}[htb]
\centering
\includegraphics[width=3.2in]{eps/ttdd_avg_delay.eps}
\bfcaption{Average Delay (in seconds) versus Sink Size for TTDD}
\label{fig:delay2}
\end{figure}

\subsection{Suggestions on protocol improvement}
\label{sec:improve}

Based on insights gained from our experimental evaluation, we now
briefly describe proposed improvements to the two protocols we
studied. 

\begin{enumerate}\cramplist
\item {\bf DD:} In DD, network-level broadcast (for advertising
      interest in specific sensing data) and sending exploratory data
      packets are one of the most expensive operations and hence
      network performance will be greatly affected if the cost
      associated with these operations is reduced. One possible
      solution is diffusing interests locally instead of broadcast,
      such as using passive clustering~\cite{Handziski:04}, where the
      redundant transmissions during broadcast operations are reduced
      effectively reducing the costs. Furthermore, cost reduction can
      be done by exploring multiple paths instead of a single
      reinforced path since a single path depletes the nodes that
      make up this path faster. 

\item {\bf TTDD:} In TTDD, the flooding is restricted to a single home
      cell of a sink node, thus aiming to reduce the associated
      cost. However, the flooding area is not dynamic and thus once
      set, the same area will be flooded with sensing data request. A
      possible enhancement to TTDD can be that if the current density
      of the network and average energy consumption makes cell-level
      broadcast costly, a new tier could be introduced at the
      cell-level. A new dissemination point can be appointed inside
      the cells themselves. This is better than changing the cell
      size~\cite{Bokareva:04} because changing cell-size dynamically
      means reconstructing the grid structure, which is a very costly
      operation. In the worst case scenario, for a sink lying on the
      grid but at a distance $\alpha/2$ from each of the closest
      dissemination points, the flooding will be done for a maximum of
      0.785 unit area for unit $\alpha$. The worst case value for the
      plain two grid structure without the suggested improvement
      is 1.57 unit area, thus giving a reduction of almost 50\%. 

\end{enumerate}

