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@ -1,6 +1,5 @@
\documentclass[journal]{IEEEtran}
\usepackage{amsmath,amsfonts}
\usepackage{float}
\usepackage{algorithmic}
@ -16,7 +15,6 @@
sorting=nty,
]{biblatex}
\usepackage{tikz}
\usetikzlibrary{spy, arrows.meta,arrows}
@ -29,14 +27,12 @@
\hyphenation{op-tical net-works semi-conduc-tor IEEE-Xplore}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Inputs & Global Options
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
% Figures
%
@ -67,27 +63,22 @@
\addbibresource{paper.bib}
\AtBeginBibliography{\footnotesize}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Title, Header, Footer, etc.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\newcommand\todo[1]{\textcolor{red}{#1}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Title, Header, Footer, etc.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\begin{document}
\title{The Effect of the Choice of Hydration Strategy on Average Academic
Performance}
@ -101,14 +92,12 @@
\maketitle
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Abstract & Index Terms
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\begin{abstract}
We evaluate the \todo{\ldots} and project that by using the right button of
the water dispenser to fill up their water bottles, students can potentially
@ -120,17 +109,14 @@
KIT Library, Academic Performance, Hydration
\end{IEEEkeywords}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Content
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\vspace*{-1mm}
%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Introduction}
@ -147,7 +133,6 @@ In this work, we quantify this relationship in the context of studying at the
KIT library and subsequently develop a novel and broadly applicable strategy
to leverage it to improve the academic performance of KIT students.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Experimental Setup}
@ -170,11 +155,9 @@ for the behavioral measurement $113$ in total.
% TODO: Describe the actual measurement setup? (e.g., filling up a 0.7l bottle
% and timing with a standard smartphone timer)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Experimental Results}
\begin{figure}[H]
\centering
@ -185,7 +168,8 @@ for the behavioral measurement $113$ in total.
boxplot/draw direction = x,
grid,
ytick = {1, 2, 3},
yticklabels = {$S_\text{B}$ (Both buttons), $S_\text{R}$ (Right button), $S_\text{L}$ (Left button)},
yticklabels = {$S_\text{B}$ (Both buttons),
$S_\text{R}$ (Right button), $S_\text{L}$ (Left button)},
xlabel = {Flowrate (\si{\milli\litre\per\second})},
]
\addplot[boxplot, fill, scol1, draw=black]
@ -204,7 +188,8 @@ for the behavioral measurement $113$ in total.
\vspace*{-3mm}
\caption{Flow rate of the water dispenser depending on the hydration strategy.}
\caption{Flow rate of the water dispenser depending on the
hydration strategy.}
\label{fig:System}
\end{figure}
@ -222,10 +207,13 @@ for the behavioral measurement $113$ in total.
grid,
ymin = 0,
enlarge x limits=0.3,
xticklabels = {\footnotesize{$S_\text{L}$ (Left button)}, \footnotesize{$S_\text{R}$ (Right button)}, \footnotesize{$S_\text{B}$} (Both buttons)},
xticklabels = {\footnotesize{$S_\text{L}$ (Left
button)}, \footnotesize{$S_\text{R}$ (Right
button)}, \footnotesize{$S_\text{B}$} (Both buttons)},
ylabel = {No. chosen},
]
\addplot+[ybar,mark=no,fill=scol1] table[skip first n=1, col sep=comma, x=button, y=count]
\addplot+[ybar,mark=no,fill=scol1] table[skip first n=1,
col sep=comma, x=button, y=count]
{res/left_right_distribution.csv};
\end{axis}
\end{tikzpicture}
@ -236,7 +224,6 @@ for the behavioral measurement $113$ in total.
\label{fig:Behavior}
\end{figure}
Fig. \ref{fig:System} shows the results of the system measurement.
We observe that $S_\text{L}$ is the slowest strategy, while $S_\text{R}$
and $S_\text{B}$ are similar. Due to the small sample size and the
@ -249,7 +236,6 @@ Fig. \ref{fig:Behavior} shows the results of the behavioral measurement.
% needed to fill up their bottle. Using the measured flowrates we calculated
% the mean refill volume to be $\SI{673.92}{\milli\liter}$.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Discussion}
@ -258,30 +244,42 @@ system, specifically an M/G/1 queue \cite{stewart_probability_2009}.
The expected response time, i.e., the time spent waiting as well as
the time dispensing water, is \cite[Section 14.3]{stewart_probability_2009}%
\begin{align*}
W = E\mleft\{ S \mright\} + \frac{\lambda E\mleft\{ S^2 \mright\}}{2\mleft( 1-\rho \mright)}
W = E\mleft\{ S \mright\} + \frac{\lambda E\mleft\{ S^2
\mright\}}{2\mleft( 1-\rho \mright)}
,%
\end{align*}%
where $S$ denotes the service time (i.e., the time spent refilling a bottle),
$\lambda$ the mean arrival time, and $\rho = \lambda \cdot E\mleft\{ S \mright\}$ the system utilization. Using our
$\lambda$ the mean arrival time, and $\rho = \lambda \cdot E\mleft\{
S \mright\}$ the system utilization. Using our
experimental data we can approximate all parameters and obtain
\todo{$W \approx 123$}.
% We examine the effects of the choice of hydration strategy. To
% this end, we start by estimating the potential time savings possible by always
% choosing the fastest strategy:%
% %
% % We can model the time needed for one person to refill their bottle as a random
% % variable (RV) $T_1 = V/R$ and the time saved by choosing the fastest strategy
% % We can model the time needed for one person to refill their
% bottle as a random
% % variable (RV) $T_1 = V/R$ and the time saved by choosing the
% fastest strategy
% % as $\Delta T_1 = T_1 - V/\max r$, where $V$ and $R$ are RVs representing the
% % bottle volume and flowrate. The potential time saving for the last person in a
% % queue of $N$ people is thus $\Delta T_N = N\cdot\Delta T_1$. We can then model
% % bottle volume and flowrate. The potential time saving for the
% last person in a
% % queue of $N$ people is thus $\Delta T_N = N\cdot\Delta T_1$. We
% can then model
% % the total time savings as $\Delta T_\text{tot} = \sum_{n=1}^{N} \Delta T_n$,
% % where N is an RV describing the queue length. Assuming the independence of all
% % where N is an RV describing the queue length. Assuming the
% independence of all
% % RVs we can compute the mean total time savings as
% %
% \begin{gather*}
% T_1 = V/R, \hspace{3mm} \Delta T_1 = T_1 - V/\max R, \hspace{3mm} \Delta T_n = n \cdot \Delta T_1 \\
% \Delta T_\text{tot} = \sum_{n=1}^{N} \Delta T_\text{n} = \sum_{n=1}^{N} n \cdot \Delta T_1 = \Delta T_1 \frac{N\mleft( N+1 \mright)}{2} \\
% \Delta t := E\mleft\{ \Delta T_\text{tot} \mright\} = E\mleft\{ \Delta T_1 \mright\} \cdot \mleft[ E\mleft\{ N^2 \mright\} + E\mleft\{ N \mright\} \mright]/2
% T_1 = V/R, \hspace{3mm} \Delta T_1 = T_1 - V/\max R,
% \hspace{3mm} \Delta T_n = n \cdot \Delta T_1 \\
% \Delta T_\text{tot} = \sum_{n=1}^{N} \Delta T_\text{n} =
% \sum_{n=1}^{N} n \cdot \Delta T_1 = \Delta T_1 \frac{N\mleft( N+1
% \mright)}{2} \\
% \Delta t := E\mleft\{ \Delta T_\text{tot} \mright\} = E\mleft\{
% \Delta T_1 \mright\} \cdot \mleft[ E\mleft\{ N^2 \mright\} +
% E\mleft\{ N \mright\} \mright]/2
% ,%
% \end{gather*}
% %
@ -289,11 +287,13 @@ experimental data we can approximate all parameters and obtain
% bottle and the flowrate, $\Delta T_n$ describes the time the last of $n$
% people saves, $\Delta T_\text{tot}$ the total time savings and $N$ the length
% of the queue. It is plausible to assume independence of $R,V$ and $N$.
% Using our experimental measurements we estimate $\todo{\Delta t = \SI{20}{\second}}$
% Using our experimental measurements we estimate $\todo{\Delta t =
% \SI{20}{\second}}$
Many attempts have been made in the literature to relate the time spent
studying to academic achievement - see, e.g.
\cite{schuman_effort_1985, zulauf_use_1999, michaels_academic_1989, dickinson_effect_1990}.
\cite{schuman_effort_1985, zulauf_use_1999, michaels_academic_1989,
dickinson_effect_1990}.
The overwhelming consensus is that there is a significant relationship,
though it is a weak one.
%
@ -306,11 +306,9 @@ though it is a weak one.
% generlizing these results. Nevertheless, the overwhelming consensus in the
% literature is that a significant relationship exists, though it is a weak one.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Conclusion}
In this study, we investigated how the choice of hydration strategy affects
the average academic performance. We found that always choosing to
press the right button leads to an average time gain of \todo{\SI{10}{\second}}
@ -327,14 +325,12 @@ academic performance of KIT students: always pressing the right button.
% foundation and hope that our results will find widespread acceptance among the
% local student population.
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Bibliography
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\printbibliography
% \appendix
@ -347,13 +343,15 @@ academic performance of KIT students: always pressing the right button.
% We want to compute the response time of our queueing system, i.e.,
% \cite[Section 14.3]{stewart_probability_2009}
% \begin{align*}
% W = E\mleft\{ S \mright\} + \frac{\lambda E\mleft\{ S^2 \mright\}}{2\mleft( 1-\rho \mright)}
% W = E\mleft\{ S \mright\} + \frac{\lambda E\mleft\{ S^2
% \mright\}}{2\mleft( 1-\rho \mright)}
% .%
% \end{align*}%
% We start by modelling the service time and subsequently calculate $\lambda$
% and $\rho$.
%
% Let $S, V$ and $R$ be random variables denoting the service time, refill volume
% Let $S, V$ and $R$ be random variables denoting the service time,
% refill volume
% and refill rate, respectively. Assuming that $V$ and $R$ are independent, we
% have
% \begin{gather*}
@ -364,8 +362,11 @@ academic performance of KIT students: always pressing the right button.
% \end{array}\right.
% \end{gather*}%
% \begin{align*}
% E\mleft\{ S^2 \mright\} &= E\mleft\{ V^2 \mright\}E\mleft\{ 1 / R^2 \mright\} \\
% & = E\mleft\{ V^2 \mright\} \mleft( P(S_\text{L})\frac{1}{r^2_{S_\text{L}}} + \mleft( 1 - P(S_\text{L}) \mright)\frac{1}{r^2_{S_\text{R}}} \mright)
% E\mleft\{ S^2 \mright\} &= E\mleft\{ V^2 \mright\}E\mleft\{ 1 /
% R^2 \mright\} \\
% & = E\mleft\{ V^2 \mright\} \mleft(
% P(S_\text{L})\frac{1}{r^2_{S_\text{L}}} + \mleft( 1 - P(S_\text{L})
% \mright)\frac{1}{r^2_{S_\text{R}}} \mright)
% .%
% \end{align*}
% We now use our experimental data (having calculated $v_n, n\in [1:N]$ from the
@ -373,8 +374,10 @@ academic performance of KIT students: always pressing the right button.
% \begin{align*}
% \left.
% \begin{array}{r}
% E\mleft\{ V^2 \mright\} \approx \frac{1}{N+1} \sum_{n=1}^{N} v_n^2 = \todo{15}\\
% P(S_\text{L}) \approx \frac{\text{\# times $S_\text{L}$ was chosen}}{N} = \todo{123} \\
% E\mleft\{ V^2 \mright\} \approx \frac{1}{N+1}
% \sum_{n=1}^{N} v_n^2 = \todo{15}\\
% P(S_\text{L}) \approx \frac{\text{\# times $S_\text{L}$ was
% chosen}}{N} = \todo{123} \\
% r^2_{S_\text{L}} \approx \todo{125} \\
% r^2_{S_\text{R}} \approx \todo{250}
% \end{array}
@ -401,6 +404,4 @@ academic performance of KIT students: always pressing the right button.
% \end{itemize}
% }
\end{document}