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