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\begin{document}

\title{\vspace{-3mm}The Effect of the Choice of Hydration Strategy on
    Average Academic
Performance}

\author{Some concerned fellow students%
    \thanks{The authors would like to thank their hard-working peers as well as
        the staff of the KIT library for their unknowing - but vital -
participation.}}

\markboth{Journal of the Association of KIT Bibliophiles}{The
Effect of the Choice of Hydration Strategy on Average Academic Performance}

\maketitle

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\begin{abstract}
    We evaluate the relationship between hydration strategy and
    academic performance and project that by using the right button of
    the water dispenser to fill up their water bottles, students can potentially
    gain up to \SI{4.14}{\second} of study time per refill, which is amounts to
    raising their grades by up to 0.00103 points.
\end{abstract}

\begin{IEEEkeywords}
    KIT Library, Academic Performance, Hydration
\end{IEEEkeywords}

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\vspace*{-5mm}

%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Introduction}

\IEEEPARstart{T}{he} concepts of hydration and study have always been tightly
interwoven. As an example, an investigation was once conducted by Bell Labs
into the productivity of their employees that found that ``workers with the
most patents often shared lunch or breakfast with a Bell Labs electrical
engineer named Harry Nyquist'' \cite{gertner_idea_2012}, and we presume that
they also paired their food with something to drink. We can see that
intellectual achievement and fluid consumption are related even for the most
prestigious research institutions.

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}

Over a period of one week, we monitored the usage of the water dispenser
on the ground floor of the KIT library at random times during the day.
The experiment comprised two parts, a system measurement to determine the
flowrate of the water dispenser, and a behavioural measurement, i.e.,
a recording
of the choice of hydration strategy of the participants: $S_\text{L}$ denotes
pressing the left button of the water dispenser, $S_\text{R}$ the right one,
and $S_\text{B}$ pressing both buttons.

For the system measurement $10$ datapoints were recorded for each strategy,
for the behavioural measurement $113$ in total.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Experimental Results}

\begin{figure}[H]
    \centering

    \vspace*{-4mm}
    \begin{tikzpicture}
        \begin{axis}[
                width=0.8\columnwidth,
                height=0.35\columnwidth,
                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)},
                xlabel = {Flowrate (\si{\milli\litre\per\second})},
            ]
            \addplot[boxplot, fill, scol1, draw=black]
            table[col sep=comma, x=flowrate]
            {res/flowrate_both.csv};

            \addplot[boxplot, fill, scol2, draw=black]
            table[col sep=comma, x=flowrate]
            {res/flowrate_right.csv};

            \addplot[boxplot, fill, scol3, draw=black]
            table[col sep=comma, x=flowrate]
            {res/flowrate_left.csv};
        \end{axis}
    \end{tikzpicture}

    \vspace*{-3mm}

    \caption{Flow rate of the water dispenser depending on the
    hydration strategy.}
    \label{fig:System}
    \vspace*{-2mm}
\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
unknown distribution, the test we chose to verify this observation is a Mann
Whitney U test. We found that $S _\text{L}$ is faster than $S_\text{R}$ with a
significance of $p < 0.0001$, while no significant statement could be made
about $S_\text{R}$ and $S_\text{B}$.
Fig. \ref{fig:Behavior} shows the results of the behavioural measurement.

\begin{figure}[H]
    \centering

    \vspace*{-2mm}
    \begin{tikzpicture}
        \begin{axis}[
                ybar,
                bar width=15mm,
                width=\columnwidth,
                height=0.35\columnwidth,
                area style,
                xtick = {0, 1, 2},
                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)},
                ylabel = {No. chosen},
            ]
            \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}

    \vspace*{-3mm}

    \caption{Distribution of the choice of hydration strategy.}
    \label{fig:Behavior}
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Modelling}

We can consider the water dispenser and students as comprising a queueing
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)}
    ,%
\end{align*}%
where $S$ denotes the service time (i.e., the time spent refilling a bottle),
$\lambda$ the mean arrival rate, and $\rho = \lambda \cdot E\mleft\{
S \mright\}$ the system utilization. Using our
experimental data we can approximate all parameters and obtain
$W \approx \SI{23.3}{\second}$. The difference to always using
the fastest strategy amounts to $\SI{4.14}{\second}$.

Strangely, it is the consensus of current research that there is only
a weak relationship between academic performance and hours studied
\cite{plant_why_2005}.
The largest investigation into the matter found a correlation of
$\rho = 0.18$ \cite{schuman_effort_1985} between GPA and average time
spend studying per day. Using a rather high estimate of 5 refills per
day, we predict a possible grade gain of up to $0.00103$ points.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Discussion and Conclusion}

Further research is needed, particularly on the modelling of the
arrival process and the relationship between the response time gain
the grade gain. Nevertheless, we believe this work serves as a solid
first step on the path towards achieving optimal study behaviour.

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \section{Conclusion}

In this study, we investigated how the choice of hydration strategy
affects average academic performance. We found that always
choosing to press the right button leads to an average time gain of
\SI{4.14}{\second} per refill, which translates into a grade
improvement of up to $0.00103$ levels. We thus propose a novel and
broadly applicable strategy to boost the average academic performance
of KIT students: always using the right button.

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