\documentclass{article}

\usepackage{graphicx}
\usepackage{amsmath}
\usepackage{natbib}
\title{poissonNMF -- blind source separation of fluorescence microscopy data}
%\author{Richard Neher, Andr\'e Zeug and Fabian Theiss}
\newcommand{\bm}[1]{\mbox{\boldmath $#1$}}
\newcommand{\EQ}[1]{Eq.~(\ref{eq:#1})}
\newcommand{\EQS}[2]{Eqs.~(\ref{eq:#1)} and (\ref{eq:#2})}
\newcommand{\FIG}[1]{Fig.~\ref{fig:#1}}
\newcommand{\REF}[1]{ref.~\citep{#1}}

\bibliographystyle{unsrtnat}
\begin{document}
\maketitle
PoissonNMF is an ImageJ plugin to decompose spectrally resolved fluorescence
microscopy data into the contribution of the labels under conditions where the
spectra are not or only inaccurately known. It employs non-negative matrix
factorization \cite{Lee_Nature_99}, suitably modified to shot-noise dominated
data \cite{Neher_BPJ_2009}.

\section*{Installation}
To install the plugin, copy the \texttt{PNMF\_.class} and
\texttt{PNMF\_\$1.class} files as well as the into folder
\texttt{PNMF\_SpectraLibrary} the plugins directory of your ImageJ
distribution.

\section*{Input Data} PoissonNMF expects a 32 bit image stack, where each
slice of the stack corresponds to the image in one spectral channel.

\section*{Parameters \& initial conditions} Upon invoking pNMF from the plugin
menu, a dialog opens, prompting the user for the number of sources expected in
the sample. This dialog is followed by a second dialog allowing the user to
provide additional input. The dialog is preset to the values of the previous
run of PoissonNMF. The dialog is shown in \FIG{dialog}. Several choices in this
dialog invoke additional dialog after the \emph{Run} button has been pressed.
% \usepackage{graphics} is needed for \includegraphics
\begin{figure}[htp]
\begin{center}
  \includegraphics[width=0.8\columnwidth]{parameterDialog}
  \caption{The parameter dialog of pNMF with default values.}
  \label{fig:dialog}
\end{center}
\end{figure}
\subsection*{Parameter Dialog}
\paragraph{First and last wavelength:}

\paragraph{Number of iterations:}
The total number of iterations the algorithm is run. Depending on the
subsampling scheme (see below), the first iteration are only applied to a
subset of the data.
\paragraph{Subsampling:}To speed up the calculation, the algorithm can be
initiated on a subset of the data and then successively uses the estimate for
the spectra for larger subsets of the data. The parameter subsampling
determines the number of subsamplings of increasing size to be made. Successive
subsamples are larger by a factor of 10, while the last is the entire data set
(above the background threshold). The number of iterations for larger subsamples
is smaller (a factor 2 between successive subsamples).
\paragraph{Segregation Bias: } A parameter determining the degree,
to which overlap of estimated label distribution is penalized. Suitable weights
of the segregation bias are around 1 or lower. Too high segregation bias will
yield in a faulty decomposition.
\paragraph{Saturation threshold:}Saturated or nearly saturated pixels have
distorted emission spectra and therefore have to be excluded from the
analysis. If the signal in any channel at a certain pixel is above this
parameter value, the pixel is excluded.
\paragraph{Background threshold:}Very faint pixels carry little information
and are likely dominated by noise, autofluorescence and the like. It is
therefore advisable to limit the spectra estimation to reasonably strong
pixels. Any pixel, where, after background subtraction, the intensity is below
this threshold in every channel is therefore excluded.
\paragraph{Background:}Any constant background has to be subtracted before the
image is processed. This background is either estimated using the minimal value
in each spectral channel. Alternatively, the background can be estimated by
specifying a ROI that contains nothing but background signal or the background
can be entered manually.
\paragraph{Start spectra:}Convergence is faster if the initial spectra are
good guesses of the actual spectra. PoissonNMF provides several options to
specify the start spectrum for each dye, which can be chosen from a
pull-down menu. The simplest choice for the initial spectra are equally spaced
Gaussians. Other options to specify start spectra are ROI selection, manual
entry of the spectra and the choice of spectra from the spectra library.
\paragraph{Fix Spectra:}The initial spectrum of each dye can be kept fixed
during the PoissonNMF run by checking the appropriate checkbox.
\paragraph{Channel boundaries:}To display the spectra correctly and to read
spectra from the library, the boundaries of the spectral channels have to be
entered. To do so, check the check box and you will be prompted for the channel
boundaries later.

\begin{figure}[htp]
\begin{center}
  \includegraphics[width=0.7\columnwidth]{spectraSelection}
  \caption{The user is asked to specify the background and the initial spectra
  for the run of PoissonNMF.}
  \label{fig:spectraSelection}
\end{center}
\end{figure}

While PoissonNMF processes the image, the current spectra are continuously
displayed. At any point, the user can cancel the PoissonNMF or use the current
spectra for least squares unmixing of the image.

\section*{Output}
PoissonNMF displays an image stack with the estimated label
distributions and opens a window with a number of buttons that allow to save
the spectra, examine the background spectrum and the set of background pixels
and construct RGB overlays of a triplet of dye distributions.

\begin{figure}[htp]
\begin{center}
  \includegraphics[width=0.8\columnwidth]{spectra}
  \caption{An example estimated spectra delivered by PoissonNMF.}
  \label{fig:spectra}
\end{center}
\end{figure}
\begin{figure}[htp]
\begin{center}
  \includegraphics[width=0.9\columnwidth]{RGBoverlay}
  \caption{For three sources, PoissonNMF calculates a composite image with
  each source specifying one color channel. }
  \label{fig:RGBoverlay}
\end{center}
\end{figure}

\section*{Spectra Library}
PoissonNMF can make use of literature spectra or spectra determined in previous
runs, for example by using them as start spectra or keeping them fixed while
optimizing other unknown spectra. For a spectrum to be available in PoissonNMF,
it has to be placed in the folder \texttt{PNMF\_SpectraLibrary} located in the
plugins folder of ImageJ. The files are assumed to be text files with the
wavelength in column one and the emission in column two, conform with the
output format of PoissonNMF.

\bibliography{image_decomp.bib}

\end{document}


% The Karlin-Altschul equation (advanced)

\subsection{The Karlin-Altschul Equation (advanced)}
\begin{frame}
  \frametitle{Assumptions}
  \begin{itemize}
    \item The Karlin-Altschul equation
    \begin{equation*}
      E = k m n e^{-\lambda S}
    \end{equation*}
    \item Assumptions:
    \begin{itemize}
      \item A positive score must be possible
      \item The scoring matrix \emph{expected score} must be negative
      \item Sequences are infinitely long
      \item Alignments do not contain gaps
      \item Sequence symbols (bases, residues) are independent and identically-distributed
    \end{itemize}
  \end{itemize}
\end{frame}


\documentclass{article}

\usepackage{a4wide}
\usepackage{latexsym,amssymb,amsthm,amsmath}

\allowdisplaybreaks

\begin{document}

\begin{align*}
\mathcal{T}_1 =\{ %
%
AcademicStaff &\sqsubseteq Staff,\\
ResearchStaff &\sqsubseteq Staff,\\
NonAcademicStaff &\sqsubseteq Staff,\\
%
Senior &\sqsubseteq AcademicStaff,\\
Junior &\sqsubseteq AcademicStaff,\\
%
Professor &\sqsubseteq Senior,\\
Reader &\sqsubseteq Senior,\\
%
ProbationStaff &\sqsubseteq Junior,\\
Lecturer &\sqsubseteq Junior,\\
%
Junior &\sqsubseteq \exists mentor^-,\\
\exists mentor &\sqsubseteq Senior,\\
RA &\sqsubseteq ResearchStaff,\\
RF &\sqsubseteq ResearchStaff,\\
VisitingStaff &\sqsubseteq ResearchStaff,\\
%
Admin &\sqsubseteq NonAcademicStaff,\\
Systems &\sqsubseteq NonAcademicStaff,\\
Others &\sqsubseteq NonAcademicStaff,\\
%
UG &\sqsubseteq Course,\\
PG &\sqsubseteq Course,\\
%
UGTaught &\sqsubseteq UG,\\
UGProject &\sqsubseteq UG,\\
%
PGTaught &\sqsubseteq PG,\\
PGProject &\sqsubseteq PG,\\
%
ExternalProject &\sqsubseteq Project,\\
InternalProject &\sqsubseteq Project,\\
%
EUProject &\sqsubseteq ExternalProject,\\
UKProject &\sqsubseteq ExternalProject,\\
%
CollaborationProject &\sqsubseteq InternalProject,\\
ImpactProject &\sqsubseteq InternalProject,\\
%
AcademicStaff &\sqsubseteq \exists teaches,\\
\exists teaches^- &\sqsubseteq Course,\\
%
UGTaught &\sqsubseteq \exists assists^-,\\
PGTaught &\sqsubseteq \exists assists^-,\\
\exists assists &\sqsubseteq ResearchStaff,\\
%
\exists supervises &\sqsubseteq AcademicStaff,\\
RA &\sqsubseteq \exists supervises^-,\\
RF &\sqsubseteq \exists supervises^-,\\
%
RA &\sqsubseteq \exists worksOn,\\
RF &\sqsubseteq \exists worksOn,\\
\exists worksOn^- &\sqsubseteq Project,\\
\exists worksOn &\sqsubseteq ResearchStaff,\\
%
RA &\sqsubseteq \exists isPaidBy,\\
\exists isPaidBy^- &\sqsubseteq ExternalProject,\\
%
Project &\sqsubseteq \exists manages^-,\\
\exists manages &\sqsubseteq AcademicStaff,\\
Senior &\sqsubseteq \exists manages,\\
%
\exists supports &\sqsubseteq Systems,\\
\exists supports^- &\sqsubseteq Project,\\
%
\exists administers &\sqsubseteq Admin,\\
Course &\sqsubseteq \exists administers^-,\\
Project &\sqsubseteq \exists administers^-,\\
%
teaches &\sqsubseteq teachingWork,\\
assists &\sqsubseteq teachingWork,\\
administers &\sqsubseteq supportWork,\\
supports &\sqsubseteq supportWork,\\
isPaidBy &\sqsubseteq worksOn,\\
manages &\sqsubseteq researchWork,\\
supervises &\sqsubseteq researchWork,\\
mentor &\sqsubseteq works,\\
researchWork &\sqsubseteq works,\\
supportWork &\sqsubseteq works,\\
teachingWork &\sqsubseteq works,\\
\}
\end{align*}

Queries:
%
\begin{enumerate}
\item $q_1(x,y) = \exists u,v (Staff(x) \land Staff(y) \land supervises(x,y) \land teaches(x,u) \land teaches(y,v))$

\item $q'_1(x,y,z) = \exists u,v (Staff(x) \land Staff(y) \land supervises(x,y) \land teaches(x,u) \land teaches(y,u) \land Staff(z) \land manages(z,v) \land manages(y,v))$

\item $q_2(x,y,z) = q_1 \land Staff(z) \land administers(z,u) \land administers(z,v)$

\item $q'_2(x,y) = q_1 \land \exists z (Staff(z) \land administers(z,u) \land administers(z,v))$

\item $q_3(x,y,z) = \exists u (Staff(x) \land assists(y,u) \land teaches(x,u) \land Staff(z) \land administers(z,u))$

\item $q'_3(x,y) = \exists u,z (Staff(x) \land assists(y,u) \land teaches(x,u) \land Staff(z) \land administers(z,u))$

\item $q_4(x,y,z) = \exists u( Staff(x) \land assists(x,u) \land Staff(y) \land worksOn(y,u) \land Staff(z) \land supports(z,u)
)$

\item $q'_4(x,y) = \exists u,z( Staff(x) \land assists(x,u) \land Staff(y) \land worksOn(y,u) \land Staff(z) \land supports(z,u)
)$

\item $q_5(x,y,z) = \exists u,v(teaches (x,u) \land teaches(y,u) \land supervises(y,v) \land supervises(z,v))$

\item $q_6(x) = \exists u (Staff(x) \land works (x,u))$

\item $q_7(x,y) = \exists u,v (Staff(x) \land works (x,u) \land works (y,v) \land works (v,u))$

\item $q_8(x) = \exists u,v (Staff(x) \land works (x,u) \land works (x,v) \land works (v,u))$
\end{enumerate}

%**************

\section{Crown query}

\begin{align*}
q_n(x_1, \ldots, x_n) &= \exists y_1 \ldots \exists y_{n-1} \bigwedge_{i=1}^{n-1} (x_i R_i y_i \land x_{i+1} R_i y_i),\\
%
\mathcal{T}_n &= \{A_i \sqsubseteq \exists R_i \mid 1 \le i \le n-1 \},\\
%
q'_n &= \bigwedge_{i = 1}^{n-1} \Big(\big( (x_i = x_{i+1}) \land A_i(x_i) \big)\lor
\exists y_i (x_i R_i y_i \land x_{i+1} R_i y_i) \Big).
\end{align*}

%\begin{verbatim}
%PREFIX : <http://www.dcs.bbk.ac.uk/~michael/bbk.owl#>
%PREFIX rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#>
%select ?x ?y where {?x rdf:type :AcademicStaff.
%?x :supervises ?y.
%?y rdf:type :Staff.
%?x :teaches ?a.
%?y :teaches ?b.} \end{verbatim}

%*******************

\section{Complete ABox}

An ABox $\mathcal{A}$ is \emph{complete} for a TBox $\mathcal{T}$ if, for all individuals $a,b \in \mathsf{Ind}(\mathcal{A})$, all concepts $B$, $C$, and all roles $R$,
%
\begin{description}
\item[(1)] if $R(a,b) \in \mathcal{A}$ then $\exists R (a) \in \mathcal{A}$ and $\exists R^-(b) \in \mathcal{A}$;

\item[(2)] if $\mathcal{T} \models B \sqsubseteq C$ and $B(a) \in \mathcal{A}$, then $C(a) \in \mathcal{A}$.
\end{description}

\end{document}


\chapter{Accessing model properties}

\section{General simulation data}

\begin{itemize}

\item
\cmd{SimTime()} or \cmd{TNow()}:\\
Gets the current simulation time in seconds.

\item
\cmd{WarmUp()} or \cmd{isWarmUp()}:\\
Get 1 if the simulation is in the warm-up phase, otherwise 0.

\item
\cmd{RepeatCurrent()}:\\
Gets the current repeat number of the simulation (1-based value).

\item
\cmd{RepeatCount()}:\\
Gets the number of planned repeats of the simulation.

\item
\cmd{\$("Name")}:\\
Gets the ID of the element with the name which is enter between the quotation marks.
If there is not station with this name, the function will return -1.

\item
\cmd{\$("Key")}:\\
Returns the value from the map which can be accessed by \cm{getMapGlobal()} at scripting elements.

\end{itemize}

\section{Clients in the system}

\subsection{Number of clients in the system}

\begin{itemize}

\item
\cmd{WIP()} or \cmd{N()} or \cmd{Station()}:\\
Gets the current total number of clients in the system.

\item
\cmd{WIP\_avg()} or \cmd{Station\_avg()} or \cmd{N\_avg()} or \cmd{WIP\_Mittelwert()} or\\
\cmd{Station\_Mittelwert()} or \cmd{N\_Mittelwert()}:\\
Gets the average number of clients in the system.

\cmd{WIP\_median()} or \cmd{Station\_median()} or \cmd{N\_median()}:\\
Gets the median of the number of clients in the system.

\cmd{WIP\_quantil(p)} or \cmd{Station\_quantil(p)} or \cmd{N\_quantil(p)}:\\
Gets the quantil for the probability p of the number of clients in the system.

\item
\cmd{WIP\_min()} or \cmd{Station\_min()} or \cmd{N\_min()} or \cmd{WIP\_Minimum()} or\\
\cmd{Station\_Minimum()} or \cmd{N\_Minimum()}:\\
Gets the minimal number of clients in the system.

\item
\cmd{WIP\_max()} or \cmd{Station\_max()} or \cmd{N\_max()} or \cmd{WIP\_Maximum()} or\\
\cmd{Station\_Maximum()} or \cmd{N\_Maximum()}:\\
Gets the maximal number of clients in the system.

\item
\cmd{WIP\_var()} or \cmd{Station\_var()} or \cmd{N\_var()} or \cmd{WIP\_Varianz()} or\\
\cmd{Station\_Varianz()} or \cmd{N\_Varianz()}:\\
Gets the variation of the number of clients in the system.

\item
\cmd{WIP\_sd()} or \cmd{Station\_sd()} or \cmd{N\_sd()} or \cmd{WIP\_Standardabweichung()} or\\
\cmd{Station\_Standardabweichung()} or \cmd{N\_Standardabweichung()}:\\
Gets the standard deviation of the number of clients in the system.

\item
\cmd{WIP\_cv()} or \cmd{Station\_cv()} or \cmd{N\_cv()}:\\
Gets the coefficient of variation of the number of clients in the system.

\item
\cmd{WIP\_scv()} or \cmd{Station\_scv()} or \cmd{N\_scv()}:\\
Gets the squared coefficient of variation of the number of clients in the system.

\item
\cmd{WIP\_sk()} or \cmd{Station\_sk()} or \cmd{N\_sk()}:\\
Gets the skewness of the number of clients in the system.

\end{itemize}

\subsection{Number of waiting clients in the system}

\begin{itemize}

\item
\cmd{NQ()} or \cmd{Queue()} or \cmd{Schlange()} or \cmd{Warteschlange()}:\\
Gets the current total number of waiting clients in the system.

\item
\cmd{NQ\_avg()} or \cmd{Queue\_avg()} or \cmd{Schlange\_avg()} or \cmd{Warteschlange\_avg()} or\\
\cmd{NQ\_Mittelwert()} or \cmd{Queue\_Mittelwert()} or \cmd{Schlange\_Mittelwert()} or\\
\cmd{Warteschlange\_Mittelwert()}:\\
Gets the average number of waiting clients in the system.

\item
\cmd{NQ\_median()} or \cmd{Queue\_median()} or \cmd{Schlange\_median()} or \cmd{Warteschlange\_median()}:\\
Gets the median of the number of clients in all queues.

\item
\cmd{NQ\_quantil(p)} or \cmd{Queue\_quantil(p)} or \cmd{Schlange\_quantil(p)} or\\
\cmd{Warteschlange\_quantil(p)}:\\
Gets the quantil for the probability p of the number of clients in all queues.

\item
\cmd{NQ\_min()} or \cmd{Queue\_min()} or \cmd{Schlange\_min()} or \cmd{Warteschlange\_min()} or\\
\cmd{NQ\_Minimum()} or \cmd{Queue\_Minimum()} or \cmd{Schlange\_Minimum()} or\\
\cmd{Warteschlange\_Minimum()}:\\
Gets the minimal number of waiting clients in the system.

\item
\cmd{NQ\_max()} or \cmd{Queue\_max()} or \cmd{Schlange\_max()} or \cmd{Warteschlange\_max()} or\\
\cmd{NQ\_Maximum()} or \cmd{Queue\_Maximum()} or \cmd{Schlange\_Maximum()} or\\
\cmd{Warteschlange\_Maximum()}:\\
Gets the maximal number of waiting clients in the system.

\item
\cmd{NQ\_var()} or \cmd{Queue\_var()} or \cmd{Schlange\_var()} or \cmd{Warteschlange\_var()} or\\
\cmd{NQ\_Varianz()} or \cmd{Queue\_Varianz()} or \cmd{Schlange\_Varianz()} or\\
\cmd{Warteschlange\_Varianz()}:\\
Gets the variation of the number of waiting clients in the system.

\item
\cmd{NQ\_sd()} or \cmd{Queue\_sd()} or \cmd{Schlange\_sd()} or \cmd{Warteschlange\_sd()} or\\
\cmd{NQ\_Standardabweichung()} or \cmd{Queue\_Standardabweichung()} or\\
\cmd{Schlange\_Standardabweichung()} or \cmd{Warteschlange\_Standardabweichung()}:\\
Gets the standard deviation of the number of waiting clients in the system.

\item
\cmd{NQ\_cv()} or \cmd{Queue\_cv()} or \cmd{Schlange\_cv()} or \cmd{Warteschlange\_cv()}:\\
Gets the coefficient of variation of the number of waiting clients in the system.

\item
\cmd{NQ\_scv()} or \cmd{Queue\_scv()} or \cmd{Schlange\_scv()} or \cmd{Warteschlange\_scv()}:\\
Gets the squared coefficient of variation of the number of waiting clients in the system.

\item
\cmd{NQ\_sk()} or \cmd{Queue\_sk()} or \cmd{Schlange\_sk()} or \cmd{Warteschlange\_sk()}:\\
Gets the skewness of the number of waiting clients in the system.

\end{itemize}

\section{Clients at the stations}

\subsection{Number of clients at a station}

\begin{itemize}

\item
\cmd{WIP(id)} or \cmd{N(id)} or \cmd{Station(id)}:\\
Gets the current total number of clients at station \cm{id}.

\item
\cmd{WIP(id1;id2)} or \cmd{N(id1;id2)} or \cmd{Station(id1;id2)}:\\
Gets the current total number of clients at station \cm{id1}.
Only clients of the type, whos name appears at the source or the type assignment \cm{id2}, are respected.

\item
\cmd{WIP\_avg(id)} or \cmd{Station\_avg(id)} or \cmd{N\_avg(id)} or \cmd{WIP\_Mittelwert(id)} or\\
\cmd{Station\_Mittelwert(id)} or \cmd{N\_Mittelwert(id)}:\\
Gets the average number of clients at station \cm{id}.

\item
\cmd{WIP\_median(id)} or \cmd{Station\_median(id)} or \cmd{N\_median(id)}:\\
Gets the medium of the number of clients at station \cm{id}.

\item
\cmd{WIP\_quantil(p;id)} or \cmd{Station\_quantil(p;id)} or \cmd{N\_quantil(p;id)}:\\
Gets the quantil for the probability p of the clients at station \cm{id}.

\item
\cmd{WIP\_min(id)} or \cmd{Station\_min(id)} or \cmd{N\_min(id)} or \cmd{WIP\_Minimum(id)} or\\
\cmd{Station\_Minimum(id)} or \cmd{N\_Minimum(id)}:\\
Gets the minimal number of clients at station \cm{id}.

\item
\cmd{WIP\_max(id)} or \cmd{Station\_max(id)} or \cmd{N\_max(id)} or \cmd{WIP\_Maximum(id)} or\\
\cmd{Station\_Maximum(id)} or \cmd{N\_Maximum(id)}:\\
Gets the maximal number of clients at station \cm{id}.

\item
\cmd{WIP\_var(id)} or \cmd{Station\_var(id)} or \cmd{N\_var(id)} or \cmd{WIP\_Varianz(id)} or\\
\cmd{Station\_Varianz(id)} or \cmd{N\_Varianz(id)}:\\
Gets the variation of the number of clients at station \cm{id}.

\item
\cmd{WIP\_sd(id)} or \cmd{Station\_sd(id)} or \cmd{N\_sd(id)} or \cmd{WIP\_Standardabweichung(id)} or\\
\cmd{Station\_Standardabweichung(id)} or \cmd{N\_Standardabweichung(id)}:\\
Gets the standard deviation of the number of clients at station \cm{id}.

\item
\cmd{WIP\_cv(id)} or \cmd{Station\_cv(id)} or \cmd{N\_cv(id)}:\\
Gets the coefficient of variation of the number of clients at station \cm{id}.

\item
\cmd{WIP\_scv(id)} or \cmd{Station\_scv(id)} or \cmd{N\_scv(id)}:\\
Gets the squared coefficient of variation of the number of clients at station \cm{id}.

\item
\cmd{WIP\_sk(id)} or \cmd{Station\_sk(id)} or \cmd{N\_sk(id)}:\\
Gets the skewness of the number of clients at station \cm{id}.

\item
\cmd{WIP\_hist(id;state)} or \cmd{Station\_hist(id;state)} or \cmd{N\_hist(id;state)}:\\
Gets the fraction of time, the system was in the given \cm{state} in relation of the number of clients at stations \cm{id}.

\item
\cmd{WIP\_hist(id;stateA;stateB)} or \cmd{Station\_hist(id;stateA;stateB)} or\\
\cmd{N\_hist(id;stateA;stateB)}:\\
Gets the fraction of time, when there are more than \cm{stateA} and at most \cm{stateB} clients at station \cm{id}.

\end{itemize}

\subsection{Number of clients at the queue at a station}

\begin{itemize}

\item
\cmd{NQ(id)} or \cmd{Queue(id)} or \cmd{Schlange(id)} or \cmd{Warteschlange(id)}:\\
Gets the current total number of clients in the queue at station \cm{id}.

\item
\cmd{NQ(id;nr)} or \cmd{Queue(id;nr)} or \cmd{Schlange(id;nr)} or \cmd{Warteschlange(id;nr)}:\\
Gets the current total number of clients in the partial queue <\cm{nr} (1 based) at station \cm{id}.
(This command can only be used with "Match" elements.)

\item
\cmd{NQ\_avg(id)} or \cmd{Queue\_avg(id)} or \cmd{Schlange\_avg(id)} or \cmd{Warteschlange\_avg(id)} or\\
\cmd{NQ\_Mittelwert(id)} or \cmd{Queue\_Mittelwert(id)} or \cmd{Schlange\_Mittelwert(id)} or\\
\cmd{Warteschlange\_Mittelwert(id)}:\\
Gets the average number of clients in the queue at station \cm{id}.

\item
\cmd{NQ\_median(id)} or \cmd{Queue\_median(id)} or \cmd{Schlange\_median(id)} or\\
\cmd{Warteschlange\_median(id)}:\\
Gets the median of the number of clients in the queue at station \cm{id}.

\item
\cmd{NQ\_quantil(p;id)} or \cmd{Queue\_quantil(p;id)} or \cmd{Schlange\_quantil(p;id)} or\\
\cmd{Warteschlange\_quantil(p;id)}:\\
Gets the quantil for the probability p of the number of clients in the queue at station \cm{id}.

\item
\cmd{NQ\_min(id)} or \cmd{Queue\_min(id)} or \cmd{Schlange\_min(id)} or \cmd{Warteschlange\_min(id)} or\\
\cmd{NQ\_Minimum(id)} or \cmd{Queue\_Minimum(id)} or \cmd{Schlange\_Minimum(id)} or\\
\cmd{Warteschlange\_Minimum(id)}:\\
Gets the minimal number of clients in the queue at station \cm{id}.

\item
\cmd{NQ\_max(id)} or \cmd{Queue\_max(id)} or \cmd{Schlange\_max(id)} or \cmd{Warteschlange\_max(id)} or\\
\cmd{NQ\_Maximum(id)} or \cmd{Queue\_Maximum(id)} or \cmd{Schlange\_Maximum(id)} or\\
\cmd{Warteschlange\_Maximum(id)}:\\
Gets the maximal number of clients in the queue at station \cm{id}.

\item
\cmd{NQ\_var(id)} or \cmd{Queue\_var(id)} or \cmd{Schlange\_var(id)} or \cmd{Warteschlange\_var(id)} or\\
\cmd{NQ\_Varianz(id)} or \cmd{Queue\_Varianz(id)} or \cmd{Schlange\_Varianz(id)} or\\
\cmd{Warteschlange\_Varianz(id)}:\\
Gets the variation of the number of clients in the queue at station \cm{id}.

\item
\cmd{NQ\_sd(id)} or \cmd{Queue\_sd(id)} or \cmd{Schlange\_sd(id)} or \cmd{Warteschlange\_sd(id)} or\\
\cmd{NQ\_Standardabweichung(id)} or \cmd{Queue\_Standardabweichung(id)} or\\
\cmd{Schlange\_Standardabweichung(id)} or \cmd{Warteschlange\_Standardabweichung(id)}:\\
Gets the standard deviation of the number of clients in the queue at station \cm{id}.

\item
\cmd{NQ\_cv(id)} or \cmd{Queue\_cv(id)} or \cmd{Schlange\_cv(id)} or \cmd{Warteschlange\_cv(id)}:\\
Gets the coefficient of variation of the number of clients in the queue at station \cm{id}.

\item
\cmd{NQ\_scv(id)} or \cmd{Queue\_scv(id)} or \cmd{Schlange\_scv(id)} or \cmd{Warteschlange\_scv(id)}:\\
Gets the squared coefficient of variation of the number of clients in the queue at station \cm{id}.

\item
\cmd{NQ\_sk(id)} or \cmd{Queue\_sk(id)} or \cmd{Schlange\_sk(id)} or \cmd{Warteschlange\_sk(id)}:\\
Gets the skewness of the number of clients in the queue at station \cm{id}.

\item
\cmd{NQ\_hist(id;state)} or \cmd{Queue\_hist(id;state)} or \cmd{Schlange\_hist(id;state)} or\\ \cmd{Warteschlange\_hist(id;state)}:\\
Gets the fraction of time, when there are \cm{state} clients in the queue at station \cm{id}.

\item
\cmd{NQ\_hist(id;stateA;stateB)} or \cmd{Queue\_hist(id;stateA;stateB)} or\\ \cmd{Schlange\_hist(id;stateA;stateB)} or \cmd{Warteschlange\_hist(id;stateA;stateB)}:\\
Gets the fraction of time, when there are more than \cm{stateA} and at most \cm{stateB} clients in the queue at station \cm{id}.

\end{itemize}

\subsection{Number of clients just being served at a station}

\begin{itemize}

\item
\cmd{Process(id)}:\\
Gets the current number of clients just being served at station \cm{id}.

\end{itemize}

\subsection{Number of arrivals and departures at a station}

\begin{itemize}

\item
\cmd{NumberIn(id)} or \cmd{CountIn(id)}:\\
Gets the number of client arrivals at station \cm{id}.

\item
\cmd{NumberOut(id)} or \cmd{CountOut(id)}:\\
Gets the number of client departures at station \cm{id}.

\end{itemize}

\section{Clients in system by client type}

\subsection{Number of clients in the system by client type}

\begin{itemize}

\item
\cmd{WIP(id)} or \cmd{N(id)} or \cmd{Station(id)}:\\
Gets the current total number of clients, whos name appears at the source or the type assignment \cm{id}.

\item
\cmd{WIP\_avg(id)} or \cmd{Station\_avg(id)} or \cmd{N\_avg(id)} or \cmd{WIP\_Mittelwert(id)} or\\
\cmd{Station\_Mittelwert(id)} or \cmd{N\_Mittelwert(id)}:\\
Gets the average number of clients, whos name appears at the source or the type assignment \cm{id}.

\item
\cmd{WIP\_median(id)} or \cmd{Station\_median(id)} or \cmd{N\_median(id)}:\\
Gets the median of the number of clients, whos name appears at the source or the type assignment \cm{id}, in the system.

\item
\cmd{WIP\_quantil(p;id)} or \cmd{Station\_quantil(p;id)} or \cmd{N\_quantil(p;id)}:\\
Gets the quantil for the probability p of the number of clients, whos name appears at the source or the type assignment \cm{id}, in the system.

\item
\cmd{WIP\_min(id)} or \cmd{Station\_min(id)} or \cmd{N\_min(id)} or \cmd{WIP\_Minimum(id)} or\\
\cmd{Station\_Minimum(id)} or \cmd{N\_Minimum(id)}:\\
Gets the minimal number of clients, whos name appears at the source or the type assignment \cm{id}.

\item
\cmd{WIP\_max(id)} or \cmd{Station\_max(id)} or \cmd{N\_max(id)} or \cmd{WIP\_Maximum(id)} or\\
\cmd{Station\_Maximum(id)} or \cmd{N\_Maximum(id)}:\\
Gets the maximal number of clients, whos name appears at the source or the type assignment \cm{id}.

\item
\cmd{WIP\_var(id)} or \cmd{Station\_var(id)} or \cmd{N\_var(id)} or \cmd{WIP\_Varianz(id)} or\\
\cmd{Station\_Varianz(id)} or \cmd{N\_Varianz(id)}:\\
Gets the variation of the number of clients, whos name appears at the source or the type assignment \cm{id}.

\item
\cmd{WIP\_sd(id)} or \cmd{Station\_sd(id)} or \cmd{N\_sd(id)} or \cmd{WIP\_Standardabweichung(id)} or\\
\cmd{Station\_Standardabweichung(id)} or \cmd{N\_Standardabweichung(id)}:\\
Gets the standard deviation of the number of clients, whos name appears at the source or the type assignment \cm{id}.

\item
\cmd{WIP\_cv(id)} or \cmd{Station\_cv(id)} or \cmd{N\_cv(id)}:\\
Gets the coefficient of variation of the number of clients, whos name appears at the source or the type assignment \cm{id}.

\item
\cmd{WIP\_scv(id)} or \cmd{Station\_scv(id)} or \cmd{N\_scv(id)}:\\
Gets the squared coefficient of variation of the number of clients, whos name appears at the source or the type assignment \cm{id}.

\item
\cmd{WIP\_sk(id)} or \cmd{Station\_sk(id)} or \cmd{N\_sk(id)}:\\
Gets the skewness of the number of clients, whos name appears at the source or the type assignment \cm{id}.

\item
\cmd{WIP\_hist(id;state)} or \cmd{Station\_hist(id;state)} or \cmd{N\_hist(id;state)}:\\
Gets the fraction of time, the system was in the given \cm{state} in relation of the number of clients, whos name appears at the source or the type assignment \cm{id}.

\item
\cmd{WIP\_hist(id;stateA;stateB)} or \cmd{Station\_hist(id;stateA;stateB)} or\\
\cmd{N\_hist(id;stateA;stateB)}:\\
Gets the fraction of time, when there are more than \cm{stateA} and at most \cm{stateB} clients, whos name appears at the source or the type assignment \cm{id}, in the system.

\end{itemize}

\subsection{Number of waiting clients in the system by client type}

\begin{itemize}

\item
\cmd{NQ(id)} or \cmd{Queue(id)} or \cmd{Schlange(id)} or \cmd{Warteschlange(id)}:\\
Gets the current total number of waiting clients, whos name appears at the source or the type assignment \cm{id}.

\item
\cmd{NQ\_avg(id)} or \cmd{Queue\_avg(id)} or \cmd{Schlange\_avg(id)} or \cmd{Warteschlange\_avg(id)} or\\
\cmd{NQ\_Mittelwert(id)} or \cmd{Queue\_Mittelwert(id)} or \cmd{Schlange\_Mittelwert(id)} or\\
\cmd{Warteschlange\_Mittelwert(id)}:\\
Gets the average number of waiting clients, whos name appears at the source or the type assignment \cm{id}.

\item
\cmd{NQ\_median(id)} or \cmd{Queue\_median(id)} or \cmd{Schlange\_median(id)} or\\
\cmd{Warteschlange\_median(id)}:\\
Gets the median of the number of waiting clients, whos name appears at the source or the type assignment id, in the system.

\item
\cmd{NQ\_quantil(p;id)} or \cmd{Queue\_quantil(p;id)} or \cmd{Schlange\_quantil(p;id)} or\\
\cmd{Warteschlange\_quantil(p;id)}:\\
Gets the quantil for the probability p of the number of waiting clients, whos name appears at the source or the type assignment id, in the system.

\item
\cmd{NQ\_min(id)} or \cmd{Queue\_min(id)} or \cmd{Schlange\_min(id)} or \cmd{Warteschlange\_min(id)} or\\
\cmd{NQ\_Minimum(id)} or \cmd{Queue\_Minimum(id)} or \cmd{Schlange\_Minimum(id)} or\\
\cmd{Warteschlange\_Minimum(id)}:\\
Gets the minimal number of waiting clients, whos name appears at the source or the type assignment \cm{id}.

\item
\cmd{NQ\_max(id)} or \cmd{Queue\_max(id)} or \cmd{Schlange\_max(id)} or \cmd{Warteschlange\_max(id)} or\\
\cmd{NQ\_Maximum(id)} or \cmd{Queue\_Maximum(id)} or \cmd{Schlange\_Maximum(id)} or\\
\cmd{Warteschlange\_Maximum(id)}:\\
Gets the maximal number of waiting clients, whos name appears at the source or the type assignment \cm{id}.

\item
\cmd{NQ\_var(id)} or \cmd{Queue\_var(id)} or \cmd{Schlange\_var(id)} or \cmd{Warteschlange\_var(id)} or\\
\cmd{NQ\_Varianz(id)} or \cmd{Queue\_Varianz(id)} or \cmd{Schlange\_Varianz(id)} or\\
\cmd{Warteschlange\_Varianz(id)}:\\
Gets the variation of the number of waiting clients, whos name appears at the source or the type assignment \cm{id}.

\item
\cmd{NQ\_sd(id)} or \cmd{Queue\_sd(id)} or \cmd{Schlange\_sd(id)} or \cmd{Warteschlange\_sd(id)} or\\
\cmd{NQ\_Standardabweichung(id)} or \cmd{Queue\_Standardabweichung(id)} or\\
\cmd{Schlange\_Standardabweichung(id)} or \cmd{Warteschlange\_Standardabweichung(id)}:\\
Gets the standard deviation of the number of waiting clients, whos name appears at the source or the type assignment \cm{id}.

\item
\cmd{NQ\_cv(id)} or \cmd{Queue\_cv(id)} or \cmd{Schlange\_cv(id)} or \cmd{Warteschlange\_cv(id)}:\\
Gets the coefficient of variation of the number of waiting clients, whos name appears at the source or the type assignment \cm{id}.

\item
\cmd{NQ\_scv(id)} or \cmd{Queue\_scv(id)} or \cmd{Schlange\_scv(id)} or \cmd{Warteschlange\_scv(id)}:\\
Gets the squared coefficient of variation of the number of waiting clients, whos name appears at the source or the type assignment \cm{id}.

\item
\cmd{NQ\_sk(id)} or \cmd{Queue\_sk(id)} or \cmd{Schlange\_sk(id)} or \cmd{Warteschlange\_sk(id)}:\\
Gets the skewness of the number of waiting clients, whos name appears at the source or the type assignment \cm{id}.

\item
\cmd{NQ\_hist(id;state)} or \cmd{Queue\_hist(id;state)} or \cmd{Schlange\_hist(id;state)} or\\ \cmd{Warteschlange\_hist(id;state)}:\\
Gets the fraction of time, when there are \cm{state} waiting clients, whos name appears at the source or the type assignment \cm{id}, are in the system.

\item
\cmd{NQ\_hist(id;stateA;stateB)} or \cmd{Queue\_hist(id;stateA;stateB)} or\\ \cmd{Schlange\_hist(id;stateA;stateB)} or \cmd{Warteschlange\_hist(id;stateA;stateB)}:\\
Gets the fraction of time, when there are more than \cm{stateA} and at most \cm{stateB} waiting clients, whos name appears at the source or the type assignment \cm{id}, in the system.

\end{itemize}

\section{Counter and throughput}

\begin{itemize}

\item
\cmd{Counter(id)} or \cmd{Value(id)}:\\
Gets the value of the counter at station \cm{id}.\\
(Can only be applied on "Difference counter", "Counter" and "Throughput" elements.)

\item
\cmd{Anteil(id)} or \cmd{Part(id)}:\\
Gets the share of the counter value in the counter group.\\
(Can only be applied on "Counter" elements.)

\end{itemize}

\section{Waiting times}

\subsection{Waiting times at a station}

\begin{itemize}

\item \cmd{WaitingTime\_sum(id)} or \cmd{WaitingTime\_gesamt(id)} or \cmd{WaitingTime\_summe(id)}:\\
Gets the sum of the waiting times at the station \cm{id} (in seconds).

\item
\cmd{WaitingTime\_avg(id)} or \cmd{WaitingTime\_average(id)} or \cmd{WaitingTime\_Mittelwert(id)}:\\
Gets the average waiting time of the clients at station \cm{id} (in seconds).

\item
\cmd{WaitingTime\_median(id)}:\\
Gets the median of the waiting times of the clients at station \cm{id} (in seconds).

\item
\cmd{WaitingTime\_quantil(p;id)}:\\
Gets the quantil for the probability p of the waiting times of the clients at station \cm{id} (in seconds).

\item
\cmd{WaitingTime\_min(id)} or \cmd{WaitingTime\_Minimum(id)}:\\
Gets the minimum waiting time of the clients at station \cm{id} (in seconds).

\item
\cmd{WaitingTime\_max(id)} or \cmd{WaitingTime\_Maximum(id)}:\\
Gets the maximum waiting time of the clients at station \cm{id} (in seconds).

\item
\cmd{WaitingTime\_var(id)} or \cmd{WaitingTime\_Varianz(id)}:\\
Gets the variation of the waiting times of the clients at station \cm{id} (based on seconds).

\item
\cmd{WaitingTime\_sd(id)} or \cmd{WaitingTime\_Standardabweichung(id)}:\\
Gets the standard deviation of the waiting times of the clients at station \cm{id} (based on seconds).

\item
\cmd{WaitingTime\_cv(id)}:\\
Gets the coefficient of variation of the waiting times of the clients at station \cm{id}.

\item
\cmd{WaitingTime\_scv(id)}:\\
Gets the squared coefficient of variation of the waiting times of the clients at station \cm{id}.

\item
\cmd{WaitingTime\_sk(id)}:\\
Gets the skewness of the waiting times of the clients at station \cm{id}.

\item
\cmd{WaitingTime\_hist(id;time)}:\\
Gets the fraction of clients for which the waiting time at stations \cm{id} was \cm{time} seconds.

\item
\cmd{WaitingTime\_hist(id;timeA;timeB)}:\\
Gets the fraction of clients for which the waiting time at stations \cm{id} was more than \cm{timeA} and at most \cm{timeB} seconds.

\end{itemize}

\subsection{Waiting times over all client types}

\begin{itemize}

\item
\cmd{WaitingTime\_avg()} or \cmd{WaitingTime\_average()} or \cmd{WaitingTime\_Mittelwert()}:\\
Get the average waiting time over all clients (in seconds).

\item
\cmd{WaitingTime\_median()}:\\
Get the median of the waiting times over all clients (in seconds).

\item
\cmd{WaitingTime\_quantil(p)}:\\
Gets the quantil for the probability p of the waiting times over all clients (in seconds).

\item
\cmd{WaitingTime\_min()} or \cmd{WaitingTime\_Minimum()}:\\
Get the minimum waiting time over all clients (in seconds).

\item
\cmd{WaitingTime\_max()} or \cmd{WaitingTime\_Maximum()}:\\
Get the maximum waiting time over all clients (in seconds).

\item
\cmd{WaitingTime\_var()} or \cmd{WaitingTime\_Varianz()}:\\
Gets the variation of the waiting times over all clients (based on seconds).

\item
\cmd{WaitingTime\_sd()} or \cmd{WaitingTime\_Standardabweichung()}:\\
Gets the standard deviation of the waiting times over all clients (based on seconds).

\item
\cmd{WaitingTime\_cv()}:\\
Gets the coefficient of variation of the waiting times over all clients.

\item
\cmd{WaitingTime\_scv()}:\\
Gets the squared coefficient of variation of the waiting times over all clients.

\item
\cmd{WaitingTime\_sk()}:\\
Gets the skewness of the waiting times over all clients.

\item
\cmd{WaitingTime\_histAll(time)}:\\
Gets the fraction of clients for which the waiting time was \cm{time} seconds.

\item
\cmd{WaitingTime\_histAll(timeA;timeB)}:\\
Gets the fraction of clients for which the waiting time was more than \cm{timeA} and at most \cm{timeB} seconds.

\end{itemize}

\subsection{Waiting times for a specific client type}

\begin{itemize}

\item
\cmd{WaitingTime\_sum(id)} or \cmd{WaitingTime\_gesamt(id)} or \cmd{WaitingTime\_summe(id)}:\
Gets the sum of the waiting times of the clients, whos name appears at the source or the type assignment \cm{id} (in seconds).

\item
\cmd{WaitingTime\_avg(id)} or \cmd{WaitingTime\_average(id)} or \cmd{WaitingTime\_Mittelwert(id)}:\\
Gets the average waiting time of the clients, whos name appears at the source or the type assignment \cm{id} (in seconds).

\item
\cmd{WaitingTime\_median(id)}:\\
Gets the median of the waiting times of the clients, whos name appears at the source or the type assignment \cm{id} (in seconds).

\item
\cmd{WaitingTime\_quantil(p;id)}:\\
Gets the quantil for the probability p of the waiting times of the clients, whos name appears at the source or the type assignment \cm{id} (in seconds).

\item
\cmd{WaitingTime\_min(id)} or \cmd{WaitingTime\_Minimum(id)}:\\
Gets the minimum waiting time of the clients, whos name appears at the source or the type assignment \cm{id} (in seconds).

\item
\cmd{WaitingTime\_max(id)} or \cmd{WaitingTime\_Maximum(id)}:\\
Gets the maximum waiting time of the clients, whos name appears at the source or the type assignment \cm{id} (in seconds).

\item
\cmd{WaitingTime\_var(id)} or \cmd{WaitingTime\_Varianz(id)}:\\
Gets the variation of the waiting times of the clients, whos name appears at the source or the type assignment \cm{id} (based on seconds).

\item
\cmd{WaitingTime\_sd(id)} or \cmd{WaitingTime\_Standardabweichung(id)}:\\
Gets the standard deviation of the waiting times of the clients, whos name appears at the source or the type assignment \cm{id} (based on seconds).

\item
\cmd{WaitingTime\_cv(id)}:\\
Gets the coefficient of variation of the waiting times of the clients, whos name appears at the source or the type assignment \cm{id}.

\item
\cmd{WaitingTime\_scv(id)}:\\
Gets the squared coefficient of variation of the waiting times of the clients, whos name appears at the source or the type assignment \cm{id}.

\item
\cmd{WaitingTime\_sk(id)}:\\
Gets the skewness of the waiting times of the clients, whos name appears at the source or the type assignment \cm{id}.

\end{itemize}

\section{Transfer times}

\subsection{Transfer times at a station}

\begin{itemize}

\item
\cmd{TransferTime\_sum(id)} or \cmd{TransferTime\_gesamt(id)} or \cmd{TransferTime\_summe(id)}:\\
Gets the sum of the transfer times at the station \cm{id} (in seconds).

\item
\cmd{TransferTime\_avg(id)} or \cmd{TransferTime\_average(id)} or\\
\cmd{TransferTime\_Mittelwert(id)}:\\
Gets the average transfer time of the clients at station \cm{id} (in seconds).

\item
\cmd{TransferTime\_median(id)}:\\
Gets the median of the transfer times of the clients at station \cm{id} (in seconds).

\item
\cmd{TransferTime\_quantil(p;id)}:\\
Gets the quantil for the probability p of the transfer times of the clients at station \cm{id} (in seconds).

\item
\cmd{TransferTime\_min(id)} or \cmd{TransferTime\_Minimum(id)}:\\
Gets the minimum transfer time of the clients at station \cm{id} (in seconds).

\item
\cmd{TransferTime\_max(id)} or \cmd{TransferTime\_Maximum(id)}:\\
Gets the maximum transfer time of the clients at station \cm{id} (in seconds).

\item
\cmd{TransferTime\_var(id)} or \cmd{TransferTime\_Varianz(id)}:\\
Gets the variation of the transfer times of the clients at station \cm{id} (based on seconds).

\item
\cmd{TransferTime\_sd(id)} or \cmd{TransferTime\_Standardabweichung(id)}:\\
Gets the standard deviation of the transfer times of the clients at station \cm{id} (based on seconds).

\item
\cmd{TransferTime\_cv(id)}:\\
Gets the coefficient of variation of the transfer times of the clients at station \cm{id}.

\item
\cmd{TransferTime\_scv(id)}:\\
Gets the squared coefficient of variation of the transfer times of the clients at station \cm{id}.

\item
\cmd{TransferTime\_sk(id)}:\\
Gets the skewness of the transfer times of the clients at station \cm{id}.

\item
\cmd{TransferTime\_hist(id;time)}:\\
Gets the fraction of clients for which the transfer time at stations \cm{id} was \cm{time} seconds.

\item
\cmd{TransferTime\_hist(id;timeA;timeB)}:\\
Gets the fraction of clients for which the transfer time at stations \cm{id} was more than \cm{timeA} and at most \cm{timeB} seconds.

\end{itemize}

\subsection{Transfer times over all client types}

\begin{itemize}

\item
\cmd{TransferTime\_avg()} or \cmd{TransferTime\_average()} or \cmd{TransferTime\_Mittelwert()}:\\
Get the average waiting time over all clients (in seconds).

\item
\cmd{TransferTime\_median()}:\\
Get the median of the transfer times over all clients (in seconds).

\item
\cmd{TransferTime\_quantil(p)}:\\
Gets the quantil for the probability p of the transfer times over all clients (in seconds).

\item
\cmd{TransferTime\_min()} or \cmd{TransferTime\_Minimum()}:\\
Get the minimum transfer time over all clients (in seconds).

\item
\cmd{TransferTime\_max()} or \cmd{TransferTime\_Maximum()}:\\
Get the maximum transfer time over all clients (in seconds).

\item
\cmd{TransferTime\_var()} or \cmd{TransferTime\_Varianz()}:\\
Gets the variation of the transfer times over all clients (based on seconds).

\item
\cmd{TransferTime\_sd()} or \cmd{TransferTime\_Standardabweichung()}:\\
Gets the standard deviation of the transfer times over all clients (based on seconds).

\item
\cmd{TransferTime\_cv()}:\\
Gets the coefficient of variation of the transfer times over all clients.

\item
\cmd{TransferTime\_scv()}:\\
Gets the squared coefficient of variation of the transfer times over all clients.

\item
\cmd{TransferTime\_sk()}:\\
Gets the skewness of the transfer times over all clients.

\item
\cmd{TransferTime\_histAll(time)}:\\
Gets the fraction of clients for which the transfer time was \cm{time} seconds.

\item
\cmd{TransferTime\_histAll(timeA;timeB)}:\\
Gets the fraction of clients for which the transfer time was more than \cm{timeA} and at most \cm{timeB} seconds.

\end{itemize}

\subsection{Transfer times for a specific client type}

\begin{itemize}

\item
\cmd{TransferTime\_sum(id)} or \cmd{TransferTime\_gesamt(id)} or \cmd{TransferTime\_summe(id)}:\\
Gets the sum of the transfer times of the clients, whos name appears at the source or the type assignment \cm{id} (in seconds).

\item
\cmd{TransferTime\_avg(id)} or \cmd{TransferTime\_average(id)} or\\
\cmd{TransferTime\_Mittelwert(id)}:\\
Gets the average transfer time of the clients, whos name appears at the source or the type assignment \cm{id} (in seconds).

\item
\cmd{TransferTime\_median(id)}:\\
Gets the median of the transfer times of the clients, whos name appears at the source or the type assignment \cm{id} (in seconds).

\item
\cmd{TransferTime\_quantil(p;id)}:\\
Gets the quantil for the probability p of the transfer times of the clients, whos name appears at the source or the type assignment \cm{id} (in seconds).

\item
\cmd{TransferTime\_min(id)} or \cmd{TransferTime\_Minimum(id)}:\\
Gets the minimum transfer time of the clients, whos name appears at the source or the type assignment \cm{id} (in seconds).

\item
\cmd{TransferTime\_max(id)} or \cmd{TransferTime\_Maximum(id)}:\\
Gets the maximum transfer time of the clients, whos name appears at the source or the type assignment \cm{id} (in seconds).

\item
\cmd{TransferTime\_var(id)} or \cmd{TransferTime\_Varianz(id)}:\\
Gets the variation of the transfer times of the clients, whos name appears at the source or the type assignment \cm{id} (based on seconds).

\item
\cmd{TransferTime\_sd(id)} or \cmd{TransferTime\_Standardabweichung(id)}:\\
Gets the standard deviation of the transfer times of the clients, whos name appears at the source or the type assignment \cm{id} (based on seconds).

\item
\cmd{TransferTime\_cv(id)}:\\
Gets the coefficient of variation of the transfer times of the clients, whos name appears at the source or the type assignment \cm{id}.

\item
\cmd{TransferTime\_scv(id)}:\\
Gets the squared coefficient of variation of the transfer times of the clients, whos name appears at the source or the type assignment \cm{id}.

\item
\cmd{TransferTime\_sk(id)}:\\
Gets the skewness of the transfer times of the clients, whos name appears at the source or the type assignment \cm{id}.

\end{itemize}

\section{Process times}

\subsection{Process times at a station}

\begin{itemize}

\item
\cmd{ProcessTime\_sum(id)} or \cmd{ProcessTime\_gesamt(id)} or \cmd{ProcessTime\_summe(id)}:\\
Gets the sum of the process times at the station \cm{id} (in seconds).

\item
\cmd{ProcessTime\_avg(id)} or \cmd{ProcessTime\_average(id)} or \cmd{ProcessTime\_Mittelwert(id)}:\\
Gets the average process time of the clients at station \cm{id} (in seconds).

\item
\cmd{ProcessTime\_median(id)}:\\
Gets the median of the process times of the clients at station \cm{id} (in seconds).

\item
\cmd{ProcessTime\_quantil(p;id)}:\\
Gets the quantil for the probability p of the process times of the clients at station \cm{id} (in seconds).

\item
\cmd{ProcessTime\_min(id)} or \cmd{ProcessTime\_Minimum(id)}:\\
Gets the minimum process time of the clients at station \cm{id} (in seconds).

\item
\cmd{ProcessTime\_max(id)} or \cmd{ProcessTime\_Maximum(id)}:\\
Gets the maximum process time of the clients at station \cm{id} (in seconds).

\item
\cmd{ProcessTime\_var(id)} or \cmd{ProcessTime\_Varianz(id)}:\\
Gets the variation of the process times of the clients at station \cm{id} (based on seconds).

\item
\cmd{ProcessTime\_sd(id)} or \cmd{ProcessTime\_Standardabweichung(id)}:\\
Gets the standard deviation of the process times of the clients at station \cm{id} (based on seconds).

\item
\cmd{ProcessTime\_cv(id)}:\\
Gets the coefficient of variation of the process times of the clients at station \cm{id}.

\item
\cmd{ProcessTime\_scv(id)}:\\
Gets the squared coefficient of variation of the process times of the clients at station \cm{id}.

\item
\cmd{ProcessTime\_sk(id)}:\\
Gets the skewness of the process times of the clients at station \cm{id}.

\item
\cmd{ProcessTime\_hist(id;time)}:\\
Gets the fraction of clients for which the process time at stations \cm{id} was \cm{time} seconds.

\item
\cmd{ProcessTime\_hist(id;timeA;timeB)}:\\
Gets the fraction of clients for which the process time at stations \cm{id} was more than \cm{timeA} and at most \cm{timeB} seconds.

\end{itemize}

\subsection{Process times over all client types}

\begin{itemize}

\item
\cmd{ProcessTime\_avg()} or \cmd{ProcessTime\_average()} or \cmd{ProcessTime\_Mittelwert()}:\\
Get the average process time over all clients (in seconds).

\item
\cmd{ProcessTime\_median()}:\\
Get the median of the process times over all clients (in seconds).

\item
\cmd{ProcessTime\_quantil(p)}:\\
Gets the quantil for the probability p of the process times over all clients (in seconds).

\item
\cmd{ProcessTime\_min()} or \cmd{ProcessTime\_Minimum()}:\\
Get the minimum process time over all clients (in seconds).

\item
\cmd{ProcessTime\_max()} or \cmd{ProcessTime\_Maximum()}:\\
Get the maximum process time over all clients (in seconds).

\item
\cmd{ProcessTime\_var()} or \cmd{ProcessTime\_Varianz()}:\\
Gets the variation of the process times over all clients (based on seconds).

\item
\cmd{ProcessTime\_sd()} or \cmd{ProcessTime\_Standardabweichung()}:\\
Gets the standard deviation of the process times over all clients (based on seconds).

\item
\cmd{ProcessTime\_cv()}:\\
Gets the coefficient of variation of the process times over all clients.

\item
\cmd{ProcessTime\_scv()}:\\
Gets the squared coefficient of variation of the process times over all clients.

\item
\cmd{ProcessTime\_sk()}:\\
Gets the skewness of the process times over all clients.

\item
\cmd{ProcessTime\_histAll(time)}:\\
Gets the fraction of clients for which the process \cm{time} was time seconds.

\item
\cmd{ProcessTime\_histAll(timeA;timeB)}:\\
Gets the fraction of clients for which the process time was more than \cm{timeA} and at most \cm{timeB} seconds.

\end{itemize}

\subsection{Process times for a specific client type}

\begin{itemize}

\item
\cmd{ProcessTime\_sum(id)} or \cmd{ProcessTime\_gesamt(id)} or \cmd{ProcessTime\_summe(id)}:\\
Gets the sum of the process times of the clients, whos name appears at the source or the type assignment \cm{id} (in seconds).

\item
\cmd{ProcessTime\_avg(id)} or \cmd{ProcessTime\_average(id)} or \cmd{ProcessTime\_Mittelwert(id)}:\\
Gets the average process time of the clients, whos name appears at the source or the type assignment \cm{id} (in seconds).

\item
\cmd{ProcessTime\_median(id)}:\\
Gets the median of the process times of the clients, whos name appears at the source or the type assignment \cm{id} (in seconds).

\item
\cmd{ProcessTime\_quantil(p;id)}:\\
Gets the quantil for the probability p of the process times of the clients, whos name appears at the source or the type assignment \cm{id} (in seconds).

\item
\cmd{ProcessTime\_min(id)} or \cmd{ProcessTime\_Minimum(id)}:\\
Gets the minimum process time of the clients, whos name appears at the source or the type assignment \cm{id} (in seconds).

\item
\cmd{ProcessTime\_max(id)} or \cmd{ProcessTime\_Maximum(id)}:\\
Gets the maximum process time of the clients, whos name appears at the source or the type assignment \cm{id} (in seconds).

\item
\cmd{ProcessTime\_var(id)} or \cmd{ProcessTime\_Varianz(id)}:\\
Gets the variation of the process times of the clients, whos name appears at the source or the type assignment \cm{id} (based on seconds).

\item
\cmd{ProcessTime\_sd(id)} or \cmd{ProcessTime\_Standardabweichung(id)}:\\
Gets the standard deviation of the process times of the clients, whos name appears at the source or the type assignment \cm{id} (based on seconds).

\item
\cmd{ProcessTime\_cv(id)}:\\
Gets the coefficient of variation of the process times of the clients, whos name appears at the source or the type assignment \cm{id}.

\item
\cmd{ProcessTime\_scv(id)}:\\
Gets the squared coefficient of variation of the process times of the clients, whos name appears at the source or the type assignment \cm{id}.

\item
\cmd{ProcessTime\_sk(id)}:\\
Gets the skewness of the process times of the clients, whos name appears at the source or the type assignment \cm{id}.

\end{itemize}

\section{Residence times}

\subsection{Residence times at a station}

\begin{itemize}

\item \cmd{ResidenceTime\_sum(id)} or \cmd{ResidenceTime\_gesamt(id)} or \cmd{ResidenceTime\_summe(id)}:\\
Gets the sum of the residence times at the station \cm{id} (in seconds).

\item
\cmd{ResidenceTime\_avg(id)} or \cmd{ResidenceTime\_average(id)} or\\ \cmd{ResidenceTime\_Mittelwert(id)}:\\
Gets the average residence time of the clients at station \cm{id} (in seconds).

\item
\cmd{ResidenceTime\_median(id)}:\\
Gets the median of the residence times of the clients at station \cm{id} (in seconds).

\item
\cmd{ResidenceTime\_quantil(p;id)}:\\
Gets the quantil for the probability p of the residence times of the clients at station \cm{id} (in seconds).

\item
\cmd{ResidenceTime\_min(id)} or \cmd{ResidenceTime\_Minimum(id)}:\\
Gets the minimum residence time of the clients at station \cm{id} (in seconds).

\item
\cmd{ResidenceTime\_max(id)} or \cmd{ResidenceTime\_Maximum(id)}:\\
Gets the maximum residence time of the clients at station \cm{id} (in seconds).

\item
\cmd{ResidenceTime\_var(id)} or \cmd{ResidenceTime\_Varianz(id)}:\\
Gets the variation of the residence times of the clients at station \cm{id} (based on seconds).

\item
\cmd{ResidenceTime\_sd(id)} or \cmd{ResidenceTime\_Standardabweichung(id)}:\\
Gets the standard deviation of the residence times of the clients at station \cm{id} (based on seconds).

\item
\cmd{ResidenceTime\_cv(id)}:\\
Gets the coefficient of variation of the residence times of the clients at station \cm{id}.

\item
\cmd{ResidenceTime\_scv(id)}:\\
Gets the squared coefficient of variation of the residence times of the clients at station \cm{id}.

\item
\cmd{ResidenceTime\_sk(id)}:\\
Gets the skewness of the residence times of the clients at station \cm{id}.

\item
\cmd{ResidenceTime\_hist(id;time)}:\\
Gets the fraction of clients for which the residence time at stations \cm{id} was \cm{time} seconds.

\item
\cmd{ResidenceTime\_hist(id;timeA;timeB)}:\\
Gets the fraction of clients for which the residence time at stations \cm{id} was more than \cm{timeA} and at most \cm{timeB} seconds.

\end{itemize}

\subsection{Residence times over all client types}

\begin{itemize}

\item
\cmd{ResidenceTime\_avg()} or \cmd{ResidenceTime\_average()} or \cmd{ResidenceTime\_Mittelwert()}:\\
Get the average residence time over all clients (in seconds).

\item
\cmd{ResidenceTime\_median()}:\\
Get the median of the residence times over all clients (in seconds).

\item
\cmd{ResidenceTime\_quantil(p)}:\\
Gets the quantil for the probability p of the residence times over all clients (in seconds).

\item
\cmd{ResidenceTime\_min()} or \cmd{ResidenceTime\_Minimum()}:\\
Get the minimum residence time over all clients (in seconds).

\item
\cmd{ResidenceTime\_max()} or \cmd{ResidenceTime\_Maximum()}:\\
Get the maximum residence time over all clients (in seconds).

\item
\cmd{ResidenceTime\_var()} or \cmd{ResidenceTime\_Varianz()}:\\
Gets the variation of the residence times over all clients (based on seconds).

\item
\cmd{ResidenceTime\_sd()} or \cmd{ResidenceTime\_Standardabweichung()}:\\
Gets the standard deviation of the residence times over all clients (based on seconds).

\item
\cmd{ResidenceTime\_cv()}:\\
Gets the coefficient of variation of the residence times over all clients.

\item
\cmd{ResidenceTime\_scv()}:\\
Gets the squared coefficient of variation of the residence times over all clients.

\item
\cmd{ResidenceTime\_sk()}:\\
Gets the skewness of the residence times over all clients.

\item
\cmd{ResidenceTime\_histAll(time)}:\\
Gets the fraction of clients for which the residence time was \cm{time} seconds.

\item
\cmd{ResidenceTime\_histAll(timeA;timeB)}:\\
Gets the fraction of clients for which the residence time was more than \cm{timeA} and at most \cm{timeB} seconds.

\end{itemize}

\subsection{Residence times for a specific client type}

\begin{itemize}

\item
\cmd{ResidenceTime\_sum(id)} or \cmd{ResidenceTime\_gesamt(id)} or \cmd{ResidenceTime\_summe(id)}:\
Gets the sum of the residence times of the clients, whos name appears at the source or the type assignment \cm{id} (in seconds).

\item
\cmd{ResidenceTime\_avg(id)} or \cmd{ResidenceTime\_average(id)} or\\ \cmd{ResidenceTime\_Mittelwert(id)}:\\
Gets the average residence time of the clients, whos name appears at the source or the type assignment \cm{id} (in seconds).

\item
\cmd{ResidenceTime\_median(id)}:\\
Gets the median of the residence times of the clients, whos name appears at the source or the type assignment \cm{id} (in seconds).

\item
\cmd{ResidenceTime\_quantil(p;id)}:\\
Gets the quantil for the probability p of the residence times of the clients, whos name appears at the source or the type assignment \cm{id} (in seconds).

\item
\cmd{ResidenceTime\_min(id)} or \cmd{ResidenceTime\_Minimum(id)}:\\
Gets the minimum residence time of the clients, whos name appears at the source or the type assignment \cm{id} (in seconds).

\item
\cmd{ResidenceTime\_max(id)} or \cmd{ResidenceTime\_Maximum(id)}:\\
Gets the maximum residence time of the clients, whos name appears at the source or the type assignment \cm{id} (in seconds).

\item
\cmd{ResidenceTime\_var(id)} or \cmd{ResidenceTime\_Varianz(id)}:\\
Gets the variation of the residence times of the clients, whos name appears at the source or the type assignment \cm{id} (based on seconds).

\item
\cmd{ResidenceTime\_sd(id)} or \cmd{ResidenceTime\_Standardabweichung(id)}:\\
Gets the standard deviation of the residence times of the clients, whos name appears at the source or the type assignment \cm{id} (based on seconds).

\item
\cmd{ResidenceTime\_cv(id)}:\\
Gets the coefficient of variation of the residence times of the clients, whos name appears at the source or the type assignment \cm{id}.

\item
\cmd{ResidenceTime\_scv(id)}:\\
Gets the squared coefficient of variation of the residence times of the clients, whos name appears at the source or the type assignment \cm{id}.

\item
\cmd{ResidenceTime\_sk(id)}:\\
Gets the skewness of the residence times of the clients, whos name appears at the source or the type assignment \cm{id}.

\end{itemize}

\section{Utilization of the resources}

\subsection{Utilization of a resource}

\begin{itemize}

\item
\cmd{resource\_count(id)} or \cmd{resource\_capacity(id)} or \cmd{MR(id)}:\\
Gets the number of currently existing operators in the specified resource.

\item
\cmd{resource\_down(id)}:\\
Gets the number of operators that are currently in down time in the specified resource.

\item
\cmd{resource(id)} or \cmd{utilization(id)} or \cmd{NR(id)}:\\
Gets the number of currently busy operators in the specified resource.

\item
\cmd{resource\_avg(id)} or \cmd{resource\_average(id)} or \cmd{resource\_Mittelwert(id)} or\\
\cmd{utilization\_avg(id)} or \cmd{utilization\_average(id)} or \cmd{utilization\_Mittelwert(id)}:\\
Gets the average number of busy operators in the specified resource.

\item
\cmd{resource\_min(id)} or \cmd{resource\_Minimum(id)} or \cmd{utilization\_min(id)} or\\
\cmd{utilization\_Minimum(id)}:\\
Gets the minimum number of busy operators in the specified resource.

\item
\cmd{resource\_max(id)} or \cmd{resource\_Maximum(id)} or \cmd{utilization\_max(id)} or\\
\cmd{utilization\_Maximum(id)}:\\
Gets the maximum number of busy operators in the specified resource.

\item
\cmd{resource\_var(id)} or \cmd{resource\_Varianz(id)} or \cmd{utilization\_var(id)} or\\
\cmd{utilization\_Varianz(id)}:\\
Gets the variation of the number of busy operators in the specified resource.

\item
\cmd{resource\_sd(id)} or \cmd{resource\_Standardabweichung(id)} or \cmd{utilization\_sd(id)} or\\
\cmd{utilization\_Standardabweichung(id)}:\\
Gets the standard deviation of the number of busy operators in the specified resource.

\item
\cmd{resource\_cv(id)} or \cmd{utilization\_cv(id)}:\\
Gets the coefficient of variation of the number of busy operators in the specified resource.

\item
\cmd{resource\_scv(id)} or \cmd{utilization\_scv(id)}:\\
Gets the squared coefficient of variation of the number of busy operators in the specified resource.

\item
\cmd{resource\_sk(id)} or \cmd{utilization\_sk(id)}:\\
Gets the skewness of the number of busy operators in the specified resource.

\item
\cmd{resource\_hist(id;state)} or \cmd{utilization\_hist(id;state)}:\\
Gets the fraction of time, at which \cm{state} of the operators in the specified resource have been busy.

\item
\cmd{resource\_hist(id;stateA;stateB)} or \cmd{utilization\_hist(id;stateA;stateB)}:\\
Gets the fraction of time, at which more than \cm{stateA} and at most \cm{stateB} of the operators in the specified resource have been busy.

\end{itemize}

\subsection{Utilization of all resource together}

\begin{itemize}

\item
\cmd{resource\_count()} or \cmd{resource\_capacity()} or \cmd{MR()}:\\
Gets the number of currently existing operators in all resources.

\item
\cmd{resource\_down()}:\\
Gets the number of operators that are currently in down time in all resources.

\item
\cmd{resource()} or \cmd{utilization()} or \cmd{NR()}:\\
Gets the number of currently busy operators in all resources.

\item
\cmd{resource\_avg()} or \cmd{resource\_average()} or \cmd{resource\_Mittelwert()} or\\
\cmd{utilization\_avg()} or \cmd{utilization\_average()} or \cmd{utilization\_Mittelwert()}:\\
Gets the average number of busy operators in all resources.

\item
\cmd{resource\_min()} or \cmd{resource\_Minimum()} or \cmd{utilization\_min()} or\\
\cmd{utilization\_Minimum()}:\\
Gets the minimum number of busy operators in all resources.

\item
\cmd{resource\_max()} or \cmd{resource\_Maximum()} or \cmd{utilization\_max()} or\\
\cmd{utilization\_Maximum()}:\\
Gets the maximum number of busy operators in all resources.

\end{itemize}

\section{Utilization of the transporters}

\subsection{Utilization of a transporter group}

\begin{itemize}

\item
\cmd{transporter\_count(id)}:\\
Gets the number of transporter in the specified transporter group.

\item
\cmd{transporter\_capacity(id)}:\\
Gets the number of clients a transporter in the specified transporter group can carry.

\item
\cmd{transporter\_down(id)}:\\
Gets the number of transporters that are currently in down time in the specified transporter group.

\item
\cmd{transporter(id)} or \cmd{transporter\_utilization(id)}:\\
Gets the number of currently busy transporters in the specified transporter group.

\item
\cmd{transporter\_avg(id)} or \cmd{transporter\_average(id)} or \cmd{transporter\_Mittelwert(id)} or \cmd{transporter\_utilization\_avg(id)} or \cmd{transporter\_utilization\_average(id)} or\\
\cmd{transporter\_utilization\_Mittelwert(id)}:\\
Gets the average number of busy transporters in the specified transporter group.

\item
\cmd{transporter\_min(id)} or \cmd{transporter\_Minimum(id)} or \cmd{transporter\_utilization\_min(id)} or \cmd{transporter\_utilization\_Minimum(id)}:\\
Gets the minimum number of busy transporters in the specified transporter group.

\item
\cmd{transporter\_max(id)} or \cmd{transporter\_Maximum(id)} or \cmd{transporter\_utilization\_max(id)} or \cmd{transporter\_utilization\_Maximum(id)}:\\
Gets the maximum number of busy transporters in the specified transporter group.

\item
\cmd{transporter\_var(id)} or \cmd{transporter\_Varianz(id)} or \cmd{transporter\_utilization\_var(id)} or \cmd{transporter\_utilization\_Varianz(id)}:\\
Gets the variation of the number of busy transporters in the specified transporter group.

\item
\cmd{transporter\_sd(id)} or \cmd{transporter\_Standardabweichung(id)} or\\
\cmd{transporter\_utilization\_sd(id)} or \cmd{transporter\_utilization\_Standardabweichung(id)}:\\
Gets the standard deviation of the number of busy transporters in the specified transporter group.

\item
\cmd{transporter\_cv(id)} or \cmd{transporter\_utilization\_cv(id)}:\\
Gets the coefficient of variation of the number of busy transporters in the specified transporter group.

\item
\cmd{transporter\_scv(id)} or \cmd{transporter\_utilization\_scv(id)}:\\
Gets the squared coefficient of variation of the number of busy transporters in the specified transporter group.

\item
\cmd{transporter\_sk(id)} or \cmd{transporter\_utilization\_sk(id)}:\\
Gets the skewness of the number of busy transporters in the specified transporter group.

\item
\cmd{transporter\_hist(id;state)} or \cmd{transporter\_utilization\_hist(id;state)}:\\
Gets the fraction of time, at which \cm{state} of the transporters in the specified transporter group have been busy.

\item
\cmd{transporter\_hist(id;stateA;stateB)} or\\
\cmd{transporter\_utilization\_hist(id;stateA;stateB)}:\\
Gets the fraction of time, at which more than \cm{stateA} and at most \cm{stateB} of the transporters in the specified transporter group have been busy.

\end{itemize}

\subsection{Utilization of all transporters together}

\begin{itemize}

\item
\cmd{transporter\_count()}:\\
Gets the number of currently existing transporters in all transporter groups.

\item
\cmd{transporter\_down()}:\\
Gets the number of transporters that are currently in down time in all transporter groups.

\item
\cmd{transporter()} or \cmd{transporter\_utilization()}:\\
Gets the number of currently busy transporters in all transporter groups.

\item
\cmd{transporter\_avg()} or \cmd{transporter\_average()} or \cmd{transporter\_Mittelwert()} or\\
\cmd{transporter\_utilization\_avg()} or \cmd{transporter\_utilization\_average()} or\\
\cmd{transporter\_utilization\_Mittelwert()}:\\
Gets the average number of busy transporters in all transporter groups.

\item
\cmd{transporter\_min()} or \cmd{transporter\_Minimum()} or \cmd{transporter\_utilization\_min()} or\\
\cmd{transporter\_utilization\_Minimum()}:\\
Gets the minimum number of busy transporters in all transporter groups.

\item
\cmd{transporter\_max()} or \cmd{transporter\_Maximum()} or \cmd{transporter\_utilization\_max()} or\\
\cmd{transporter\_utilization\_Maximum()}:\\
Gets the maximum number of busy transporters in all transporter groups.

\end{itemize}

\section{Accessing the Statistics stations records}

\begin{itemize}

\item
\cmd{Statistics(id;nr)}:\\
Gets the current value of record \cm{nr} (1 based) at Statistics station \cm{id}.

\item
\cmd{Statistics\_avg(id;nr)} or \cmd{Statistics\_average(id;nr)}:\\
Gets the average value of record \cm{nr} (1 based) at Statistics station \cm{id}.

\item
\cmd{Statistics\_median(id;nr)}:\\
Gets the median of the value of record \cm{nr} (1 based) at Statistics station \cm{id}.
(This command is not available for continuous-time user-defined statistics entries).

\item
\cmd{Statistics\_quantil(id;nr;p)}:\\
Gets the quantil for the probability p of the value of record \cm{nr} (1 based) at Statistics station \cm{id}.
(This command is not available for continuous-time user-defined statistics entries).

\item
or \cmd{Statistics\_min(id;nr)} or \cmd{Statistics\_Minimum(id;nr)}:\\
Gets the minimum value of record \cm{nr} (1 based) at Statistics station \cm{id}.

\item
\cmd{Statistics\_max(id;nr)} or \cmd{Statistics\_Maximum(id;nr)}:\\
Gets the maximum value of record \cm{nr} (1 based) at Statistics station \cm{id}.

\item
\cmd{Statistics\_var(id;nr)}:\\
Gets the variance of record \cm{nr} (1 based) at Statistics station \cm{id}.

\item
\cmd{Statistics\_std(id;nr)}:\\
Gets the standard deviation of record \cm{nr} (1 based) at Statistics station \cm{id}.

\item
\cmd{Statistics\_cv(id;nr)}:\\
Gets the coefficient of variation of record \cm{nr} (1 based) at Statistics station \cm{id}.

\item
\cmd{Statistics\_scv(id;nr)}:\\
Gets the squared coefficient of variation of record \cm{nr} (1 based) at Statistics station \cm{id}.

\item
\cmd{Statistics\_sk(id;nr)}:\\
Gets the skewness of record \cm{nr} (1 based) at Statistics station \cm{id}.

\item
\cmd{Statistics\_hist(id;nr;state)}:\\
Get the part in which the value of record \cm{nr} (1 based) at Statistics station \cm{id} was \cm{state}.
(This command is not available for continuous-time user-defined statistics entries).

\item
\cmd{Statistics\_hist(id;nr;stateA;stateB)}:\\
Get the part in which the value of record \cm{nr} (1 based) at Statistics station \cm{id} was bigger than \cm{stateA} and smaller or equal \cm{stateB}.
(This command is not available for continuous-time user-defined statistics entries).

\end{itemize}

\section{Accessing analog values}

\begin{itemize}

\item
\cmd{AnalogValue(id)}:\\
Gets the current value of the "Analog value" element or the "Tank" element \cm{id}.

\item
\cmd{AnalogRate(id)}:\\
Gets the current change rate of the value of the "Analog value" element \cm{id}.

\item
\cmd{ValveMaximumFlow(id;nr)}:\\
Gets the current maximum flow at valve \cm{nr} (1 based) at "Tank" element \cm{id}.

\end{itemize}

\section{Accessing the client object specific data fields}

\begin{itemize}

\item
\cmd{WarmUpKunde()} or \cmd{WarmUpClient()} or \cmd{isWarmUpClient()}:\\
Gets 0 or 1 depending on whether the client was generated during the warm-up phase (1) or not (0).

\item
\cmd{KundeInStatistik()} or \cmd{ClientInStatistics()} or \cmd{isClientInStatistics()}:\\
Gets 0 or 1 depending on whether the client is to be recorded in the statistics (1) or nor (0). Additionally the client has to be generated after the warm-up phase to be actually recorded.

\item
\cmd{KundeNummer()} or \cmd{ClientNumber()}:\\
Returns the 1-based consecutive number of the current client. If using multiple simulation threads this number is thread-local.

\item
\cmd{ClientData(index)}:\\
Gets the data field at position \cm{index} from the current client object.\\
The "Variable" elements can be used to write to these fields.

\item
\cmd{Alternative()}:\\
Indicates which operator alternative has been chosen at the last process station the client has passed to serve the client. If the client has not passed any process station yet, the function will return 0. Otherwise a value of 1 or larger will be returned.

\item
\cmd{PreviousStation()}:\\
Gets the ID of the station where the client was before he entered the current station.

\item
\cmd{CurrentWaitingTime()}:\\
Gets the waiting time of the current client at the current station.

\end{itemize}

\section{Accessing the costs}

\begin{itemize}

\item
\cmd{costs\_waiting\_sum(id)}:\\
Gets the waiting time costs of the clients, whos name appears at the source or the type assignment \cm{id}.

\item
\cmd{costs\_waiting\_avg(id)} or \cmd{costs\_waiting\_average(id)} or\\
\cmd{Kosten\_WaitingTime\_Mittelwert(id)}:\\
Gets the average waiting time costs of the clients, whos name appears at the source or the type assignment \cm{id}.

\item
\cmd{costs\_waiting\_sum()} or \cmd{Kosten\_WaitingTime\_Summe()}:\\
Gets the sum of the waiting time costs of all clients.

\item
\cmd{costs\_waiting\_avg()} or \cmd{costs\_waiting\_average()}:\\
Gets the average waiting time costs of all clients.

\item
\cmd{costs\_waiting()}:\\
Gets the waiting time costs of the current client.

\item
\cmd{costs\_transfer\_sum(id)}:\\
Gets the transfer time costs of the clients, whos name appears at the source or the type assignment \cm{id}.

\item
\cmd{costs\_transfer\_avg(id)} or \cmd{costs\_transfer\_average(id)}:\\
Gets the average transfer time costs of the clients, whos name appears at the source or the type assignment \cm{id}.

\item
\cmd{costs\_transfer\_sum()}:\\
Gets the sum of the transfer time costs of all clients.

\item
\cmd{costs\_transfer\_avg()} or \cmd{costs\_transfer\_average()}:\\
Gets the average transfer time costs of all clients.

\item
\cmd{costs\_transfer()}:\\
Gets the transfer time costs of the current client.

\item
\cmd{costs\_process\_sum(id)}:\\
Gets the process time costs of the clients, whos name appears at the source or the type assignment \cm{id}.

\item
\cmd{costs\_process\_avg(id)} or \cmd{costs\_process\_average(id)}:\\
Gets the average process time costs of the clients, whos name appears at the source or the type assignment \cm{id}.

\item
\cmd{costs\_process\_sum()}:\\
Gets the sum of the process time costs of all clients.

\item
\cmd{costs\_process\_avg()} or \cmd{costs\_process\_average()}:\\
Gets the average process time costs of all clients.

\item
\cmd{costs\_process()}:\\
Gets the process time costs of the current client.

\item
\cmd{costs(id)}:\\
Provides the station costs, which so far have occurred at station \cm{id}.

\item
\cmd{costs()}:\\
Provides the station costs, which so far have occurred in total at all stations.

\item
\cmd{costs\_resource(id)}:\\
Returns the costs incurred by the specified resource so far.

\item
\cmd{costs\_resource()}:\\
Returns the costs incurred by all resources so far.

\end{itemize}

\chapter{Comparison}

\begin{itemize}

\item
\cmd{a == b}:\\
Gets true, if $a$ has the same value as $b$.

\item
\cmd{a != b} or \cmd{a <> b}:\\
Gets true, if $a$ and $b$ have different values.

\item
\cmd{a < b}:\\
Gets true, if $a$ is less than $b$.

\item
\cmd{a <= b} or \cmd{a =< b}:\\
Gets true, if $a$ is less or equal to $b$.

\item
\cmd{a > b}:\\
Gets true, if $a$ is larger than $b$.

\item
\cmd{a >= b} or \cmd{a => b}:\\
Gets true, if $a$ is larger or equal to $b$.

\item
\cmd{A || B}:\\
Gets true, if $A$ or $B$ (or both) are true.

\item
\cmd{A \&\& B}:\\
Gets true, if $A$ and $B$ are both true.

\item
\cmd{!(A)}:\\
Gets true, if $A$ is not true.

\end{itemize}

The lowercase characters $a$ and $b$ are placeholders for calculation expressions like \cmd{WIP()}.
The capital letters $A$ and $B$ stand for comparisons like \cmd {WIP()<5}.

\section{Comparison function}

Additionally normal calculation commands an \cmd{If} function is available. This functions expects an odd number
of parameters:

\cmd{If(condition1;value1;condition2;value2;...;valueElse)}

If \cm{condition1}$>0$ the function returns \cm{value1}.
Otherwise \cm{condition2}$>0$ is tested and if its fulfilled \cm{value2} is returned and so on.
If non of the conditions is fulfilled the function returns \cm{valueElse}.