diff --git a/report/MatejSutyBP.pdf b/report/MatejSutyBP.pdf
index a7899b02755810327107a14864aa25790f277623..4f03364abd1b81df678e15ba55b1514843369b40 100644
Binary files a/report/MatejSutyBP.pdf and b/report/MatejSutyBP.pdf differ
diff --git a/report/MatejSutyBP.tex b/report/MatejSutyBP.tex
index 92fb50991d5cccbccf450c1d99c2c47cc410216e..d26f09a09c761c5f1c37b8717f777cbdfaa3b595 100644
--- a/report/MatejSutyBP.tex
+++ b/report/MatejSutyBP.tex
@@ -180,7 +180,8 @@ A cellular automaton (CA) is a complex mathematic or computational system with d
\subsection{Floor field CA}
The inspiration for model used in this thesis is the floor field cellular model described by Katsuhiro Nishinari and Andreas Schadschneider in Article ~\cite{floor_field_ca_nishinari}. Main characteristic of this model is in the use of several floor fields --- \textit{static}, \textit{dynamic}, \textit{fire hazard}, \dots{}
-These can be explained as two-dimensional lattices made of discrete cells that hold some value and abide to certain rules. Pedestrians in the evacuation, who are agents with individual parameters, move in the rectangular two-dimensional grid and interact with these lattices. Agents are updated in synchronous intervals but thanks to their individual and heterogeneous period of movement, they can have different speed on the grid. \textit{"For the case of evacuation processes, the static floor field $S$ describes the shortest distance to an exit door. The field strength $S_{ij}$ is set inversely proportional to the distance from the door. The dynamic floor field $D$ is a virtual trace left by the pedestrians similar to the pheromone in chemotaxis ~\cite{nishinari_ref_chemotaxi}. It has its own dynamics, namely diffusion and decay, which leads to broadening, dilution and finally vanishing of the trace. At $t = 0$ for all sites $(i, j)$ of the lattice the dynamic field is zero, i.e., $D_{ij} = 0$. Whenever a particle jumps from site~$(i, j)$ to one of the neighboring cells, $D$ at the origin cell is increased by one"}~\cite{floor_field_ca_nishinari}.
+These can be explained as two-dimensional lattices made of discrete cells that hold some value and abide to certain rules. Pedestrians in the evacuation, who are agents with individual parameters, move in the rectangular two-dimensional
+ and interact with these lattices. Agents are updated in synchronous intervals but thanks to their individual and heterogeneous period of movement, they can have different speed on the grid. \textit{"For the case of evacuation processes, the static floor field $S$ describes the shortest distance to an exit door. The field strength $S_{ij}$ is set inversely proportional to the distance from the door. The dynamic floor field $D$ is a virtual trace left by the pedestrians similar to the pheromone in chemotaxis ~\cite{nishinari_ref_chemotaxi}. It has its own dynamics, namely diffusion and decay, which leads to broadening, dilution and finally vanishing of the trace. At $t = 0$ for all sites $(i, j)$ of the lattice the dynamic field is zero, i.e., $D_{ij} = 0$. Whenever a particle jumps from site~$(i, j)$ to one of the neighboring cells, $D$ at the origin cell is increased by one"}~\cite{floor_field_ca_nishinari}.
\subsection{Cellular automata of today}
@@ -239,7 +240,7 @@ The agents are somewhat autonomous and react to the environment. They generally
The collective motion of agents is reproduced using various strategies: choosing destination cell and solving conflicts, and using heterogeneity in the parameters. The strategies work with parameters of aggressivity and sensitivity of each agent. The parameter of aggressivity plays a role in situations when two or more agents attempt to enter the same cell.
-
+\pagebreak
@@ -267,24 +268,38 @@ $(y_1, y_2):~y_1\in{\{0,1,\dots{},W-1\}},$ $y_2~\in{\{0,1,\dots{},H-1\}}$ is a c
\subsubsection*{EXIT}\label{exit}
Agents can leave the grid only through exit cell $e$ placed on the border of the grid. Exit has the lowest static potential $S(e)=0$. This models uses only one exit.
-\subsubsection*{CELLS}\label{cells}
-Cell $y$ is an element of grid $G$ in position $(y_1, y_2):~y_1\in{\{0,1,\dots{},W-1\}},$ $y_2~\in{\{0,1,\dots{},H-1\}}$.
-Each cell can be occupied by one agent at a given time-frame. Agents can move in 8 directions to cells in Moore neighborhood or decide to stay in the same cell.
-Cell $y$ holds the normalized value of static potential $S_{norm}(y)\in{[0,1]}$. These values are normalized to fit the lowest value at exit $e: S(e) = 0$ and the highest value of cell $y: S(y) = q, q\in{\mathbb{R}}$ that is furthest away from the exit.
-For cell $y$ and exit $e$ in grid $G$ is $S(y) = L_1(y, e)$ where $L_1(y, e)$ is Manhattan distance~\cite{distance_metric} from cell $y$ to exit $e$.
-
\subsubsection*{STEP}\label{step}
Evacuation is simulated in a sequence of $m$ steps $\{s_1,\dots{},s_m\}$ executed by model. Each step consists of several phases (see Section \ref{schedule}) to select destination cells for agents, solve conflicts and move agents on grid.
+
+
\subsubsection*{TIME FRAME}\label{tf}
Continuous real life duration $T$ of evacuation is divided to $m$ time-frames $\textbf{t}=\{t_1,\dots{},t_m\}$.
One step $s_i$ of model takes $\Delta{t_i}=[t_i, t_{i+1}]$ time. Time-frame $t_i$ covers one step $s_i$ of model.
Agents move in two-dimensional grid in 8 directions. The vertical or horizontal movement takes nominal duration of $\tau$. The movement in diagonal direction takes $\sqrt{2}$ times longer. To allow for more periodic update $\sqrt{2}$ is approximated by rational constant $\frac{3}{2}$~\cite{timespan} resulting in duration of diagonal movement equal to $\frac{3}{2}\cdot{}\tau$.
-\subsection{Methods}
+\subsubsection*{CELLS}\label{cells}
+Cell $y$ is an element of grid $G$ in position $(y_1, y_2):~y_1\in{\{0,1,\dots{},W-1\}},$ $y_2~\in{\{0,1,\dots{},H-1\}}$.
+Each cell can be occupied by one agent at a given time-frame. Agents can move in 8 directions to cells in Moore neighborhood or decide to stay in the same cell.
+Cell $y$ holds the normalized value of static potential $S_{norm}(y)\in{[0,1]}$. These values are normalized to fit the lowest value at exit $e: S(e) = 0$ and the highest value of cell $y: S(y) = q, q\in{\mathbb{R}}$ that is furthest away from the exit.
+For cell $y$ and exit $e$ in grid $G$ is $S(y) = L_1(y, e)$ where $L_1(y, e)$ is Manhattan distance~\cite{distance_metric} from cell $y$ to exit $e$.
+
+\begin{figure}[h!]
+\begin{center}
+ \begin{subfigure}[b]{0.5\linewidth}
+ \includegraphics[width=\linewidth]{img/vector/cell.pdf}
+
+ \end{subfigure}
+\end{center}
+ \caption{Possible moves of a cell.}
+ \label{fig:cell}
+\end{figure}
+
+\newpage
+\subsection{Methods}
\subsubsection*{STRATEGY FOR CHOOSING DESTINATION CELL}\label{strategy_destination_cell}
In each step of the simulation all agents calculate the attractiveness $P$ of cells in their neighborhood $N$. Attractiveness or attractivity $P\in{[0,1]}$ is the probability of agent selecting this cell as his preferred destination cell. The selection is executed in stochastic manner.
@@ -385,6 +400,20 @@ Aggressivity $\gamma\in{[0, 1]}$ is the ability of agent to win conflict. This t
There are various methods (see Section \ref{agent}) to assign $\gamma$ to $n$ agents and generally the values are discreet with certain granularity $h: h<n$. When only $h$ values are assigned to the agents, the conflicts occur more frequently.
+\subsubsection*{BONDS}\label{bonds}
+
+In every step $s_i$ at most one agent can be present in a cell $x$. The principle of bonds~\cite{timespan} is used in order to allow agent $a_1$ in cell $y_1$ to move to a cell $y_2$ occupied by agent $a_2$ in following step $s_\text{i+1}$. Immediately when $a_2$ leaves $y_2$ to move to other cell, $a_1$ will enter now empty $y_2$. \textit{This principle enables the motion in lines within one algorithm step, which is desired phenomenon of pedestrian flow} (Hrab{\'a}k et al, 2014, p.~7)~\cite{timespan}.
+\newline\newline
+
+\begin{figure}[h]
+ \centerline{ \includegraphics[scale=0.5]{img/raster/conflict_3x3_example_LOW.png}}
+ \caption{
+ Conflict solution for $\protect\gamma_1 \textless \protect\gamma_2$. Left: more aggressive wins the conflict over two less aggressive. Right: the conflict of two more aggressive can resolve by the blocking of the movement. \textit{Taken from} ~\cite{aggressive}.
+ }
+ \label{yadayada}
+\end{figure}
+
+\newpage
\subsubsection*{STRATEGY FOR SOLVING CONFLICTS}\label{strategy_solving_conflicts}
Conflicts happen when two or more agents choose cell $y$ as their destination cell. There are two strategies for choosing winning agent.
@@ -405,18 +434,6 @@ To prevent jamming the sensitivity parameter $\mu$ could be set to lower value b
This strategy selects the winning agent $a_i$ stochastically with probability $P_i$ proportional to agent's respective aggressivity $\gamma_i$. Set of agents $\{a_1,\dots{},a_k\}$
with respective aggressivity parameters $\{\gamma_1,\dots{},\gamma_k\}$ produces for each agent $a_i$ a probability $P_i = \frac{\gamma_i}{\sum_{j\in{k}} \gamma_j}$.
\end{itemize}
-\subsubsection*{BONDS}\label{bonds}
-
-In every step $s_i$ at most one agent can be present in a cell $x$. The principle of bonds~\cite{timespan} is used in order to allow agent $a_1$ in cell $y_1$ to move to a cell $y_2$ occupied by agent $a_2$ in following step $s_\text{i+1}$. Immediately when $a_2$ leaves $y_2$ to move to other cell, $a_1$ will enter now empty $y_2$. \textit{This principle enables the motion in lines within one algorithm step, which is desired phenomenon of pedestrian flow} (Hrab{\'a}k et al, 2014, p.~7)~\cite{timespan}.
-\newline\newline
-
-\begin{figure}[h]
- \centerline{ \includegraphics[scale=0.5]{img/raster/conflict_3x3_example_LOW.png}}
- \caption{
- Conflict solution for $\protect\gamma_1 \textless \protect\gamma_2$. Left: more aggressive wins the conflict over two less aggressive. Right: the conflict of two more aggressive can resolve by the blocking of the movement. \textit{Taken from} ~\cite{aggressive}.
- }
- \label{yadayada}
-\end{figure}
@@ -439,10 +456,6 @@ My research of available agent-based modeling frameworks revealed Mesa as an up-
\caption{Simulation with moving agents in different states.}
\label{MESA-map}
\end{figure}
-\pagebreak
-\subsubsection*{Ansys OptiSLang}
-The sensitivity analysis of input parameters was performed on OptiSLang. This software was developed by Dynardo GmbH. \textit{TBA: More text will be added when I use the software. }
-
\subsection{Evacuation model}
\subsubsection*{PModel}
@@ -571,10 +584,16 @@ J_{ij} &= \frac{m}{\Delta{t}}
\end{equation}
\newpage
+
+
+
\section{Methods of analysis}
To measure the influence of the parameters, OptiSLang software uses Metamodel of Optimal Prognosis (MOP). At first it calculates the quality of each available model (Polynomial, MLS, Kriging) using Coefficient of Prognosis(COP) and then chooses the one with the highest quality. This model then evaluates the simulation data --- input parameters and output --- using cross validation and approximates the influence of input variables.
\textit{The variance contribution of a single input variable is quantified by the product of the CoP and the total effect sensitivity index estimated from the approximation model.}~\cite{MOP_COP2011}
+\subsubsection*{Ansys OptiSLang}
+The sensitivity analysis of input parameters was performed on OptiSLang. This software was developed by Dynardo GmbH. \textit{TBA: More text will be added when I use the software. }
+
\section{Simulations}
At first, the simulations were observed on the Mesa framework web interface, that is depicted in~Figure~\ref{MESA-map}. They were used mostly during implementation of the model and in testing the new strategies.
Later, batch simulations on wide range of intervals were performed. The input parameters of simulations $S_1,\ S_2,\ S_3,\ S_4$ are in Table~\ref{table_simulations} below. All simulations had the same model configuration of grid $15 \times 15$, exit placed at border $(0, 8)$, same seed $I = 1245$ for PRNG $G_1$. Each iteration had different seed $J$ for PRNG $G_2$, that solves conflicts and selects destination cells.
@@ -651,7 +670,8 @@ Figure~\ref{ks_influence} shows very high total evacuation time on axis $T$ for
\label{ks_influence}
\end{figure}
-The range $[1.5, 4.5]$ was used for further simulations and $k_S$ was assigned the constant values of $k_S\in{}\{1.5,3.5,4.5\}$. This interval brings meaningful results and allows other parameters to influence the simulation. For $k_S\gg{}4.5$ the influence of $k_O, k_D$ is marginal. Parameters $k_O, k_D, \mu{}$ were set to cover the $[0,1]$ range in uniform discreet steps as follows: $k_0~\in{}\{0.1,0.2,\dots{},1.0\}$ and~$k_D,\mu{}~\in{}\{0.0, 0.2,\dots{},1.0\}$.
+
+The values $k_S\in{}[1.5, 4.5]$ bring meaningful results and allow other parameters to influence the simulation. For~$k_S~\gg{}~4.5$ the influence of $k_O, k_D$ is marginal. For further simulations $k_S$ was assigned the constant values of $k_S\in{}\{1.5,3.5,4.5\}$. Parameters $k_O, k_D, \mu{}$ were set to cover the $[0,1]$ range in uniform discreet steps as follows: $k_0~\in{}\{0.1,0.2,\dots{},1.0\}$ and~$k_D,\mu{}~\in{}\{0.0, 0.2,\dots{},1.0\}$.
\begin{figure}[h!]
\begin{center}
@@ -739,16 +759,28 @@ Due to the these factors, total evacuation time increases with lower $k_O$, as c
\section{Sensitivity to diagonal movement $\protect{k_D}$}
Agent that moves to adjacent diagonal cells increases his inner time period by $\frac{3}{2}$ of nominal movement duration. At the start of the simulation, agents closest to the exit have a free path, and move rapidly towards exit. Movement in diagonal directions allows agents, that are not in a straight line from the \textit{exit}, to get there with less movements. However, they are penalized by increased movement duration --- after two diagonal movements the agents are 'exhausted' and do not move. Especially at the start of the simulation, with low $k_D$, agents can move in waves, as can be seen in Figure~\ref{exhausted_agents} in Appendix~\ref{exhausted_appendix}. Diagonal movement is also useful when a queue or other congestion structure forms. The agents can overtake the queue when they move diagonally.
-Even though the microscopic behavior of agents can be significantly affected by $k_D$ , the effect on the $T_\text{TET}$ is marginal. Sensitivity analysis using MOP in Figure~\ref{kd_influence} shows that $k_D$ has very low influence on the total evacuation time.
+Even though the microscopic behavior of agents can be significantly affected by $k_D$, the effect on the $T_\text{TET}$ is marginal. Sensitivity analysis using MOP in Figure~\ref{kd_influence} shows that $k_D$ has very low influence on the total evacuation time for high $k_S$.
+
+
+\begin{figure}[h!]
+\begin{center}
+\begin{subfigure}[b]{0.8\linewidth}
+ \includegraphics[width=\linewidth]{img/visuals/45/COP45.pdf}
+ \end{subfigure}
+\end{center}
+ \caption{High $\protect{k_S=4.5}$. Compared to other parameters, influence of $\protect{k_D}$ is marginal.}
+ \label{kd_influence}
+\end{figure}
+
\begin{figure}[h!]
\begin{center}
\begin{subfigure}[b]{0.8\linewidth}
- \includegraphics[width=\linewidth]{img/visuals/15/COP15.pdf}
+ \includegraphics[width=\linewidth]{img/visuals/45/3D 45 lq OD.png}
\end{subfigure}
\end{center}
- \caption{Compared to other parameters, influence of $\protect{k_D}$ is marginal.}
+ \caption{High $\protect{k_S=4.5}$. Compared to other parameters, influence of $\protect{k_D}$ is marginal.}
\label{kd_influence}
\end{figure}
diff --git a/report/img/vector/cell.pdf b/report/img/vector/cell.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..55614883f936628b8c00162847fab1115b55478d
Binary files /dev/null and b/report/img/vector/cell.pdf differ