Several operational models are implemented in jpscore. An operational model defines how pedestrians interact with each other and with their environment.

## Introduction

In the definition of agent’s properties it is mandatory to precise the number of the model to be used e.g.:

 <agents operational_model_id="n">


The definition of any model parameter is composed of two different sections:

• model_parameters: Model specific parameter. See below in the different model sections.
• agent_parameters: These parameter are mainly specific for the shape of pedestrians or other pedestrian properties like desired speed, reaction time etc.

## Model parameters (in general)

• <solver>euler</solver>
• The solver for the ODE. Only Euler. No other options.
• <stepsize>0.001</stepsize>:
• The time step for the solver. This should be choosed with care. For force-based model it is recommended to take a value between $10^{-2}$ and $10^{-3}$ s. For first-order models, a value of 0.05 s should be OK. A larger time step leads to faster simulations, however it is too risky and can lead to numerical instabilities, collisions and overlapping among pedestrians.
• Unit: s
• <exit_crossing_strategy>3</exit_crossing_strategy>
• Positive values in $[1, 9]$. See Direction strategies for the definition of the strategies.
• <linkedcells enabled="true" cell_size="2"/>
• Defines the size of the cells. This is important to get the neighbors of a pedestrians, which are all pedestrians within the eight neighboring cells. Larger cells, lead to slower simulations, since more pedestrian-pedestrian interactions need to be calculated.
• Unit: m

## Agent’s parameter (in general)

The agent parameters are mostly identical for all models. Exceptions will be mentioned explicitly.

The parameters that can be specified in this section are Gauss distributed (default value are given).

### Desired speed

• <v0 mu="1.2" sigma="0.0" />
• Desired speed
• Unit: m/s
• <v0_upstairs mu="0.6" sigma="0.167" />
• Desired speed upstairs
• Unit: m/s
• <v0_downstairs mu="0.6" sigma="0.188" />
• Desired speed downstairs
• Unit: m/s
• <v0_idle_escalator_upstairs mu="0.6" sigma="0.0" />
• Speed of idle escalators upstairs
• Unit: m/s
• <v0_idle_escalator_downstairs mu="0.6" sigma="0.0" />
• Speed of idle escalators downstairs
• Unit: m/s

The reduced speed on stairs (up) is according to Tab 1 in Burghardt2014.

Handbook Speed Stair Up
PM 0.63 m/s
WM 0.61 m/s
NM 0.8 m/s
FM 0.55 m/s

### Shape of pedestrians

Pedestrians are modeled as ellipses with two semi-axes: $a$ and $b$, where

and

$v$ is the speed of a pedestrian.

• <bmax mu="0.15" sigma="0.0" />
• Maximal length of the shoulder semi-axis
• Unit: m
• <bmin mu="0.15" sigma="0.0" />
• Minimal length of the shoulder semi-axis
• Unit: m
• <amin mu="0.15" sigma="0.0" />
• Minimal length of the movement semi-axis. This is the case when $v=0$.
• Unit: m
• <atau mu="0." sigma="0.0" />
• (Linear) speed-dependency of the movement semi-axis
• Unit: s

## Generalized Centrifugal Force Model

Generalized Centrifugal Force Model (preprint) is a force-based model.

Usage:

 <model operational_model_id="1" description="gcfm">


## Collision-free Speed Model

Collision-free speed model is a velocity-based model. See also this talk for more details about the model.

Usage:

 <model operational_model_id="3" description="Tordeux2015">


### Model parameters (Tordeux2015)

Besides the options defined in Model parameters the following options are necessary for this model:

• <force_ped a="5" D="0.2"/>
• The influence of other pedestrians is triggered by $a$ and $D$ where $a$ is the strength of the interaction and $D$ gives its range. The naming may be misleading, since the model is not force-based, but velocity-based.
• Unit: m
• <force_wall a="5" D="0.02"/>:
• The influence of walls is triggered by $a$ and $D$ where $a$ is the strength of the interaction and $D$ gives its range. A larger value of $D$ may lead to blockades, especially when passing narrow bottlenecks.
• Unit: m

The names of the aforementioned parameters might be misleading, since the model is not force-based. The naming will be changed in the future.

### Agent parameters (Tordeux2015)

Actually, this model assumes circular pedestrian’s shape, therefore the parameter for the semi-axes should be chosen, such that circles with constant radius can be obtained. For example:

 <bmax mu="0.15" sigma="0.0" />
<bmin mu="0.15" sigma="0.0" />
<amin mu="0.15" sigma="0.0" />
<atau mu="0." sigma="0.0" />


This defines circles with radius 15 cm.

Other parameters in this section are:

• <tau mu="0.5" sigma="0.0" />
• Reaction time. This constant is used in the driving force of the force-based forces. Small $\rightarrow$ instantaneous acceleration.
• Unit: s
• <T mu="1" sigma="0.0" />
• Specific parameter for model 3 (Tordeux2015). Defines the slope of the speed function.

In summary the relevant section for this model could look like:

 <model operational_model_id="3" description="Tordeux2015">
<model_parameters>
<solver>euler</solver>
<stepsize>0.05</stepsize>
<exit_crossing_strategy>3</exit_crossing_strategy>
<force_ped  a="5" D="0.2"/>
<force_wall a="5" D="0.02"/>
</model_parameters>
<agent_parameters agent_parameter_id="1">
<v0 mu="1.34" sigma="0.0" />
<v0_upstairs mu="0.668" sigma="0.167" />
<v0_downstairs mu="0.750" sigma="0.188" />
<v0_idle_escalator_upstairs mu="0.5" sigma="0.0" />
<v0_idle_escalator_downstairs mu="0.5" sigma="0.0" />
<bmax mu="0.15" sigma="0.0" />
<bmin mu="0.15" sigma="0.0" />
<amin mu="0.15" sigma="0.0" />
<atau mu="0." sigma="0.0" />
<tau mu="0.5" sigma="0.0" />
<T mu="1" sigma="0.0" />
</agent_parameters>
</model>

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