Several operational models are implemented in jpscore. An operational model defines how pedestrians moves from one time step to the next. 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">


where n is 1, 2, 3, 4 or 5.

### General model parameters (for all models)

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’s parameter

• <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 instability, collisions and overlapping among pedestrians.
• Unit: s
• <periodic>0</periodic>
• Set to 1 if a system with closed boundary conditions should be simulated. Default setting is 0.
• This option is only implemented in Tordeux2015 and is very geometry-specific (only for corridors) with predefined settings. See Utest/Validation/1test_1D/ for a use case.
• <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 so slower simulations, since more pedestrian-pedestrian interactions need to be calculated.
• Unit: m

### Agent’s parameter

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

#### Shape of pedestrians

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

and

$v$ is the peed 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

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.

### Generalized Centrifugal Force Model

Generalized Centrifugal Force Model is a force-based model.

Usage:

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


### Gompertz model

Gompertz Model is a force-based model.

Usage:

<model operational_model_id="2" description="gompertz">


### 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

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 if 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 if 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 (recommendations)

Actually, this model assumes circular pedestrian’s shape, therefore the parameter for the semi-axes Agent_parameters 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.

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>


### Wall-avoidance model

Wall-avoidance model is a velocity-based model. The Wall-Avoidance Model focuses on valid pedestrian positions. The interaction of agents with walls takes precedence over the agent-to-agent interaction. There are two key aspects:

• In the vicinity to walls, agents take on a different behaviour, slowing them down (parameter: slowdowndistance)

• Agents follow special floorfields, directing them to the targets/goals, which will have them avoid walls if possible (free space)

Valid exit strategies are {6, 8, 9}. Please see details below.

(Sample) Usage:

 <model operational_model_id="4" description="gradnav">
<model_parameters>
<solver>euler</solver>
<stepsize>0.01</stepsize>
<exit_crossing_strategy>9</exit_crossing_strategy>
<floorfield delta_h="0.0625" wall_avoid_distance="0.4"
use_wall_avoidance="true" />
<force_ped nu="3" b="1.0" c="3.0" />
<force_wall nu="1" b="0.70" c="3.0" />
<anti_clipping slow_down_distance=".2" />
</model_parameters>
<agent_parameters agent_parameter_id="0">
<v0 mu="1.5" sigma="0.0" />
<bmax mu="0.25" sigma="0.001" />
<bmin mu="0.20" sigma="0.001" />
<amin mu="0.18" sigma="0.001" />
<tau mu="0.5" sigma="0.001" />
<atau mu="0.23" sigma="0.001" />
</agent_parameters>
</model>


#### Parameters

• <exit_crossing_strategy>[6, 8, 9]</exit_crossing_strategy> The strategies 6, 8 and 9 differ only in the way the floorfield is created:
• 6: one floorfield over all geometry (building); only in 2D geometries; directing every agent to the closest exit
• 8: multiple floorfield-objects (one for every room); each object can create a floor field on the fly to a target line (or vector of lines) within the room; working in multi-floor-buildings; requires a router that provides intermediate targets in the same room
• 9: (recommended) multiple floorfield-objects (one for every subroom); each object can create a floor field on the fly to a target line (or vector of lines) within the same subroom; working in multi-floor-buildings; requires a router that provides intermediate targets in the same subroom;
• <floorfield delta_h="0.0625" wall_avoid_distance="0.4" use_wall_avoidance="true" />
• The parameters define:
• delta_h: discretization/stepsize of grid-points used by the floor field
• wall_avoid_distance: below this wall-distance, the floor field will show a wall-repulsive character, directing agents away from the wall
• use_wall_avoidance: {true, false} switch to turn on/off the enhancement of the floor field

• <linkedcells enabled="true" cell_size="4.2" />
• range in which other pedestrians are considered neighbours and can influence the current agent. This value defines cell-size of the cell-grid.

### Generalized Centrifugal Force Model with lateral swaying

The Generalized Centrifugal Force Model with lateral swaying is mostly identical to the GCFM Model, but instead of a variable semi-axis $b$ of the ellipse simulating the pedestrian, pedestrians perform an oscillation perpendicular to their direction of motion. As a consequence the parameter Bmax is ignored.

Usage:

 <model operational_model_id="5" description="krausz">


Four Parameters can be passed to control the lateral swaying, for example:

<sway ampA="-0.14" ampB="0.21" freqA="0.44" freqB="0.35" />

• ampA and ampB determine the amplitude of the oscillation according to the linear relation $A = \texttt{ampA} \cdot \| v_i \| + \texttt{ampB}$.

• freqA and freqB determine the frequency of the oscillation according to $f = \texttt{freqA} \cdot \| v_i \| + \texttt{freqB}$.

Setting ampA and ampB to 0 disables lateral swaying. If not specified, the empirical values given in Krausz, 2012 are used, that is:

• ampA = -0.14, ampB = 0.21 and
• freqA = 0.44, freqB = 0.25.