Parameters

Table of Contents

• Examples
• Format
  • Path
  • InputFiles
  • LearningModel
    • Linear learning model
    • Exponential learning model
    • Unadjusted Exponential learning model
    • Quadratic learning model
    • Genetic learning model
  • RoadNetworkParameters

The parameters of a METROPOLIS2’s simulation are defined in a JSON file.

Examples

Minimal working example:

{
  "input_files": {
    "agents": "input/agents.parquet",
    "alternatives": "input/alternatives.parquet"
  },
  "period": [21600.0, 43200.0]
}

Complete example:

{
  "input_files": {
    "agents": "input/agents.parquet",
    "alternatives": "input/alts.parquet",
    "trips": "input/trips.parquet",
    "edges": "input/edges.parquet",
    "vehicle_types": "input/vehicles.parquet",
    "road_network_conditions": "input/edge_ttfs.parquet"
  },
  "output_directory": "output/",
  "period": [0.0, 86400.0],
  "road_network": {
      "recording_interval": 50.0,
      "approximation_bound": 1.0,
      "spillback": true,
      "backward_wave_speed": 4.0,
      "max_pending_duration": 20.0,
      "constrain_inflow": true,
      "algorithm_type": "Best"
  },
  "learning_model": {
    "type": "Exponential",
    "value": 0.01
  },
  "init_iteration_counter": 1,
  "max_iterations": 2,
  "update_ratio": 1.0,
  "random_seed": 19960813,
  "nb_threads": 8,
  "saving_format": "Parquet",
  "only_compute_decisions": false
}

Format

The following table describes all the possible key-value pairs in the parameters JSON file.

Path

The input files and output directory of the simulation are defined in the parameters JSON file as paths.

Each path is a string representing either a relative path or an absolute path. The relative paths are interpreted as being relative to the directory where the parameters file is located. In case of issues when working with relative paths, try with absolute paths.

We recommend using slash / instead of backslash \ in the paths.

InputFiles

The value corresponding to the key input_files must be a JSON Object with the following key-value pairs.

LearningModel

Let \( \hat{T}_{\kappa} \) be the expected travel-time function for iteration \( \kappa \) and let \( T_{\kappa} \) be the simulated travel-time function at iteration \( \kappa \).

METROPOLIS2 supports the following learning models.

Linear learning model

\[ \hat{T}_{\kappa+1} = \frac{1}{\kappa + 1} T_{\kappa} + \frac{\kappa}{\kappa + 1} \hat{T}_{\kappa}, \] such that, by recurrence, \[ \hat{T}_{\kappa+1} = \frac{1}{\kappa} \sum_{i=0}^{\kappa} T_{\kappa}. \]

JSON representation:

{
  [...]
  "learning_model": {
    "type": "Linear"
  }
  [...]
}

Exponential learning model

\[ \hat{T}_{\kappa+1} = \frac{\lambda}{a_{\kappa+1}} T_{\kappa} + (1 - \lambda) \frac{a_{\kappa}}{a_{\kappa+1}} \hat{T}_{\kappa}, \] with \[ a_{\kappa} = 1 - (1 - \lambda)^{\kappa}, \] such that, by recurrence, \[ \hat{T}_{\kappa+1} = \frac{1}{a_{\kappa}} \lambda \sum_{i=0}^{\kappa} (1 - \lambda)^i T_{\kappa}. \]

The parameter \( \lambda \) is called the smoothing factor. With \( \lambda = 0 \), the exponential learning model is equivalent to a linear learning model (see above). With \( \lambda = 1 \), the predicted values for the next iteration are equal to the simulated values, i.e., \( \hat{T}_{\kappa+1} = T_{\kappa} \).

The parameter \( \lambda \) must be between 0 and 1.

JSON representation (where “value” corresponds to the \( \lambda \) parameter):

{
  [...]
  "learning_model": {
    "type": "Exponential",
    "value": 0.05
  }
  [...]
}

Unadjusted Exponential learning model

\[ \hat{T}_{\kappa+1} = \lambda T_{\kappa} + (1 - \lambda) \hat{T}_{\kappa}. \]

The parameter \( \lambda \) must be between 0 and 1.

JSON representation (where “value” corresponds to the \( \lambda \) parameter):

{
  [...]
  "learning_model": {
    "type": "ExponentialUnadjusted",
    "value": 0.05
  }
  [...]
}

Quadratic learning model

\[ \hat{T}_{\kappa+1} = \frac{\sqrt{\kappa}}{\sqrt{\kappa} + 1} T_{\kappa} + \frac{1}{\sqrt{\kappa} + 1} \hat{T}_{\kappa}. \]

JSON representation:

{
  [...]
  "learning_model": {
    "type": "Quadratic"
  }
  [...]
}

Genetic learning model

\[ \hat{T}_{\kappa+1} = \big(T_{\kappa} \cdot \hat{T}_{\kappa}^{\kappa}\big)^{1 / (\kappa + 1)}. \]

JSON representation:

{
  [...]
  "learning_model": {
    "type": "Genetic"
  }
  [...]
}

RoadNetworkParameters

The RoadNetworkParameters value is an Object with the following key-value pairs: