Note

Go to the end to download the full example code.

Forecasting#

In this example, we present a full forecasting workflow for the Sioux Falls example model.

We start creating the skim matrices, running the assignment for the base-year, and then distributing these trips into the network. Later, we estimate a set of future demand vectors which are going to be the input of a future year assignnment with select link analysis.

See also

Several functions, methods, classes and modules are used in this example:

# Imports
from uuid import uuid4
from os.path import join
from tempfile import gettempdir

import pandas as pd

from aequilibrae.utils.create_example import create_example

# We create the example project inside our temp folder
fldr = join(gettempdir(), uuid4().hex)

project = create_example(fldr)
logger = project.logger

Traffic assignment with skimming#

In this step, we’ll set the skims for the variable free_flow_time, and execute the traffic assignment for the base-year.

from aequilibrae.paths import TrafficAssignment, TrafficClass

# We build all graphs
project.network.build_graphs()
# We get warnings that several fields in the project are filled with NaNs.
# This is true, but we won't use those fields.

# We grab the graph for cars
graph = project.network.graphs["c"]

# Let's say we want to minimize the free_flow_time
graph.set_graph("free_flow_time")

# And will skim time and distance while we are at it
graph.set_skimming(["free_flow_time", "distance"])

# And we will allow paths to be computed going through other centroids/centroid connectors
# required for the Sioux Falls network, as all nodes are centroids
graph.set_blocked_centroid_flows(False)

Let’s get the demand matrix directly from the project record, and inspect what matrices we have in the project.

proj_matrices = project.matrices
proj_matrices.list()
name file_name cores procedure procedure_id timestamp description status
0 demand_omx demand.omx 1 None None 2020-11-24 08:47:18 Original data imported to OMX format
1 demand_mc demand_mc.omx 3 None None 2021-02-24 00:51:35 None
2 skims skims.omx 2 None None None Example skim
3 demand_aem demand.aem 1 None None 2020-11-24 08:46:42 Original data imported to AEM format


We get the demand matrix, and prepare it for computation

demand = proj_matrices.get_matrix("demand_omx")
demand.computational_view(["matrix"])

Let’s perform the traffic assignment

# Create the assignment class
assigclass = TrafficClass(name="car", graph=graph, matrix=demand)

assig = TrafficAssignment()

# We start by adding the list of traffic classes to be assigned
assig.add_class(assigclass)

# Then we set these parameters, which an only be configured after adding one class to the assignment
assig.set_vdf("BPR")  # This is not case-sensitive

# Then we set the volume delay function and its parameters
assig.set_vdf_parameters({"alpha": "b", "beta": "power"})

# The capacity and free flow travel times as they exist in the graph
assig.set_capacity_field("capacity")
assig.set_time_field("free_flow_time")

# And the algorithm we want to use to assign
assig.set_algorithm("bfw")

# Since we haven't checked the parameters file, let's make sure convergence criteria is good
assig.max_iter = 1000
assig.rgap_target = 0.001

# we then execute the assignment
assig.execute()

car                                               :   0%|          | 0/24 [00:00<?, ?it/s]
Equilibrium Assignment                            :   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car               :   0%|          | 1/1000 [00:00<00:00, 36472.21it/s]
All-or-Nothing - Traffic Class: car               :   0%|          | 1/1000 [00:00<00:00, 7037.42it/s]
All-or-Nothing - Traffic Class: car               :   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 0/24 :   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 10/24:   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 20/24:   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 24/24:   0%|          | 0/1000 [00:00<?, ?it/s]
Equilibrium Assignment - Iteration: 1/1000 - RGap: inf:   0%|          | 0/1000 [00:00<?, ?it/s]
Equilibrium Assignment                            :   0%|          | 2/1000 [00:00<00:02, 421.94it/s]
All-or-Nothing - Traffic Class: car               :   0%|          | 2/1000 [00:00<00:02, 410.98it/s]
All-or-Nothing - Traffic Class: car               :   0%|          | 2/1000 [00:00<00:02, 400.89it/s]
All-or-Nothing - Traffic Class: car               :   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 0/24 :   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 10/24:   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 20/24:   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 24/24:   0%|          | 0/1000 [00:00<?, ?it/s]
Equilibrium Assignment - Iteration: 2/1000 - RGap: 0.855075:   0%|          | 0/1000 [00:00<?, ?it/s]
Equilibrium Assignment                            :   0%|          | 3/1000 [00:00<00:01, 676.61it/s]
All-or-Nothing - Traffic Class: car               :   0%|          | 3/1000 [00:00<00:01, 657.83it/s]
All-or-Nothing - Traffic Class: car               :   0%|          | 3/1000 [00:00<00:01, 640.55it/s]
All-or-Nothing - Traffic Class: car               :   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 0/24 :   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 10/24:   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 20/24:   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 24/24:   0%|          | 0/1000 [00:00<?, ?it/s]
Equilibrium Assignment - Iteration: 3/1000 - RGap: 0.476346:   0%|          | 0/1000 [00:00<?, ?it/s]
Equilibrium Assignment                            :   0%|          | 4/1000 [00:00<00:01, 879.77it/s]
All-or-Nothing - Traffic Class: car               :   0%|          | 4/1000 [00:00<00:01, 856.24it/s]
All-or-Nothing - Traffic Class: car               :   0%|          | 4/1000 [00:00<00:01, 834.48it/s]
All-or-Nothing - Traffic Class: car               :   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 0/24 :   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 10/24:   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 20/24:   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 24/24:   0%|          | 0/1000 [00:00<?, ?it/s]
Equilibrium Assignment - Iteration: 4/1000 - RGap: 0.235513:   0%|          | 0/1000 [00:00<?, ?it/s]
Equilibrium Assignment                            :   0%|          | 5/1000 [00:00<00:00, 1078.78it/s]
All-or-Nothing - Traffic Class: car               :   0%|          | 5/1000 [00:00<00:00, 1050.36it/s]
All-or-Nothing - Traffic Class: car               :   0%|          | 5/1000 [00:00<00:00, 1024.45it/s]
All-or-Nothing - Traffic Class: car               :   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 0/24 :   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 10/24:   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 20/24:   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 24/24:   0%|          | 0/1000 [00:00<?, ?it/s]
Equilibrium Assignment - Iteration: 5/1000 - RGap: 0.109241:   0%|          | 0/1000 [00:00<?, ?it/s]
Equilibrium Assignment                            :   1%|          | 6/1000 [00:00<00:00, 1350.17it/s]
All-or-Nothing - Traffic Class: car               :   1%|          | 6/1000 [00:00<00:00, 1312.77it/s]
All-or-Nothing - Traffic Class: car               :   1%|          | 6/1000 [00:00<00:00, 1278.62it/s]
All-or-Nothing - Traffic Class: car               :   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 0/24 :   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 10/24:   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 20/24:   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 24/24:   0%|          | 0/1000 [00:00<?, ?it/s]
Equilibrium Assignment - Iteration: 6/1000 - RGap: 0.198095:   0%|          | 0/1000 [00:00<?, ?it/s]
Equilibrium Assignment                            :   1%|          | 7/1000 [00:00<00:00, 1166.80it/s]
All-or-Nothing - Traffic Class: car               :   1%|          | 7/1000 [00:00<00:00, 1143.22it/s]
All-or-Nothing - Traffic Class: car               :   1%|          | 7/1000 [00:00<00:00, 1121.09it/s]
All-or-Nothing - Traffic Class: car               :   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 0/24 :   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 10/24:   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 20/24:   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 24/24:   0%|          | 0/1000 [00:00<?, ?it/s]
Equilibrium Assignment - Iteration: 7/1000 - RGap: 0.0668172:   0%|          | 0/1000 [00:00<?, ?it/s]
Equilibrium Assignment                            :   1%|          | 8/1000 [00:00<00:00, 1790.24it/s]
All-or-Nothing - Traffic Class: car               :   1%|          | 8/1000 [00:00<00:00, 1741.28it/s]
All-or-Nothing - Traffic Class: car               :   1%|          | 8/1000 [00:00<00:00, 1696.04it/s]
All-or-Nothing - Traffic Class: car               :   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 0/24 :   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 10/24:   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 20/24:   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 24/24:   0%|          | 0/1000 [00:00<?, ?it/s]
Equilibrium Assignment - Iteration: 8/1000 - RGap: 0.0679212:   0%|          | 0/1000 [00:00<?, ?it/s]
Equilibrium Assignment                            :   1%|          | 9/1000 [00:00<00:00, 1834.42it/s]
All-or-Nothing - Traffic Class: car               :   1%|          | 9/1000 [00:00<00:00, 1787.77it/s]
All-or-Nothing - Traffic Class: car               :   1%|          | 9/1000 [00:00<00:00, 1745.28it/s]
All-or-Nothing - Traffic Class: car               :   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 0/24 :   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 10/24:   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 20/24:   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 24/24:   0%|          | 0/1000 [00:00<?, ?it/s]
Equilibrium Assignment - Iteration: 9/1000 - RGap: 0.107056:   0%|          | 0/1000 [00:00<?, ?it/s]
Equilibrium Assignment                            :   1%|          | 10/1000 [00:00<00:00, 2078.55it/s]
All-or-Nothing - Traffic Class: car               :   1%|          | 10/1000 [00:00<00:00, 2025.65it/s]
All-or-Nothing - Traffic Class: car               :   1%|          | 10/1000 [00:00<00:00, 1976.49it/s]
All-or-Nothing - Traffic Class: car               :   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 0/24 :   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 10/24:   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 20/24:   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 24/24:   0%|          | 0/1000 [00:00<?, ?it/s]
Equilibrium Assignment - Iteration: 10/1000 - RGap: 0.0403881:   0%|          | 0/1000 [00:00<?, ?it/s]
Equilibrium Assignment                            :   1%|          | 11/1000 [00:00<00:00, 2400.74it/s]
All-or-Nothing - Traffic Class: car               :   1%|          | 11/1000 [00:00<00:00, 2336.30it/s]
All-or-Nothing - Traffic Class: car               :   1%|          | 11/1000 [00:00<00:00, 2265.52it/s]
All-or-Nothing - Traffic Class: car               :   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 0/24 :   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 10/24:   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 20/24:   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 24/24:   0%|          | 0/1000 [00:00<?, ?it/s]
Equilibrium Assignment - Iteration: 11/1000 - RGap: 0.0279525:   0%|          | 0/1000 [00:00<?, ?it/s]
Equilibrium Assignment                            :   1%|          | 12/1000 [00:00<00:00, 2586.28it/s]
All-or-Nothing - Traffic Class: car               :   1%|          | 12/1000 [00:00<00:00, 2517.46it/s]
All-or-Nothing - Traffic Class: car               :   1%|          | 12/1000 [00:00<00:00, 2443.05it/s]
All-or-Nothing - Traffic Class: car               :   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 0/24 :   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 10/24:   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 20/24:   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 24/24:   0%|          | 0/1000 [00:00<?, ?it/s]
Equilibrium Assignment - Iteration: 12/1000 - RGap: 0.0327:   0%|          | 0/1000 [00:00<?, ?it/s]
Equilibrium Assignment                            :   1%|▏         | 13/1000 [00:00<00:00, 2892.93it/s]
All-or-Nothing - Traffic Class: car               :   1%|▏         | 13/1000 [00:00<00:00, 2811.05it/s]
All-or-Nothing - Traffic Class: car               :   1%|▏         | 13/1000 [00:00<00:00, 2736.15it/s]
All-or-Nothing - Traffic Class: car               :   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 0/24 :   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 10/24:   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 20/24:   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 24/24:   0%|          | 0/1000 [00:00<?, ?it/s]
Equilibrium Assignment - Iteration: 13/1000 - RGap: 0.024041:   0%|          | 0/1000 [00:00<?, ?it/s]
Equilibrium Assignment                            :   1%|▏         | 14/1000 [00:00<00:00, 2882.68it/s]
All-or-Nothing - Traffic Class: car               :   1%|▏         | 14/1000 [00:00<00:00, 2792.21it/s]
All-or-Nothing - Traffic Class: car               :   1%|▏         | 14/1000 [00:00<00:00, 2723.20it/s]
All-or-Nothing - Traffic Class: car               :   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 0/24 :   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 10/24:   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 20/24:   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 24/24:   0%|          | 0/1000 [00:00<?, ?it/s]
Equilibrium Assignment - Iteration: 14/1000 - RGap: 0.021451:   0%|          | 0/1000 [00:00<?, ?it/s]
Equilibrium Assignment                            :   2%|▏         | 15/1000 [00:00<00:00, 2238.47it/s]
All-or-Nothing - Traffic Class: car               :   2%|▏         | 15/1000 [00:00<00:00, 2194.21it/s]
All-or-Nothing - Traffic Class: car               :   2%|▏         | 15/1000 [00:00<00:00, 2153.43it/s]
All-or-Nothing - Traffic Class: car               :   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 0/24 :   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 10/24:   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 20/24:   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 24/24:   0%|          | 0/1000 [00:00<?, ?it/s]
Equilibrium Assignment - Iteration: 15/1000 - RGap: 0.0171166:   0%|          | 0/1000 [00:00<?, ?it/s]
Equilibrium Assignment                            :   2%|▏         | 16/1000 [00:00<00:00, 2869.62it/s]
All-or-Nothing - Traffic Class: car               :   2%|▏         | 16/1000 [00:00<00:00, 2802.16it/s]
All-or-Nothing - Traffic Class: car               :   2%|▏         | 16/1000 [00:00<00:00, 2741.38it/s]
All-or-Nothing - Traffic Class: car               :   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 0/24 :   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 10/24:   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 20/24:   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 24/24:   0%|          | 0/1000 [00:00<?, ?it/s]
Equilibrium Assignment - Iteration: 16/1000 - RGap: 0.0173508:   0%|          | 0/1000 [00:00<?, ?it/s]
Equilibrium Assignment                            :   2%|▏         | 17/1000 [00:00<00:00, 3768.67it/s]
All-or-Nothing - Traffic Class: car               :   2%|▏         | 17/1000 [00:00<00:00, 3563.55it/s]
All-or-Nothing - Traffic Class: car               :   2%|▏         | 17/1000 [00:00<00:00, 3460.81it/s]
All-or-Nothing - Traffic Class: car               :   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 0/24 :   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 10/24:   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 20/24:   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 24/24:   0%|          | 0/1000 [00:00<?, ?it/s]
Equilibrium Assignment - Iteration: 17/1000 - RGap: 0.0211647:   0%|          | 0/1000 [00:00<?, ?it/s]
Equilibrium Assignment                            :   2%|▏         | 18/1000 [00:00<00:00, 3798.61it/s]
All-or-Nothing - Traffic Class: car               :   2%|▏         | 18/1000 [00:00<00:00, 3695.78it/s]
All-or-Nothing - Traffic Class: car               :   2%|▏         | 18/1000 [00:00<00:00, 3601.81it/s]
All-or-Nothing - Traffic Class: car               :   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 0/24 :   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 10/24:   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 20/24:   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 24/24:   0%|          | 0/1000 [00:00<?, ?it/s]
Equilibrium Assignment - Iteration: 18/1000 - RGap: 0.0124645:   0%|          | 0/1000 [00:00<?, ?it/s]
Equilibrium Assignment                            :   2%|▏         | 19/1000 [00:00<00:00, 4300.92it/s]
All-or-Nothing - Traffic Class: car               :   2%|▏         | 19/1000 [00:00<00:00, 4108.46it/s]
All-or-Nothing - Traffic Class: car               :   2%|▏         | 19/1000 [00:00<00:00, 3992.17it/s]
All-or-Nothing - Traffic Class: car               :   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 0/24 :   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 10/24:   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 20/24:   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 24/24:   0%|          | 0/1000 [00:00<?, ?it/s]
Equilibrium Assignment - Iteration: 19/1000 - RGap: 0.0125498:   0%|          | 0/1000 [00:00<?, ?it/s]
Equilibrium Assignment                            :   2%|▏         | 20/1000 [00:00<00:00, 4243.10it/s]
All-or-Nothing - Traffic Class: car               :   2%|▏         | 20/1000 [00:00<00:00, 4124.60it/s]
All-or-Nothing - Traffic Class: car               :   2%|▏         | 20/1000 [00:00<00:00, 4017.53it/s]
All-or-Nothing - Traffic Class: car               :   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 0/24 :   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 10/24:   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 20/24:   0%|          | 0/1000 [00:00<?, ?it/s]
All-or-Nothing - Traffic Class: car - Zones: 24/24:   0%|          | 0/1000 [00:00<?, ?it/s]
Equilibrium Assignment - Iteration: 20/1000 - RGap: 0.0118607:   0%|          | 0/1000 [00:00<?, ?it/s]
Equilibrium Assignment                            :   2%|▏         | 21/1000 [00:00<00:00, 4229.14it/s]
All-or-Nothing - Traffic Class: car               :   2%|▏         | 21/1000 [00:00<00:00, 4119.18it/s]
All-or-Nothing - Traffic Class: car               :   2%|▏         | 21/1000 [00:00<00:00, 4020.10it/s]
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Equilibrium Assignment - Iteration: 21/1000 - RGap: 0.0128592:   0%|          | 0/1000 [00:00<?, ?it/s]
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All-or-Nothing - Traffic Class: car               :   2%|▏         | 23/1000 [00:00<00:00, 4929.94it/s]
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All-or-Nothing - Traffic Class: car               :   3%|▎         | 27/1000 [00:00<00:00, 5521.78it/s]
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After finishing the assignment, we can easily see the convergence report.

convergence_report = assig.report()
convergence_report.head()
iteration rgap alpha warnings beta0 beta1 beta2
0 1 inf 1.000000 1.000000 0.000000 0.0
1 2 0.855075 0.328400 1.000000 0.000000 0.0
2 3 0.476346 0.186602 1.000000 0.000000 0.0
3 4 0.235513 0.241148 1.000000 0.000000 0.0
4 5 0.109241 0.818547 0.607382 0.392618 0.0


And we can also see the results of the assignment

results = assig.results()
results.head()
matrix_ab matrix_ba matrix_tot Preload_AB Preload_BA Preload_tot Congested_Time_AB Congested_Time_BA Congested_Time_Max Delay_factor_AB Delay_factor_BA Delay_factor_Max VOC_AB VOC_BA VOC_max PCE_AB PCE_BA PCE_tot
link_id
1 4502.545113 0.0 4502.545113 0.0 0.0 0.0 6.000822 0.0 6.000822 1.000137 0.0 1.000137 0.173842 0.0 0.173842 4502.545113 0.0 4502.545113
2 8222.240524 0.0 8222.240524 0.0 0.0 0.0 4.009141 0.0 4.009141 1.002285 0.0 1.002285 0.351326 0.0 0.351326 8222.240524 0.0 8222.240524
3 4622.925028 0.0 4622.925028 0.0 0.0 0.0 6.000913 0.0 6.000913 1.000152 0.0 1.000152 0.178490 0.0 0.178490 4622.925028 0.0 4622.925028
4 5897.692905 0.0 5897.692905 0.0 0.0 0.0 6.501414 0.0 6.501414 1.300283 0.0 1.300283 1.189487 0.0 1.189487 5897.692905 0.0 5897.692905
5 8101.860609 0.0 8101.860609 0.0 0.0 0.0 4.008617 0.0 4.008617 1.002154 0.0 1.002154 0.346182 0.0 0.346182 8101.860609 0.0 8101.860609


We can export our results to CSV or get a Pandas DataFrame, but let’s put it directly into the results database

assig.save_results("base_year_assignment")

And save the skims

assig.save_skims("base_year_assignment_skims", which_ones="all", format="omx")

Trip distribution#

First, let’s have a function to plot the Trip Length Frequency Distribution.

from math import log10, floor
import matplotlib.pyplot as plt

def plot_tlfd(demand, skim, name):
    plt.clf()
    b = floor(log10(skim.shape[0]) * 10)
    n, bins, patches = plt.hist(
        np.nan_to_num(skim.flatten(), 0),
        bins=b,
        weights=np.nan_to_num(demand.flatten()),
        density=False,
        facecolor="g",
        alpha=0.75,
    )

    plt.xlabel("Trip length")
    plt.ylabel("Probability")
    plt.title(f"Trip-length frequency distribution for {name}")
    return plt

Calibration#

We will calibrate synthetic gravity models using the skims for free_flow_time that we just generated

import numpy as np
from aequilibrae.distribution import GravityCalibration

We need the demand matrix and to prepare it for computation

demand = proj_matrices.get_matrix("demand_aem")
demand.computational_view(["matrix"])

We also need the skims we just saved into our project

imped = proj_matrices.get_matrix("base_year_assignment_skims_car")

# We can check which matrix cores were created for our skims to decide which one to use
imped.names

['distance_blended', 'distance_final', 'free_flow_time_blended', 'free_flow_time_final']

Where free_flow_time_final is actually the congested time for the last iteration

But before using the data, let’s get some impedance for the intrazonals. Let’s assume it is 75% of the closest zone.

imped_core = "free_flow_time_final"
imped.computational_view([imped_core])

# If we run the code below more than once, we will be overwriting the diagonal values with non-sensical data
# so let's zero it first
np.fill_diagonal(imped.matrix_view, 0)

# We compute it with a little bit of NumPy magic
intrazonals = np.amin(imped.matrix_view, where=imped.matrix_view > 0, initial=imped.matrix_view.max(), axis=1)
intrazonals *= 0.75

# Then we fill in the impedance matrix
np.fill_diagonal(imped.matrix_view, intrazonals)

Since we are working with an OMX file, we cannot overwrite a matrix on disk. So let’s give it a new name to save.

imped.save(names=["final_time_with_intrazonals"])

This also updates these new matrices as those being used for computation

imped.view_names

['final_time_with_intrazonals']

Let’s calibrate our Gravity Model

for function in ["power", "expo"]:
    gc = GravityCalibration(matrix=demand, impedance=imped, function=function, nan_as_zero=True)
    gc.calibrate()
    model = gc.model
    # We save the model
    model.save(join(fldr, f"{function}_model.mod"))

    _ = plot_tlfd(gc.result_matrix.matrix_view, imped.matrix_view, f"{function} model")

    # We can save the result of applying the model as well
    # We can also save the calibration report
    with open(join(fldr, f"{function}_convergence.log"), "w") as otp:
        for r in gc.report:
            otp.write(r + "\n")
Trip-length frequency distribution for expo model

And let’s plot a trip length frequency distribution for the demand itself

plt = plot_tlfd(demand.matrix_view, imped.matrix_view, "demand")
plt.show()
Trip-length frequency distribution for demand

Forecast#

We create a set of ‘future’ vectors using some random growth factors. We apply the model for inverse power, as the trip frequency length distribution (TFLD) seems to be a better fit for the actual one.

from aequilibrae.distribution import Ipf, GravityApplication, SyntheticGravityModel

Compute future vectors#

First thing to do is to compute the future vectors from our matrix.

origins = np.sum(demand.matrix_view, axis=1)
destinations = np.sum(demand.matrix_view, axis=0)

# Then grow them with some random growth between 0 and 10%, and balance them
orig = origins * (1 + np.random.rand(origins.shape[0]) / 10)
dest = destinations * (1 + np.random.rand(origins.shape[0]) / 10)
dest *= orig.sum() / dest.sum()

vectors = pd.DataFrame({"origins":orig, "destinations":dest}, index=demand.index[:])

IPF for the future vectors#

Let’s balance the future vectors. The output of this step is going to be used later in the traffic assignment for future year.

args = {
    "matrix": demand,
    "vectors": vectors,
    "column_field": "destinations",
    "row_field": "origins",
    "nan_as_zero": True,
}

ipf = Ipf(**args)
ipf.fit()

When saving our vector into the project, we’ll get an output that it was recored

ipf.save_to_project(name="demand_ipfd", file_name="demand_ipfd.aem")
ipf.save_to_project(name="demand_ipfd_omx", file_name="demand_ipfd.omx")

<aequilibrae.project.data.matrix_record.MatrixRecord object at 0x7fa655307160>

Impedance#

Let’s get the base-year assignment skim for car we created before and prepare it for computation

imped = proj_matrices.get_matrix("base_year_assignment_skims_car")
imped.computational_view(["final_time_with_intrazonals"])

If we wanted the main diagonal to not be considered…

# np.fill_diagonal(imped.matrix_view, np.nan)

Now we apply the Synthetic Gravity model

for function in ["power", "expo"]:
    model = SyntheticGravityModel()
    model.load(join(fldr, f"{function}_model.mod"))

    outmatrix = join(proj_matrices.fldr, f"demand_{function}_model.aem")
    args = {
        "impedance": imped,
        "vectors": vectors,
        "row_field": "origins",
        "model": model,
        "column_field": "destinations",
        "nan_as_zero": True,
    }

    gravity = GravityApplication(**args)
    gravity.apply()

    # We get the output matrix and save it to OMX too,
    gravity.save_to_project(name=f"demand_{function}_modeled", file_name=f"demand_{function}_modeled.omx")

We update the matrices table/records and verify that the new matrices are indeed there

proj_matrices.update_database()
proj_matrices.list()
name file_name cores procedure procedure_id timestamp description status
0 demand_omx demand.omx 1 None None 2020-11-24 08:47:18 Original data imported to OMX format
1 demand_mc demand_mc.omx 3 None None 2021-02-24 00:51:35 None
2 skims skims.omx 2 None None None Example skim
3 demand_aem demand.aem 1 None None 2020-11-24 08:46:42 Original data imported to AEM format
4 base_year_assignment_skims_car base_year_assignment_skims_car.omx 4 Traffic Assignment ff3ffb86d65840708f9b2ea9db69a47c 2025-04-30 22:16:56.717530 Skimming for assignment procedure. Class car
5 demand_ipfd demand_ipfd.aem 1 Iterative Proportional fitting c5c4cb0f58b84adb8f7e3b6d77aa3178 2025-04-30 22:16:57.895934 None
6 demand_ipfd_omx demand_ipfd.omx 1 Iterative Proportional fitting c5c4cb0f58b84adb8f7e3b6d77aa3178 2025-04-30 22:16:57.895934 None
7 demand_power_modeled demand_power_modeled.omx 1 Synthetic gravity trip distribution 8e39b7b1ca5f4e7093a43908f789eb75 2025-04-30 22:16:57.994483 Synthetic gravity trip distribution. POWER
8 demand_expo_modeled demand_expo_modeled.omx 1 Synthetic gravity trip distribution 4ecc7fe2b9764ce5ba586a1b691acce2 2025-04-30 22:16:58.089247 Synthetic gravity trip distribution. EXPO