Felt¶
Felt is a Python library for estimating path flows on networks where flows are not directly observable. It is motivated by estimating vehicle flows on highway networks, but may be applied to other problems.
Quick Start¶
Installation¶
pip install felt
Example¶
We’d like to estimate path flows on a network. To start we build a model of the network. The network has two links that merge together onto a single link, and then diverge again to two links.
>>> from felt import Network, Node, Way
>>> network = Network(
... [
... Node(1, 0.0, 0.0),
... Node(2, 1.0, 0.0),
... Node(3, 2.0, 0.0),
... Node(4, 3.0, 0.0),
... Node(5, 0.0, 1.0),
... Node(6, 3.0, 1.0)
... ],
... [
... Way([1, 2, 3, 4], oneway=True),
... Way([5, 2], oneway=True),
... Way([3, 6], oneway=True)
... ]
... )
Now we make a list of all the possible paths on this network. There are two source nodes: 1 and 5; and there are two sink nodes: 4 and 6. Each source node is connected with a path to each other sink node, to make a total of four paths. Our goal is to estimate the flow on each of the four paths.
>>> paths = [
... network.shortest_path(1, 4),
... network.shortest_path(1, 6),
... network.shortest_path(5, 4),
... network.shortest_path(5, 6)
... ]
>>> paths
[Path([1, 2, 3, 4]), Path([1, 2, 3, 6]), Path([5, 2, 3, 4]), Path([5, 2, 3, 6])]
To help us with our estimation, we have movement flow observations for three movements. You can think of movements as sub-sequences of paths, where each path either has that sub-sequence or not. The movement flow observations for the three movements are 30, 70, and 40.
>>> from felt import Movement
>>> movements = [
... Movement([..., 1, 2, 3, ...]),
... Movement([..., 5, 2, 3, ...]),
... Movement([..., 2, 3, 4, ...])
... ]
>>> movement_flows = [30, 70, 40]
Now we can estimate the path flows from our movement flows. Our estimates are 12, 18, 28 and 42.
>>> from felt import estimate
>>> path_flows = estimate(paths, movements, movement_flows)
>>> print([round(v) for v in path_flows])
[12, 18, 28, 42]