In the NPM (Network Performance Model) TRE models the network performance corresponding to the input route choices (in the form of local turn probabilities) and expected demand flows.
Problem formulation
The problem is solved by two alternating models, computed for each time interval: the link model and the node model.
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The link model gets as an input:
- the link inflow,
- the link outflow,
- the link fundamental diagram.
The link model returns the potential sending flow and potential receiving flow for future instants.
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The node model gets as an input:
- the potential demand (sending flows) from the node upstream links,
- the node turn split rates (turn probabilities),
- the node turn priorities,
- the potential supply (receiving flows) from the node downstream links.
After getting this input, the node model solves a fixed-point problem and returns the actual turning flows.
In NPM uses two alternative models, described in the following, which differ in the way they use the two models above.
General Link Transmission Model (GLTM)
The traffic model is an implementation of the GLTM (General Link Transmission Model, Gentile, 2008). It performs a Dynamic Network Loading (DNL), that is the propagation of the demand flows generated at origins, according to link performances and the route choices provided in input as splitting rates (possibly time-varying).
Important advantages of this model are:
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Its high computational efficiency for handling large-scale networks (+100,000 links)
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An accurate representation of queue formation and dispersion
Due to the specific formulation in the GLTM, the problem can be solved immediately by running the node model and the link model in chronological order, with no need for fixed-point convergence.
GLTM allows for an easier interpretation of results, even when the level of convergence is still not satisfactory. On the other side, during intermediate iterations when DNL convergence is still not achieved, the simulated flows are not guaranteed to be consistent with the OD flows (i.e. the amount of flow reaching a destination can differ from the input OD matrices).
AKW-NPM
The traffic model is a modern implementation of the NPM described in Gentile G., Meschini L., Papola N. (2005), using the AKW (Average Kinematic Wave) theory. It performs a series of Arc Performance Functions propagating per each link of the network at each time interval its entry flows according to link performances and computes the result of boundary interactions at its head node according to the route choices provided in input as (possibly time-varying) splitting rates. Internal model iterations are used to achieve the dependencies at node amongst upstream and downstream links.
The AKW-NPM conveys robustness to the DTA model, as it retains more locally the congestions around their causes and thus allows modeled drivers smarter route choices. On the other side, during intermediate iterations when DNL convergence is still not achieved, the simulated flows are not guaranteed to be consistent at node (i.e. the node sum of entry and exit flow can differ). The focus of the AKW-NPM on space and time separated link performances rather than on node flow consistency make it a methodology more suitable for faster evaluations of congested performances, rather than for a proper equilibrium assignment.
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