Table 1: Summary of Main Differences between Flow-Based and Density-Based Models.

Characteristic

Flow-Based Model

Density-Based Model

General concept

Assigns vehicles per hour among the different network links for a representative time period.

Assigns vehicles per kilometre among the different network links for a representative instant in time.

Equilibrium condition

Satisfies Wardrop’s first principle for all network routes.

Satisfies Wardrop’s first principle for all network routes.

State of system

Assumes that all trips in the trip matrix are assigned to the network and that all trips enter and exit within a given modelled period.

Assumes that the total number of vehicles on the network at a given instant is the same at the instant immediately preceding and immediately following.

Link capacity

Each link is assumed to have a fixed, exogenous capacity or maximum flow. This capacity will often be exceeded.

Each link’s maximum flow, rather than being a fixed parameter, depends on vehicle density and speed across it and will vary with traffic conditions. Maximum flow is finite.

Trip matrix

Assumes a trip matrix (flows between O-D pairs) for the period modelled that is fixed and exogenous to equilibrium cost.

Assumes the number of vehicles for the instant modelled is fixed and exogenous but the trip matrix (flows between O-D pairs) is a result of the equilibrium.

Conservation of flow

By construction, assumes conservation of flow at all network nodes including cases where route time or cost is greater than the period modelled (i.e., there are travellers who do not arrive at their destination).

With the conservation of flow is satisfied.

Densities and queue lengths under congestion

Does not satisfactorily estimate either densities or queue lengths under high congestion.

Always correctly estimates densities and queue lengths, whether under low or high congestion.

Fundamental traffic equation

Under high congestion, the relationship does not hold.

By construction, the relationship always holds.

Estimation of benefits of road system project or policy

Benefits are estimated in terms of network user time savings.

Benefits are estimated as the change in consumer surplus.