- The
**transport demand**between places must either be known or estimated. For instance, the gravity model offers a methodology to estimate potential flows between locations if a set of attributes are known, such as respective distances and emission and attraction variables. - The
**transport supply**between places must also either be known or estimated. This involves establishing a set of paths between places that are generating and attracting movements. This includes the**geometric definition**of transport networks with the graph theory.

An traffic assignment problem is the distribution of traffic in a network considering a demand between a set of locations and the transport supply of the network. Assignment methods are looking for a way to model the distribution of traffic in a network according to a set of constraints, notably related to transport capacity, time and cost.

**optimization methods**.

**Uninterrupted traffic**. Traffic regulated by vehicle-vehicle interactions and interactions between vehicles and the transport infrastructure. The most common example of uninterrupted traffic is an highway.**Interrupted traffic**. Traffic regulated by an external means, such as a traffic signal, which often create a queuing. Under interrupted flow conditions, vehicle-vehicle interactions and vehicle-infrastructure interactions play a less important part. The most common example of interrupted traffic in the urban circulation regulated by traffic signals such as lights and stop signs.

- Traffic is represented in a graph (network) by its
**value**; the number of any units flowing (cars, people, tons etc.). The intensity of the traffic is proportional to the load of the network. - Traffic is also represented in a graph by its
**assignment**; how the traffic is distributed on a graph according to supply and demand.

- There must exists nodes in the graph where traffic can be generated and attracted. These nodes are generally associated to centroids in an O-D matrix.
- The minimal (l(a,b)) and maximal (k(a,b)) capacities of every link must be respected. k(a,b) is the transport supply on the link (a,b).
- Transport demand must respected. The O/D matrix has equal inputs and outputs (closed system).
- There is conservation of the traffic at every node that is not an origin or a destination.

**Maximal Load**(ML): Number of units of traffic that a network can support at a point in time. The maximal load is the summation of the capacity of all links.

**Load**(L): Number of units of traffic that a network supports while fulfilling a transport demand. Load is the summation of the traffic of all links.

**Traffic**maximization involves the determination of the maximal transport demand that a network or a section of network can support between its nodes.

**Cost minimization**involves the determination of the minimal transport costs considering a known demand. Transport costs on a link are expressed by g(Q(a,b)) and the minimization function by: