The process of allocating a given set of trip interchanges to the specified transportation system is usually referred to as traffic assignment. The fundamental aim of the traffic assignment process is to reproduce on the transportation system, the pattern of vehicular movements which would be observed when the travel demand represented by trip matrices to be assigned is satisfied. The major aims of traffic assignment procedures are:
1. To estimate the volume of traffic on the links of the network and obtain aggregate network measures.
2. To estimate interzonal travel cost.
3. To analyze the travel pattern of each origin to destination (O-D) pair.
4. To identify congested links and to collect traffic data useful for the design of future junctions.

As the flow increases towards the capacity of the stream, the average stream speed reduces from the free flow speed to the speed corresponding to the maximum flow. This can be seen in the graph shown below. That means traffic conditions worsen and congestion starts developing. The interzonal flows are assigned to the minimum paths computed on the basis of free-flow link impedances (usually travel time). But if the link flows were at the levels dictated by the assignment, the link speeds would be lower and the link travel time would be higher than those corresponding to the free-flow conditions. So the minimum path computed prior to the trip assignment will not be the minimum after the trips are assigned. The relation between the link flow and link impedance is called the link cost function and is given by the equation as shown below:
t = t0[1 + αx^β] where t is the travel time and x is the flow, respectively on the link, t0 is the free flow travel time, and k is the practical capacity. α and β are the model parameters, usually with α = 0.15 minimum and β = 4.0.

In this method the trips from any origin zone to any destination zone are loaded onto a single, minimum cost, path between them. This model is unrealistic as only one path between every O-D pair is utilized even if there is another path with the same or nearly same travel cost. Also, traffic on links is assigned without consideration of whether or not there is adequate capacity or heavy congestion; travel time is a fixed input and does not vary depending on the congestion on a link. However, this model may be reasonable in sparse and uncongested networks where there are few alternative routes and they have a large difference in travel cost. This model may also be used to identify the desired path: the path which the drivers would like to travel in the absence of congestion. In fact, this model’s most important practical application is that it acts as a building block for other types of assignment techniques. It has a limitation that it ignores the fact that link travel time is a function of link volume and when there is congestion or that multiple paths are used to carry traffic.

The user equilibrium assignment is based on Wardrop’s first principle, which states that no driver can unilaterally reduce his/her travel costs by shifting to another route. User Equilibrium (UE) conditions can be written for a given O-D pair as: f(cu)=0 for all k; cu >= 0 for all k. If c = 0, from f k ⇒ 0 implies that all used paths will have same travel time. If cu > 0, then ensures that all unused paths will have travel time greater than the minimum cost path. The assumptions in User Equilibrium Assignment are: 1. The user has perfect knowledge of the path cost.
2. Travel time on a given link is a function of the flow on that link only.
3. Travel time functions are positive and increasing.

The system optimum assignment is based on Wardrop’s second principle, which states that drivers cooperate with one another in order to minimize total system travel time. This assignment can be thought of as a model in which congestion is minimized when drivers are told which routes to use. Obviously, this is not a behaviorally realistic model, but it can be useful to transport planners and engineers trying to manage traffic to minimize travel costs and therefore achieve an optimum social equilibrium.

Let us discuss briefly some other assignments also. 10.6.1 Incremental assignment is a process in which fractions of traffic volumes are assigned in steps. In each step, a fixed proportion of total demand is assigned, based on all-or-nothing assignment. After each step, link travel times are recalculated based on link volumes. When there are many increments used, the flows may resemble an equilibrium assignment; however, this method does not yield an equilibrium solution. Consequently, there will be inconsistencies between link volumes and travel times that can lead to errors in evaluation measures. Also, incremental assignment is influenced by the order in which volumes for O-D pairs are assigned, raising the possibility of additional bias in results.