The following excerpt was taken from the Transportation Planning Handbook published in 1992 by the Institute of Transportation Engineers (pp. 115-117).
The traffic assignment process is somewhat different from the mathematical models used for trip distribution and mode choice. Traffic is assigned to available transit or roadway routes using a mathematical algorithm which determines the amount of traffic to allocate to each route. The traffic allocation is usually based on the relative time to travel along each available path, computed from the transit and roadway networks.
All or nothing
Historically all trips between two zones were assigned to the route having the minimum travel time, regardless of the available capacity; this is termed an "all-or-nothing" assignment. Such an approach is still used for identifying travel desire corridors as an initial step in locating new and improved transportation facilities. For most transit assignments the all-or-nothing approach is still used since there are rarely closely competing transit routes in an efficiently designed transit system. Similarly the all-or-nothing approach is used for assigning high occupancy vehicle trip assignments.
More common today for roadway assignments is the "capacity-restrained" assignment, a strategy which assigns traffic in steps. One option in this approach is "proportional" assignment, which allocates a portion of the trips between every origin-destination zone pair to the network at each step. An alternative is the "incremental" assignment, which allocates all of the trips between a subset of zone pairs at each step. In either case the travel times between all zone pairs are recalculated after each assignment step, considering the traffic already assigned, to adjust the speeds on all network links. The revised speeds on all links are determined by a speed-volume function that indicates the maximum speed likely for a particular volume/capacity ratio. . . . Another assignment step is then computed considering the revised travel times, after which the link speeds are again adjusted as previously. This process is iterated until all trips have been assigned. Additional fully iterated assignments may be necessary to reach an equilibrium in which there is little change in speeds throughout the network at each assignment step.