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.

Capacity restraint assignment attempts to approximate an equilibrium solution by iterating between all-or-nothing traffic loadings and recalculating link travel times based on a congestion function that reflects link capacity. Unfortunately, this method does not converge and can flip-flop back and forth in loadings on some links.

User equilibrium assignment procedures based on Wardrop’s principle assume that all drivers perceive costs in an identical manner. A solution to the assignment problem on this basis is an assignment such that no driver can reduce his journey cost by unilaterally changing route. Van Vilet considered as stochastic assignment models, all those models which explicitly allow non-minimum cost routes to be selected. Virtually all such models assume that drivers' perception of costs on any given route are not identical and that the trips between each O-D pair are divided among the routes with the most cheapest route attracting most trips. They have important advantages over other models because they load many routes between individual pairs of network nodes in a single pass through the tree-building process, the assignments are more stable and less sensitive to slight variations in network definitions or link costs to be independent of flows and are thus most appropriate for use in uncongested traffic conditions such as in off-peak periods or lightly trafficked rural areas.

Dynamic user equilibrium, expressed as an extension of Wardrop’s user equilibrium principle, may be defined as the state of equilibrium which arises when no driver can reduce his disutility of travel by choosing a new route or departure time, where disutility includes schedule delay in addition to costs generally considered. Dynamic stochastic equilibrium may be similarly defined in terms of perceived utility of travel. The existence of such equilibria in complex networks has not been proven theoretically and even if they exist the question of uniqueness remains open.