This paper reviews the range of traffic models, with particular attention to microsimulation. Although there are major types, there are so many hybrids that it is difficult to classify them all. The standard way of assigning traffic to a network is to find a static equilibrium from which no driver would be able to find a quicker route. This gives fairly good predictions of the link flows resulting from driver choices. Traffic is loaded on to shortest routes, times are modified by a speed-flow function, leading to reassignment to more routes, and the solution is iterated until all used routes between each origin-destination pair take equal time.
An alternative is stochastic user equilibrium, taking explicit account of the variability of choice. Each route between an O-D pair that does not backtrack is given an initial share by logit distribution. Again, travel times are modified to take account of congestion, and there is a somewhat messy iterative process to reach equilibrium. Curiously, stochastic user equilibrium is as deterministic as 'deterministic user equilibrium'. A criticism of equilibrium models is that the process of adjustment after a change to the network may be of more interest than the apparently stable outcome.
Microsimulation has been used for small components of the network but recent models at the single vehicle level can simulate whole urban networks, using a great deal of computer power. One uses cellular automata, such that each cell in a spatial lattice is updated according to its own state and the states of its nearby neighbours at the previous time step. More conventional microsimulations use simple rule based behaviour. Simulations are designed not only to show the emergent order but also the impact of incidents which generate spreading instabilities. Microsimulation is also used to capture the expected effects of route information, as well as indicating control and routing strategies.