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Stochastic traffic assignment, also known as stochastic user equilibrium assignment, is a variant of the more widely-used deterministic user equilibrium assignment process. It incorporates an error term in the link capacity function that adds noise to the link travel time estimates in each iteration. This noise represents the imperfect information that travelers have about network conditions. This accounts for uncertainty about travel times that they will encounter in congested conditions, information or perception errors, and as a result of using unfamiliar routes or traveling in new places. It has also been advanced that stochastic variability, if properly characterized, can better represent the inherent day-to-day variability in travel times. The amount of noise added to the calculated link travel times is controlled by a lambda parameter that should be calibrated based on observed or stated preference survey data.
Stochastic traffic assignments have been used primarily in academic research, and are rarely used in practice. Bergomi (2009) includes a well-written and approachable description for those who would like further information on this topic. Patriksson (1994) covers the topic in much greater and deeper detail.