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Various traffic assignment (TA) models are used in practice by transportation engineers and urban planners. These models allow to analyse road networks, to predict impact of potential projects and policies and to control traffic with respect to level of congestion, emissions, toll revenue (Ortúzar and Willumsen 2001). TA models aim to predict how road users will decide to travel during a given period of time. The task of predicting how a particular individual will travel is addressed by making certain assumptions on how people usually make their route choices. The classical TA model assumes that drivers travel on their fastest (or shortest) paths and network equilibrium occurs when no traveller can decrease their travel time by shifting to a new path. The assumption that each driver minimises a certain measure (eg travel time) is called the user equilibrium condition (Sheffi 1985). The key feature of TA models consists in …