The existence of equivalent mathematical programs for certain mixed equilibrium traffic assignment problems

Until recently, for the purpose of modelling equilibrium flow patterns, it has often been assumed that all the private vehicle traffic on a road network forms a single class, governed by a single set of equilibrium criteria. However, when some private vehicles are driven with the aid of a route-guidance system, this assumption may no longer be valid, since the guidance system controller may adopt different equilibrium criteria to those followed by the individual unguided drivers, resulting in ‘mixed equilibrium traffic assignment problems’. In this paper, for two alternative definitions of a mixed equilibrium traffic assignment problem, the paper investigates the existence of an equivalent mathematical program that satisfies certain conditions, restricting ourselves to deterministic equilibria and static models.