User equilibrium and system optimum with incomplete information in traffic congestion

By providing more information about traffic network, such as more feasible paths via intelligent navigation systems (INS), users in the network may change their choices of the path from a source to a destination. This paper investigates a traffic congestion model with incomplete information, in which different users have different information about the network. We introduce the notions of user equilibrium of incomplete information (UEII) and system optimum of incomplete information (SOII). Then, we prove a theorem about the effect of the change of traffic amount on each couple paths in SOII for the model. Finally, based on this theorem and a property of UEII, we reveal a relationship between UEII and SOII on the cost function.