Abstract: In the study of traffic assignment theory, the development of equilibrium model theory has attracted significant attention. The traffic equilibrium problem aims to determine the flow distribution and various performance metrics in a traffic network by using given O/D pair demand and cost functions, based on established path selection criteria. The core of this methodology lies in the fact that, under a traffic equilibrium state, no participant in the system can improve their travel time or cost by unilaterally changing their path choice, thereby maximizing the efficiency and performance of the traffic system. However, in reality, due to the diversity of traffic participants' behavior and the complexity of traffic networks, achieving a true equilibrium state is often challenging. This paper defines an approximate form of traffic equilibrium ${\varepsilon}$-equilibrium flow and verifies its existence. Additionally, it introduces a type of well-posedness for ${\varepsilon}$-equilibrium flow and establishes sufficient conditions for the validity of this well-posedness, providing new theoretical tools and methods for understanding and solving traffic equilibrium problems.

Key words: traffic equilibrium, ${\varepsilon}$-equilibrium flow, well-posedness