Most current system optimum dynamic traffic assignment (SO-DTA) models do not contain first-in-first-out (FIFO) constraints and are limited to single-destination network applications. In this study, we introduce the link transmission model (LTM) for the development of SO-DTA models either with or without FIFO constraints for general network applications. The proposed SO-DTA models include the LTM and can lead to a linear programming (LP) formulation if the FIFO constraints are not explicitly

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... tured. The vehicle holding problem can be addressed by adding a penalty term to the objective function. We also formulate FIFO constraints in terms of the relationship between link cumulative inflows and outflows and the link entry time. Optimization models that integrate the proposed FIFO constraints into the proposed LP formulations for SO-DTA problems without FIFO constraints are also developed to formulate SO-DTA problems with FIFO constraints. Based on the properties of the proposed optimization problems, branch-and-bound algorithms are developed to solve SO-DTA problems with FIFO constraints. Two methods are developed to identify FIFO violations in feasible flow patterns and to design a branching scheme for the proposed branch-andbound algorithms. Finally, numerical examples are set up to demonstrate the properties of the proposed models and the performance of the algorithms. corresponding user equilibrium (UE) static traffic assignment problem, which can be formulated as a mathematical program or a variational inequality (VI) problem with a convex solution set. However, for the dynamic extensions of SO and UE static traffic assignment problems (i.e., dynamic traffic assignment (DTA) problems), their solution sets are always non-convex, mainly because they often capture desirable properties to make the solutions consistent with actual traffic behavior. These properties include queue spillback (e.g., Queue spillback refers to the queue spilling over to its upstream links. FIFO states that vehicles exit from the link in the same order they entered it. Vehicle holding implies that traffic flows are reluctant to move forward from upstream links to their downstream links even if vacant spaces are available on the downstream links. In DTA models, capturing queue spillback can lead to the non-existence of UE solutions (Szeto and Lo 2006); the FIFO requirement can yield a nonconvex constraint set (Carey 1992), and the NVH requirement can introduce discrete decision variables, making the resultant problem more difficult to solve efficiently. Developing SO-DTA models for the benchmarking that can both capture actual traffic behavior and be solved efficiently is thus challenging.