Proposing a Simulation-Based Dynamic System Optimal Traffic Assignment Algorithm for SUMO: An Approximation of Marginal Travel Time

User equilibrium (UE) and system optimal (SO) are among the essential principles
for solving the traffic assignment problem. Many studies have been performed on
solving the UE and SO traffic assignment problem; however, the majority of them are
either static (which can lead to inaccurate predictions due to long aggregation intervals)
or analytical (which is computationally expensive for large-scale networks). Besides,
most of the well-known micro/meso traffic simulators, do not provide a SO solution of
the traffic assignment problem. To this end, this study proposes a new simulation-based
dynamic system optimal (SB-DSO) traffic assignment algorithm for the SUMO
simulator, which can be applied on large-scale networks. A new swapping/convergence
algorithm, which is based on the logit route choice model, is presented in this study.
This swapping algorithm is compared with the Method of Successive Average (MSA)
which is very common in the literature. Also, a surrogate model of marginal travel time
was implemented in the proposed algorithm, which was tested on real and abstract road
networks (both on micro and meso scales). The results indicate that the proposed
swapping algorithm has better performance than the classical swapping algorithms (e.g.
MSA). Furthermore, a comparison was made between the proposed SB-DSO and the
current simulation-based dynamic user equilibrium (SB-DUE) traffic assignment
algorithm in SUMO. This proposed algorithm helps researchers to better understand the
impacts of vehicles that may follow SO routines in future (e.g., Connected and
Autonomous Vehicles (CAVs)).