  Arc-based traffic assignment models (TAMs) are a popular framework for
modeling traffic network congestion generated by self-interested travelers who
sequentially select arcs based on their perceived latency on the network.
However, existing arc-based TAMs either assign travelers to cyclic paths, or do
not extend to networks with bi-directional arcs (or edges) between nodes. To
overcome these difficulties, we propose a new modeling framework for stochastic
arc-based TAMs. Given a traffic network with bidirectional arcs, we replicate
its arcs and nodes to construct a directed acyclic graph (DAG), which we call
the Condensed DAG (CoDAG) representation. Self-interested travelers
sequentially select arcs on the CoDAG representation to reach their
destination. We show that the associated equilibrium flow, which we call the
Condensed DAG equilibrium, exists, is unique, and can be characterized as a
strictly convex optimization problem. Moreover, we propose a discrete-time
dynamical system that captures a natural adaptation rule employed by
self-interested travelers to learn about the emergent congestion on the
network. We show that the arc flows generated by this adaptation rule converges
to a neighborhood of Condensed DAG equilibrium. To our knowledge, our work is
the first to study learning and adaptation in an arc-based TAM. Finally, we
present numerical results that corroborate our theoretical results.
