On Stackelberg Routing on Parallel Networks with Horizontal Queues

In order to address inefficiencies of Nash equilibria for congestion networks with horizontal queues, we study the Stackelberg routing game on parallel networks: assuming a coordinator has control over a fraction of the flow, and that the remaining players respond selfishly, what is an optimal Stackelberg strategy of the coordinator, i.e. a strategy that minimizes the cost of the induced equilibrium? We study Stackelberg routing for a new class of latency functions, which models congestion on horizontal queues. We introduce a candidate strategy, the non-compliant first strategy, and prove it to be optimal. Then we apply these results by modeling a transportation network in which a coordinator can choose the routes of a subset of the drivers, while the rest of the drivers choose their routes selfishly.