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.