A fast infiltration game on n arcs

Starting from a safe base, an Infiltrator tries to reach a sensitive zone within a given time limit without being detected by a Guard. the Infiltrator can move with speed at most u, while the Guard can only perform a restricted number of searches. A discrete variant of this zero-sum game played on a graph consisting of two vertices joined by n nonintersecting arcs is investigated. Optimal strategies and an explicit expression for its value are obtained.