- This article proposes a stochastic attention allocation and reactive scheduling model to prevent illegal border crossings. To intercept infiltrators, a limited pool of security agents is dynamically assigned to heterogeneous frontier segments that transmit erratic signals of crossing attempts by independent trespassers. The frontier segments may differ in terms of rates of crossing attempts, ease of crossing, and reliability of the detection systems. Due to the huge complexity of the agent scheduling decision, a relaxed Markovian model is proposed whose solution is a set of optimal steady-state allocation rates for sending security agents to any frontier segment where a crossing attempt is apparently taking place. This solution is used to derive a heuristic policy for dispatching security agents among the frontier segments based on the evolving signals. Simulation experiments demonstrate that the proposed heuristic outperforms other scheduling policies. Border crossing is just one example of a viable application for this attention allocation model, which can be extended and customized for a wide variety of other scenarios.