In this paper, we propose a robust solution for the path planning and scheduling of the moving objects in a Track-based Traffic Control System (TTCS). The moving objects in a TTCS pass over pre-specified sub-tracks. Each sub-track accommodates at most one moving object in-transit. Due to the uncertainties in the context of a TTCS, we assign an arrival time window to each moving object for each sub-track in its route, instead of an exact value. The moving object can safely enter into the sub-track in the mentioned time window. To develop a safe plan, we adapt the tagged-signal model and provide a rigorous mathematical formalism for the actor model of a TTCS. To illustrate the applicability of the provided semantics, we provide a formal model of TTCSs in the Alloy language and use its analyzer to verify the developed model against system safety properties.