According to the U.S. Department of Transportation, 36 states are experiencing shortages in rest areas, affecting the truck drivers' ability to comply with working hour regulations. Since expanding the infrastructure would require significant capital investment, this issue points to the need for better utilization of the existing truck parking capacity. In this paper, we present a mixed integer programming (MIP) model for a variant of the truck driver scheduling problem which considers the parking availability of the rest areas along the route, as well as the USA's hours-of-service (HOS) constraints for long trips. The parking availability of each rest area is modeled as a set of time-windows which is enforced only if the driver needs to stop at that location. Computational experiments using CPLEX were performed to test the impact of these constraints. The results indicate that by including parking availability constraints we can generate more realistic schedules, which will not send drivers to busy rest areas, without increasing the cost for the driver/company.