Due to increase in demand for re-configurability in embedded systems, real-time task scheduling is challenged by non-negligible reconfiguration overheads. If such overheads are not considered, tasks may not be schedulable under given deadlines, and hence, affecting the quality of service. The authors introduce the problem of real-time periodic task scheduling under transition overhead on heterogeneous reconfigurable systems. They formulate the problem as a network flow problem and provide a mixed integer linear programming solution. They compare their proposed solution with optimal scheduling under maximum fixed transition overhead.