Network-on-a-chip (NoC) is becoming a promising paradigm of core-based system. We propose a new method for test scheduling in NoC. The method is based on the use of a dedicated routing path for the test of each core. We show that test scheduling under this approach is NP-complete and present an ILP model for solving small NoC instances. For NoCs with larger number of cores, we present an efficient heuristic. We then improve the heuristic by including BISTs and precedence constraints. Experimental results for the ITC'02 SoC benchmarks show that the new method leads to substantial reduction on test application time compared to previous work. The inclusion of BIST tests and precedence constraints provides a comprehensive solution for test scheduling in NoC.