A model checking based formal verification procedure is developed to verify and validate the routing microarchitecture in a Network-on-chip (NoC) communication infrastructure. Specifically, four crucial properties of an NoC router, namely, mutual exclusion, starvation freedom, deadlock freedom, and conditions for traffic congestions are investigated. Given a recently proposed bi-directional channel direction control protocol, guidelines for constructing formal models of an NoC router are proposed, and minimal formal models essential for verifying these four properties are analyzed. A popular formal verification model checking tool State Graph Manipulators (SGM) is applied to perform the verification task. Results obtained through formal verification of these four properties provide useful insights to refine the protocol design.