A method and apparatus for selectively parking routers used for routing traffic in mesh interconnects. Various router parking (RP) algorithms are disclosed, including an aggressive RP algorithm where a minimum number of routers are kept active to ensure adequate network connectivity between active nodes and/or intercommunicating nodes, leading to a maximum reduction in static power consumption, and a conservative RP algorithm that favors network latency considerations over static power consumption while also reducing power. An adaptive RP algorithm is also disclosed that implements aspects of the aggressive and conservative RP algorithms to balance power consumption and latency considerations in response to ongoing node utilization and associated traffic. The techniques may be implemented in internal network structures, such as for single chip computers, as well as external network structures, such as computing clusters and massively parallel computer architectures. Performance modeling has demonstrated substantial power reduction may be obtained using the router parking techniques while maintaining Quality of Service performance objectives.