A packet communications system utilizes a route determining mechanism by identifying principal paths between the source and the destination in the system. Principal paths are minimum hop count paths with a transmission delay less than a specified threshold. Principal path links are accepted as legs of the optimum path, if feasible, i.e., if the resulting load on the link is less than a specified principal threshold. Secondary links are accepted only if the resulting load on the link is less than a specified secondary threshold, where the secondary threshold is less than the principal threshold. All paths must also have a transmission delay less than a specified threshold. Each request for a route includes the source node, the destination node, the load required, the maximum transmission delay and, if desired, the quality of service parameters which all of the legs of the route must satisfy. A modified Bellman-Ford breadth-first search algorithm is used to identify the principal links and, using these principal link identifications, determining the optimum path.