Arrangements and methods for improving the probability of finding a connection path that meets user specified delay requirements. The improvements offer packet switches enhanced path selection that will improve the resource utilization of networks, both flat networks and hierarchical networks incorporating such switches. The latter type of networks run the path selection algorithm in the PNNI v1.0 standard where the packet switches are asynchronous transfer mode switches. Two modes of enhanced delay-based path selection are based on two different accumulation methods, namely an additive method and an asymptotic method.