Abstract: Arrangements and methods for efficiently selecting an optimum connection path that meets user specified delay requirements with enhanced efficiency. In a basic aspect, a method is implemented by one of a plurality of algorithms to meet user QoS specifications. The user not only specifies a delay threshold T for the incoming request but also specifies a delay threshold tolerance &egr; for the path delay that will satisfy him. Two implementations are disclosed. The first is termed non-iterative and sets scaling factor &tgr;=min (T, (n−1)/&egr;), where n is a number of links in a shortest path, scales all the relevant delay parameters by &tgr;/T, truncates all the scaled values to integers, and uses a dynamic programming algorithm to accumulate the total of resulting link delay parameters values for each possible shortest path. The second method, termed iterative, is similar, except that it sets &tgr;<<T.