The quickest path problem is one of the important things for quality of services in communication networks. It is to find a path to send a given amount of data from the source to the sink with minimum transmission time, where the transmission time is dependent on both the capacities and the traversal times of the arcs in the network. This is found under the networks that the capacity and the lead time of each ring are predetermined. It is general to solve the quickest path problem using shortest path algorithms. The relevant algorithms proposed till now are based on the capacity of rings in distributed environments. When the configuration of networks is changed, there can be two a, pp.oaches to find the quickest paths. The one is to find new quickest paths, and the other is to update the current quickest paths. As one of the algorithms for the latter, the distributed quickest path update algorithm was proposed. This paper aims to propose the distributed algorithm a, pp.icable to find the quickest path, when the configuration of networks is changed, using the quickest path tree update altorithm, and to verify its possibility of a, pp.ication by analyzing the transmission amount of data from one node to another from the theoretical point of view.