The process number is the number of requests that have to be simultaneously disturbed during a routing reconfiguration phase of a connection oriented network. From a graph theory point of view, it is similar to the pathwidth. However they are not always equal in general graphs. Determining these parameters is in general NP-complete. In this paper, we propose a polynomial algorithm to compute an approximation of the process number of digraphs, improving the efficiency of the previous exponential algorithm.