The Gradient Projection Algorithm for Multiple Routing in Message-Switched Networks

Various algorithms have been proposed for determining the routing paths designed to minimize the average overall message time delay in message-switched networks. In this paper we describe the application of the gradient projection algorithm to this problem. This algorithm is a gradient-type search procedure designed to handle constrained optimization problems, into which category the routing problem falls. Calculations of the computational complexity of this algorithm indicate that it is particularly well-suited to networks with a limited number of commodities or source-destination pairs. The algorithm is applied to a representative group of distributed-type networks, of varying complexity. Execution times for this algorithm are compared with those obtained using the flow deviation routing algorithm. These agree roughly with the results of the computational requirement calculations; i.e., this algorithm generally requires less execution time for networks with a relatively small number of commodities than does the flow deviation method. (The actual running time depends significantly on the choice of the initial flows or routing paths, however.) For those networks in which all network nodes may be expected to communicate with all other nodes, however, the flow deviation method would be expected to be superior.