A BRIEF SURVEY ON DYNAMIC NETWORK FLOWS IN CONTINUOUS-TIME MODEL

Abstract

In dynamic network flows, when some commodities move from one place to another, time taken by them to traverse the path are taken into account, unlike the static flows. Time being continuous entity, network flow problems are modeled in its continuous setting to get more realistic solution to the optimization problems. Rather, it can also be discretized to get more computational results. In this paper, insight is given to the models formulated by the researchers in dynamic network flows along with some practical applications regarding the triple optimization problem in continuous time setting mainly focusing on cost minimization problems, since the quickest path problem and the maximum flow problem are considered as two important special cases of the minimum cost flow problem. Different solution strategies and their efficiencies carried out by them are also observed. Further possible modification in the existing formulations and algorithms for better solution of problems are suggested as research endeavor.