Frequency-Domain Modeling and Analysis of Stochastic Flows in Transportation Networks

In this paper, we study the transportation network flow problem with stochastic flow distribution. According to the stochastic properties of transportation network flows, we first discuss the functional relations between the arcs and the nodes for modeling the transportation network systems, and originally construct an incidence matrix of capacity in the frequency domain. Then a new frequency-domain spanning graph model to analyze the network stochastic maximum flow and the stochastic minimum flow problem is presented. A corresponding algorithm is designed to resolve the model. In our solution, through the mutual transformations of probability functions between time-domain and frequency-domain in our model, the dynamic process of origin-destination flows is analyzed qualitatively; hence the minimum flow and maximum flow are derived quantitatively. An advantage of our approach is that it can handle uniformly both the continuous probability distribution case and the discrete probability distribution case. Numerical experiment results illustrate the feasibility and effectiveness of our approach.