The paper describes a mathematical model of trade flows between the territories of a region or a country in a transportation network having one or more different types of marine or ground transport. We use the approach of modeling complex communication systems to determine the most probable values of flows in case of incomplete information about the system. Transportation costs between the territories are modeled within the framework of the gravity model. The payment for transportation depends on the distance between regions, the distance is estimated as the shortest way length in a given transportation network or geographical distance. The mathematical formulation of the problem belongs to the class of convex mathematical programming problems and assumes the numerical solution of nonlinear optimization problem with linear constraints. Based on the model, the software is implemented as a cloud service on heterogeneous computing architectures: the simulation module is made on a high-performance server platform, management and visualization modules are produced with IACPaaS cloud platform. Communication between the platforms is established via asynchronous http-queries. For information exchange between the modules the declarative model with JSON format is developed and implemented for the objects considered in the mathematical model which are products, areas and communications. Visualization module allows to present graphically the original and the resulting matrix data and to modify the input parameters of the model interactively. The paper demonstrates the use of software for the simulation of interregional freight traffic of the Russian Far East region based on input data provided by open statistics sources.