Abstract

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.

中文翻译：

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跨地区贸易流交互模拟的云服务

摘要

本文描述了具有一种或多种不同类型的海洋或陆运的运输网络中区域或国家领土之间贸易流量的数学模型。如果有关系统的信息不完整，我们将使用对复杂的通信系统建模的方法来确定最可能的流量值。区域之间的运输成本在重力模型的框架内建模。运输费用取决于区域之间的距离，该距离被估计为给定运输网络中的最短路程或地理距离。该问题的数学公式属于凸数学规划问题的类别，并且假设具有线性约束的非线性优化问题的数值解。基于该模型，该软件在异构计算架构上作为云服务实现：仿真模块是在高性能服务器平台上制作的，管理和可视化模块是使用IACPaaS云平台制作的。平台之间的通信是通过异步http查询建立的。为了模块之间的信息交换，针对数学模型中考虑的对象（产品，区域和通信）开发并实现了具有JSON格式的声明性模型。可视化模块允许以图形方式显示原始数据和所得矩阵数据，并以交互方式修改模型的输入参数。