The paper describes a mathematical model of trade ows in a transport network. Based on the model the software package is implemented as a cloud service on heterogeneous computing architectures: simulation module is realized on a high-performance server platform, control and visualization modules are produced with the IACPaaS cloud platform. Communication between the platforms is established via asynchronous http-requests. 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. The visualization module allows us 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 tra c of the Russian Far East region based on input data provided by open statistics sources.
Operation of a transport system that connects the regions of the country is essential for the safe and stable functioning regions as an economic system that ensures the processes of production and consumption. Since the creation of such a system is a timeconsuming task, a necessary condition is a preliminary analysis and assessment of the design and management solutions to their application in the real world. Such decisions can be directed to the modernization and construction of the individual sections of the region's transport network, especially in approaches to ports, large industrial areas, large urban agglomerations and new elds.
Transport systems in modern conditions characterized by an independent noncooperative behavior of a large number of heterogeneous economic agents realizing their individual interests, sharing of road network, air, pipeline, sea and railway transport for both freight and passenger tra c.
Copyright c by the paper's authors. Copying permitted for private and academic purposes. In: A. Kononov et al. (eds.): DOOR 2016, Vladivostok, Russia, published at http://ceur-ws.org
Simulation of interregional ows in the interdisciplinary setting was proposed by
Wassily Leontief [
However, approaches to constructing a mathematical model of trade ows have
the following disadvantages. They do not include export and import ows outside the
system of considered regions. Second, these models do not consider that transportation
can be both multi-product and multimodal, i.e. transportation can be implemented in
di erent ways and/or various types of transport, by road, rail, sea and air transport
modes. Third, import and export of goods corresponding the processes of supply and
demand of goods by a region can be attributed to the same regions, and not only the
di erent regions. Input data can be de ned inaccurately, in this case it is possible to
modify the model assuming interval input data as discussed in [
The purpose of the paper is a description of the mathematical model and the software package implemented on heterogeneous computing architectures for interactive simulation of interregional trade. 2
In this section the mathematical model, program implementation and visualization of trade ows for the Far East of Russia Macro-region is given. 2.1
Mathematics of trade
ows model o cial statistics and is de ned as Wir.
Consider the model of the economy of m regions in each of which there is an n products. Let xirj is an unknown number of a product of r-th type, r = 1; : : : ; n delivered from the i-th region in the j-th, i; j = 1; : : : ; m. Here and below the superscripts correspond to the product type, subscripts correspond regions. Note that the ow xiri is not necessarily assumed to be zero, this ow corresponds to the regions where the product is consumed and also produced and therefore its transportation is not carried out.
The total product ow from region r to the j-th region (\total consumption" of m the product r to the region j) is an unknown variable and it equals P xirj . The last i=1 sum also equals to Vjr that is a known cumulative import of product r to the region j given by o cial statistics. Total export of product r from the region i in other regions m (\total production" of product r to the region i) is P xirj which in turn is known from j=1
The production and consumption of each product r = 1; : : : ; n de ned in the above way is subject to obvious for a closed system of balance equation m m X X xirj = i=1 j=1
X Vjr = X Wir; j i (1) which imposes an additional restriction on the values of Vjr and Wir.
However, since the real system of regions may be not closed, the aforementioned balance (1) formed on the statistical data is not be observed. This means that there is a ow of products between these k regions and other unknown \external" regions in relation to the considered system of regions. The problem is complicated by the fact that neither the total import or export of such \external" regions are known. Obviously in this case the model requires modi cation.
To solve this problem let's aggregate the \external" regions to (m + 1)-th region r r and let's consider additional ows xi m+1 and xm+1 j which are unknown and moreover are unidenti ed.
Trade ows are carried out by economic agents under the in uence of the transportation costs which principally depends on the geographical distance between regions. Consider the gravity model for transportation costs which can be represented by virj = exp( drTij ), where virj is a priori de ned the ow of products from the i-th region in the j-th, Tij is an assessment of the geographical distance between regions i and j, and dr are the parameters that are responsible for the ow sensitivity to distance for the product r. Parameters dr are non-negative which means that the higher the value of the distance between, the smaller an amount of ow between the regions i and j is. It is additionally assumed that viri = 0 for Tii = 0 and virj = vjri because of Tij = Tji.
Calibration of non-negative parameters dr with actual o cial statistics is a separate problem of applied statistics. This assessment is carried out by methods such as least squares (LS) applied to the regression model which is represented by a linear by parameters model ln virj = drTij + r for all li; j = 1; : : : ; m and i > j where r is a normally distributed residuals of the regression for all r.
In papers [
r=1 i;j=1;i6=j
The presence of such features makes it necessary to specify strictly positive trade ows xirj which is modeled by specifying lower restrictions on ows by preassigned small parameter " > 0.
Thus for modeling of trade ows it is necessary to solve a nonlinear optimization problem with the objective function and linear constraints: n X m+1
X r=1 i;j=1;i6=j xirj ln(xirj =v^irj ) ! fmxirijng; (2) for all j = 1; 2; : : : ; m and r = 1; 2; : : : ; n, for all i = 1; 2; : : : ; m and r = 1; 2; : : : ; n, m+1 X xirj = Vjr; i=1 m+1 X xirj = Wir j=1
r xij " > 0 (3) (4) (5) where v^irj = exp( d^rTij ); d^r are known estimates of the parameters and constraints of the problem are given further: for all i; j = 1; 2; : : : ; m + 1; r = 1; 2; : : : ; n. 3
Modeling of economic relations of territories is used for decision-making on regional social and economic policy. It aims at reducing the negative e ect of interregional heterogeneity in economic development in order to prevent depression, uncompetitive, distressed areas, lagging behind the leading regions, and in general, in order to integrate economically regions of the country.
The software interregional trade simulation is intended for specialists from various ministries and departments dealing with the problem of optimizing and planning of the interregional ows of industries products based on multi-product approach and multimodal transport networks.
Base requirements for the software are the following.
1. Software implementation is a cloud service for supplying wide availability of the
developed applications. Use of application as a cloud service doesn't do extra
limitations to a platform installed on a client's computer, random-access memory and
other characteristics of a computer and also it doesn't requires special skills to
install the application [
The cloud platform IACPaaS [
A generalized architecture of the cloud service is presented in the Fig. 1. The software consists of three modules: a module of trade ow simulation, a control module and a visualization module.
Software that implements the described above mathematical model is realized. It is used
to nd the equilibrium interregional freight tra c in the transport network system of
regions. Model implementation is carried out in the MPL language [
To use the program the following input information is needed: statistical data on total import and export of products for the regions, the distance between the main transport hubs of regions in the implementation of transport by rail, road and/or sea.
An indicator of \connectedness" of the regions for a speci c industry or aggregated for all products is de ned as Lij = Ei2+(xEijj++xIij+i)Ij where xij is an out ow from the region of i to the region j and Ek is a total export of products from the region k to all other regions, and Ik is total imports to the region k from all other regions.
Output results of the program are calculated equilibrium values of the freight tra c between transport network nodes, the matrix of interregional ows and \connectivity matrix of regions in the context of NACE classi cation of economic activities and for all simulated NACE codes.
The computer program provides an output of calculated matrices of interregional ows and indicators of regions \connectedness" for each product and aggregated values of all the goods. 5
The trade ow simulation module and the visualization module are the independent sybsystems located on di erent servers. To provide interaction between them an additional module of control is required. . The main task of the control module is to get and transfer information from the simulation module and the visualization module in a previously de ned format that is understandable for them. A convenient data format for the simulation module is a matrix representation; a convenient data format for visualization is a graph. Both formats are specialized and useful for speci c tasks. Therefore, we need an intermediate format for exchanging information between them. For this aim, we have developed a declarative format for trade ow 14. That format consists of three base types of objects: products, zones and communications. A structure of each type and links between them are provided in the Fig. 2.
The control module uses the http-protocol and asynchronous requests. The visualization module sends an asynchronous http-request to the control module for getting input data from the simulation module. The control module initiates an http-request for getting or calculating data about a state of trade ows. The simulation module forms data in the declarative representation and then sends an answer to the visualization module using the control module. Then the visualization module builds a graph of trade ows by obtained data. The control module is di erent from existing methods for inter-regional ows because it provides interaction between two environments (environment of calculations and environment of visualization) which are on the di erent platforms.
A declarative representation of the objects which is realized with JSON format is shown on Fig. 2. The visualization module gives a possibility to represent complicated matrix data about di erent trade ows visually (graphically) in form of oriented graph. Arcs of that graph are trade ows and vertexes are points of destination of these ows.
The visualized transport net allows users to see results of mathematic modeling and to change them interactively, by editing parameters of vertexes and arcs by a program interface.
The visualization module displays di erent variants of the oriented graph in
depend of needed parameters. For this on base of the declarative model there are formed
automatically control elements for the graph of trade ows [
The parametrical sampling and the visualization of only part of information matters a lot for clarity of the received results especially if parts of these results are entirely (or partially) are independent from each other. Addition graphical parameters are used for the visualization of the transport ows graph: a color and thickness of arcs. The color characterizes a type of communication of ows. The thickness characterizes a volume of ows' loads.
Interactive editing of the graph supposes a change of the parameters vertexes and arcs of the graph. (Fig. 3). In accordance with user modi cation the dynamic asynchronous request is sent to the simulation module server via the control module and as a results a new declarative model of trade ows will be received and graph visualization will be changed.
Implementation of the visualization module as a cloud service gives a convenient way to use and display the results of mathematical modeling for many users via the Internet.
Software for interactive interregional trade simulation is used to determine the equilibrium interregional freight tra c in the transport network of railway, road and sea transport of the Far Eastern regions of Russia. As input data we have used information from o cial statistical handbooks of Rosstat from di erent years \The regions of Russia. Socio-economic indicators of the interregional trade". The main products (commodities) are foodstu s, fuel, goods for technical purposes.
Administrative centers of nine Far East regions are considered: Primorsky Krai (Vladivostok), Khabarovsk (Khabarovsk), the Amur Region (Blagoveshchensk), the Jewish Autonomous Region (Birobidzhan), the Republic of Sakha - Yakutia (Yakutsk), Magadan region (Magadan), Sakhalin region (Yuzhno-Sakhalinsk), Kamchatka region (Petropavlovsk-Kamchatsky), Chukotka Autonomous Okrug (Anadyr). These cities are considered as the centers of economic activities described by the model. Estimates of the distances between regions are shown in Table 1, which are corresponded by the shortest paths between the administrative centers of the regions in the transport network of railway, road and sea transport of the Far East of Russia.
The visual presentation of the data is shown in Fig. 4.
Currently we have made modeling for 25 products for various purposes: food, fuel, technical supplies and others. The result of the simulation determines the most probable movements of goods between the regions of the Russian Far East. In a case of incomplete statistical data the use of mathematical modeling allowed us to obtain interpretable results with economic sense and forecast the most probable distribution of the ow of goods between the regions of the Russian Far East.
The presented approach allows us to determine characteristics of relationship of economies of the Far East regions of Russia in the conditions of the existing spatial structure of production placement. These relationships are accompanied by spatial nonuniformity and strong product di erentiation. A new structure of the region's economy relationships is possible when parameters of the economic area are changing (transport, energy infrastructure, and spatial structure of production and consumption of the gross regional product). 8
The paper describes mathematical model and the software package that are designed for interactive simulation of interregional trade. The software package is a cloud-service and consists of three main modules: the simulation module of trade ows, the control module and visualization module. The mathematical model of trade ows is the basis of the simulation module. It is implemented on a high-performance computing platform due to high computational complexity of the modeling process in a case of huge dimension of a problem. Control and visualization modules are implemented on the cloud platform IACPaaS using a multi-agent approach. The interaction between the high-performance computing platform and the IACPaaS platform is carried out using a http-protocol with dynamic asynchronous requests. The software package is designed for professionals from various ministries and departments dealing with the problem of optimizing the planning and interregional ows industries products based on their multi-product in multimodal transport networks, and can be used for interregional trade simulation in di erent regions of Russia.