CC BY-NC-ND
22
DOI: 10.17323/2587-814X.2022.1.7.21
Simulation of migration and demographic processes using FLAME GPU
Valery L. Makarov a
E-mail: makarov@cemi.rssi.ru
Albert R. Bakhtizin a
E-mail: albert@cemi.rssi.ru
Gayane L. Beklaryan a ©
E-mail: glbeklaryan@gmail.com
Andranik S. Akopov ba ©
E-mail: aakopov@hse.ru
Nikita V. Strelkovskii c ©
E-mail: strelkon@iiasa.ac.at
a Central Economics and Mathematics Institute, Russian Academy of Sciences Address: 47, Nakhimovsky Prospect, Moscow 117418, Russia
b HSE University Address: 20, Myasnitskaya Street, Moscow 109028, Russia
c International Institute for Applied Systems Analysis (IIASA) Address: 1, Schlossplatz, Laxenburg A-2361, Austria
Abstract
This article presents an approach to modeling migration and demographic processes using a framework designed for large-scale agent-based modeling - FLAME GPU. This approach is based on the previously developed simulation model of interaction between two communities: migrants and natives that is implemented in the AnyLogic simulation software. The model has had a low dimensionality of the discrete space representing the operating environment of the agent populations and a deterministic decision-making system of each agent. At the same time, the presence of multiple interactions between agents and transitions between their states determines a high computational complexity of such a model. The use of FLAME GPU makes it possible to conduct extensive simulation experiments with the model, mainly due to the parallelization of computational processes at the level of each agent, as well as the implementation of the mechanism of multiple computations
using Monte Carlo techniques. The developed framework is used to study the impact of the most important parameters of the model (e.g., rate of migration, governmental expenditures on integration, frequency of creation of new workplaces, etc.) on the key outputs of the modeled socio-economic system (in particular, population size, share of migrants, number of assimilated migrants, GDP growth rate, etc.). The proposed approach can be used to develop decision-making systems for planning the hiring of new employees based on the forecast dynamics of migration and demographic processes.
Keywords: agent-based modeling, migration and demographic processes, population dynamics, large-scale modeling, parallel computing on GPU, supercomputer modeling, decision support
Citation: Makarov V.L., Bakhtizin A.R., Beklaryan G.L., Akopov A.S., Strelkovskii N.V. (2022) Simulation of migration and demographic processes using FLAME GPU. Business Informatics, vol. 16, no. 1, pp. 7-21. DOI: 10.17323/2587-814X.2022.1.7.21
Introduction
In modern times, many companies and organizations are faced with a deficit of labor resources and the need to form a long-term plan for hiring new employees taking into account forecasts of migration flows and demographic processes. In conditions of the degradation of the internal demographic situation, many firms try refocusing themselves to attract migrants. However, due to the presence of many barriers created by an insufficient level of proficiency in the local language, lack of necessary qualifications and some other factors, there are natural limitations in attracting external labor which can only be overcome through assimilation and integration processes implemented in conditions of financial support from the government.
The development of decision-making systems for planning the hiring of new employees and creation of new workplaces can be based on simulation models that take into account the forecast dynamics of the labor market. For instance, in the context of the spread of epidemics, the government is able to introduce restrictions on the inflow of external labor, leading to a deficit of labor resources in sectors of the economy focused on migrants. On the other hand, the development of high-tech enterprises necessitates the creation of new workplaces that are
attractive for highly skilled natives. At the same time, providing the rational coexistence of two interacting communities, migrants and indigenous people, is an important challenge for business and government.
As a result, the problem of studying and forecasting migration and demographic processes using simulation methods is being updated. Such methods, in particular, the agent-based approach (ABM), make it possible to construct and investigate the behavior of a digital community consisting of agents with their own individual rules of behavior.
Among the well-known agent-based models of discrete type (i.e., with a discrete space of agents' existence), one can single out the well-known Sugarscape model' [1], which has become widespread as a tool for analyzing the attractiveness of local areas with resources ('conditional sugar') for agents. The model of 'nomads and farmers' [2, 3], in which some agents ('conditional farmers') create resources, while others destroy them in order to expand personal space ('conditional nomads') should be noted. Also, the models of population segregation of the Schelling class [4, 5], models of movement of an ensemble of unmanned vehicles [6, 7], models of migration and demographic processes [8—10], etc. are well known.
Such systems as NetLogo, AnyLogic [11], as well as systems designed for supercomputer agent-based modeling Repast HPC [12], MASS CUDA [13, 14], FLAME GPU [1518], etc. can be highlighted among the simulation ABM-tools intended for general purposes.
Most of these systems differ in the way of software implementation of agents: either using only one central processor (for example, NetLogo, AnyLogic), or using a multi-cluster architecture based on CPU (e.g., Repast HPC) and MPI (Message Passing Interface) or they use GPU (Graphics Processing Unit) [19]. Among these platforms is FLAME GPU 21, which is characterized by a number of advantages. The framework is open source software, supports the ability to visualize a model using OpenGL [20]. Moreover, it allows multiple runs of an ensemble of models [21-24] on a personal computer (PC) using Visual Studio C++ and a Linux operating system on supercomputer systems based on NVIDIA CUDA2 (e.g., NVIDIA QUADRO RTX, NVIDIA Tesla, etc.). As a result, a flexible approach to the development of ABMs on conventional PCs and computational experiments on GPU-clusters is provided.
The FLAME GPU framework has been used to develop agent-based models in many fields ranging from biology to economics. As far as the authors of this article know, at the time of writing, the FLAME GPU platform was used to simulate migration processes in only two works [25, 26]. Other closest works are modeling the behavior of agents in the 'sugar' model described above [27]. Modeling migration processes causes additional technical complexity since dynamic creation of agent-migrants during the simulation is needed.
This work is aimed at developing the agent-based model of the dynamics of population and consists of two interacting communities:
natives and migrants with the software implementation using the supercomputer simulation system as FLAME GPU. The proposed approach made it possible to carry out a series of variation experiments and to identify important relationships in the dynamics of the migration and demographic processes under study.
1. General description of the model
An artificial socio-economic system, consisting of native and foreign populations interacting with each other through both personal contacts of the 'agent-agent' type and through message exchanges is considered. In such a system, agents are both individuals (indigenous people and migrants) and resources that have the 'ability' to assess the nearest agents and send them information about their state and correspondence to agent interests. At the same time, high technology resources correspond more to natives, and low-technology resources are associated with migrants.
Thus, an important feature of the implementation of the simulation model of the interaction of communities of migrants and natives is the mechanism of continuous messaging between agents and resources supported in the FLAME GPU.
As before, multiparticle interactions between agents are simulated in two-dimensional discrete space with a relatively small dimensionality of 100 x 100 cells and a capacity of not more than 10 000 agents. At the same time, the implementation of the model in the FLAME GPU is aimed largely at increasing the time-efficiency of the model in conditions of performing multiple recalculations using methods of the Monte Carlo type. The dimensionality of the model discrete space, which limits both the number of available workplaces and agents associated
1 https://flamegpu.com/
2 https://developer.nvidia.com/
with them, can be significantly increased almost without loss of the time-efficiency, mainly due to the parallelization of computational procedures ('agent-level functions') with the use of graphics processing units (GPUs). In such a discrete space, each agent can occupy only one cell with or without a workplace at each moment. At the same time, the complexity of the parallel implementation of the model under consideration and the difficulties of automatic synchronisation of agents in the FLAME GPU necessitate additional control of this rule and eliminate possible collisions if they occur.
As in the past, the creation of 'high-tech' and 'low-tech' workplaces, which are targeted by natives and migrants respectively, is provided. Both types of jobs provide the individual agents who occupy them with an increase in personal comfort. At the same time, the neighborhood with agent-migrants is negatively affected on the personal comfort level of natives, which is caused by the existing cultural differences and psychological characteristics of the agents.
All workplaces are created centrally and uniformly in a random way in all free cells of discrete space with different probabilities set for 'hightech' and 'low-tech' jobs, respectively. Despite the fact that this approach is the most costly for the state, it can help to avoid a shortage of jobs, which is especially important at high rates of migration. In addition, a greater number of evenly distributed jobs allows a significant increase in the number of mutual contacts between indigenous people and migrants, which has a positive effect on the level of proficiency in the local language, the possibility of obtaining a relevant local education, etc., all of which helps to reduce the time required for assimilation and integration.
The contribution of 'high-tech' and 'low-tech' workplaces, usually occupied by natives and migrants, to economic growth (GDP) and government transfers (GT) is different. The ratio of GDP to labor resources units in the 'high-tech' sectors of the economy is significantly higher
than in the 'low-tech' branches. At the same time, the creation of 'low-tech' workplaces leads to additional government spending, which also increases with the growth in the number of 'unemployed' agents.
The model provides for an inflow of migrants with the subsequent 'transformation' of arriving agents into indigenous people after the period required for assimilation has expired (1-30 years). Immigration is mainly due to the 'gravity effect' [10], which sets a reinforcing feedback between the number of available non-assimilated migrants and the inflow intensity of new agents. At the same time, in the model, the share of new immigrants (of the number of existing ones), as well as the costs of education and integration, are the key control parameters. Therefore, the migration process in such a system can be considered as 'controlled' and 'manned' by a decision-maker (i.e., the government).
At each simulation moment, agents search for the nearest workplace corresponding to their type. At the same time, a feature of implementation of the model in the FLAME GPU is the reverse order of doing this procedure, i.e., resources (jobs) search for the most suitable agents for themselves, and, in the case of a positive outcome, assign them their coordinates as target cells, while blocking access to all other agents.
In addition, agents-natives and agent-migrants search for the most suitable partner for marriage and childbirth (i.e., taking into account age, marital status, etc.). While the personal comfort level of an agent is below the threshold level, it looks for a workplace. If the agent comfort level is equal to or higher than the threshold level and it does not have a partner yet, then it searches for a partner for marriage and childbirth (taking into account, suitable age and other required agent characteristics).
Thus, all agent- individuals can be in a stationary state, a state of searching for a workplace, a state of searching for a partner, a state of being ready to have children, etc. At the same time,
agent-migrants can also transfer to an assimilation state after a certain time interval that is an endogenous characteristic of the model. Agent-natives are characterized by higher values of thresholds (in particular, their minimum level of personal comfort is higher regarding the appropriate level of agent-migrants), which determine their transition to new states, for example, the state of searching for a workplace, a stationary state, the birth of children, etc.
The abstract description of the problem statement and model dependencies (without taking into account the effect of assimilation and integration) are presented in [8] in detail.
2. Software implementation
The main computational procedures and functions of the proposed simulation model taking into account the conditional sequence of their execution are described with Table 1. Functions of the FLAMEGPU_STEP_FUNCTION type are implemented at each model time at the central processing unit (CPU) level and the functions of the FLAMEGPU_AGENT_ FUNCTION class are sequentially executed in parallel computations using graphic processors (GPUs). At the same time, higher performance of agent-based model implementation in comparison with the traditional approach is achieved by parallelizing the operations logic of each agent and exchanging messages with each other taking into account their spatial location.
In Table 1, 'agent data' refers to characteristics of agents for natives and migrants (e.g., gender, age, marital status, agent type, etc.), and 'resource data' are related to characteristics of workplaces (e.g., resource type, 'occupied / vacancy', etc.).
The developed simulation model supports two main ways of performing computational procedures:
♦ single runs, executed for one selected scenario with fixed values of control parameters
and visualization of the state of agents using the Open GL libraries [20];
♦ multiple runs implemented using the method of the Monte Carlo class [21-24] due to the parallel launch of the simulation model in the so-called 'ensemble' mode. This approach allows you to vary the values of the control parameters in specified ranges, in particular, using uniform, normal, and other distribution functions with their own characteristics.
The visualization of agent states in FLAME GPU is performed using Open GL and, in particular, is a lattice of a given dimension, in the cells of which agents (i.e. migrants and natives) and resources (i.e. 'high-tech' and 'low-tech' workplaces) have been placed. In addition, there are free cells that do not contain resources and agents. At the same time, if an agent of working age occupies a cell that does not have a workplace, then it is considered as unemployed and the level of its personal comfort will gradually decrease. Note that the visualization of agents' states and their dynamics, i.e. moving to new cells of the discrete space is realized at each moment of the model time. Such an approach makes it possible to qualitatively assess the populations' development, considering the individual choice of the most preferred workplaces by agents, as well as to study the segregation effects, etc.
3. Results of numerical experiments
All computations were performed with a FORSITE DSWS PRO supercomputer based on the QUADRO RTX 6000 over a time interval of 80 years. The total number of resource agents in the model is fixed (10 000) and it is limited by the dimension of a given discrete space (100 x 100). The number of native and migrant agents ranges from 0 to 10 000, and is the result of a simulation experiment. The values of the main parameters of the model are presented in Table 2.
Table 1.
Basic computational procedures and functions of the simulation model
Function name Appointment Input messages Output messages
FLAMEGPU_INIT_FUNCTION (init_function) The model initialization. Forming initial populations of natives, migrants and workplaces. No No
FLAMEGPU_STEP_FUNCTION (BasicOutput) The arrival of new agent- migrants, birth of new agents (natives and migrants) in married couples (with more probability) and for single agents (with the lesser probability). No No
FLAMEGPU_STEP_FUNCTION (AgentUpdate) The evaluation (i.e., collecting) of simulation results computed over the ensemble of agents at each moment of the simulation. No No
FLAMEGPU_EXIT_CONDITION (exit_condition) Check doing the criterion of stopping the simulation. No No
FLAMEGPU_AGENT_FUNCTION (check_all_agents, MsgArray2D, MsgNone) Checking and resolving the potential collisions caused by accidental placement of some agents in one cell of discrete space. Agent data No
FLAMEGPU_AGENT_FUNCTION (workplaces_creation, MsgNone, MsgNone) Creation of new workplaces based on existing population of resources. The destroying of workplaces that are to be disappearance. No Resource data
FLAMEGPU_AGENT_FUNCTION (update_cell, MsgArray2D, MsgArray2D) Information propagation among agents about available resources (workplaces). The check of a resource occupancy by another agent. Agent data Resource data
FLAMEGPU_AGENT_FUNCTION (check_cell, MsgArray2D, MsgArray2D) Information propagation among other agents (natives and migrants) about existing agents (with their characteristics) and resources occupied by them. The identification of a resource type occupied by the agent. Resource data Agent data
FLAMEGPU_AGENT_FUNCTION (agent_to_agent_contacts, MsgArray2D, MsgNone) The determination of the frequency of contacts of the 'agent-agent' type (within the 8—cells 'Moore neighborhood') to estimate (recalculate) the level of local language knowledge among migrants, and the personal comfort level of natives decreasing due to contacts with migrants. Agent data Agent data
FLAMEGPU_AGENT_FUNCTION (looking_for_partner, MsgArray2D, MsgArray2D) The function of searching for the closest partner corresponding to specified criteria (e.g., the gender, age, marital status, etc.). Agent data Agent data
FLAMEGPU_AGENT_FUNCTION (get_married, MsgArray2D, MsgNone) Getting married with an agent who sent a message with a unique identifier (ID). Agent data No
FLAMEGPU_AGENT_FUNCTION (looking_for_resource, MsgAr-ray2D, MsgArray2D) The function of searching for an agent that is closely located regarding each workplace among agents which are in a workplaces search state. Assigning a target cell with a resource to the selected agent. Agent data Resource data
FLAMEGPU_AGENT_FUNCTION (update_agent_state, MsgNone, MsgNone) Updating the state of each agent depending on the values of its characteristics (e.g., the personal comfort level, age, marital status, etc.). No No
FLAMEGPU_AGENT_FUNCTION (moving_trasaction, MsgArray2D, MsgNone) A movement transaction of an agent in discrete space in order to occupy a chosen workplace, based on data about the target cell transmitted by the corresponding resource. Resource data No
Table 2.
The main parameters of the model
Parameter name Minimum Maximum
Share of new migrants (of the number of existing agent-migrants) 0.1 0.5
Share of government expenditure on education in GDP per capita 0.1 0.5
Lifetime of 'high-tech' workplaces 5 15
Lifetime of low-tech' workplaces 5 15
Frequency of creation of new workplaces 5 15
Life expectancy of natives 70 90
Life expectancy of migrants 60 80
Minimum age for marriage and childbirth of natives 18 30
Minimum age for marriage and childbirth of migrants 18 30
Minimum level of personal comfort for natives 3 10
Minimum level of personal comfort for migrants 3 10
Retirement age 60 75
Figures 1—4 show frequency diagrams for the most important characteristics of the system under study obtained using the Monte Carlo
class method, aggregated with the proposed agent-based model through its control parameters and objective functions.
% of1 runs' of the simulation 16-..........................................................................
14-12' 10 ■ 8' 6' 4' 2 0
2000 4000 6000 8000 10000 Population size at the end of the simulation
Fig. 1. Frequency diagram for population size.
% of'runs' of the simulation
25
20 -
15
10 -
0.0 2.5
5.0
7.5 10.0 12.5 15.0 17.5 Average time for assimilation (years)
Fig. 2. Frequency diagram for the average time required for assimilation and Integration.
% of 'runs' of the simulation 80 I.....................................................................................................................................................................................
70 -..................................................................................................................................................................................................
60 -..................................................................................................................................................................................................
50 ...................................................................................................................................................................................................
40 ...................................................................................................................................................................................................
30 ....................................................................................................................................................................................................
20 ...................................................................................................................................................................................................
10 .......................=.............................................................................................................................................................
0 L-——H 1 H-1 l_T' ■—r-i-
0.0 0.1 0.2 0.3 0.4 0.5
Share of non-assimilated migrants at the end of the simulation
Fig. 3. Frequency diagram for the share of non-assimilated migrants.
In the process of conducting the numerical experiments, multiple runs of the model (more than 1000) were carried out and the scenarios most differing in the estimated characteristics were selected. They have been visualised with Figs. 1-4.
As follows from Figs. 1-4, the expected values of the modeled indicators have explicitly observed values. The frequent observability of the boundary values of indicators should be noted too. At the same time, it seems there are scenarios of some improvement in the required objective characteristics (e.g., the average time needed for assimilation), but they require a significant government expenditure on education, increasing the number of workplaces, etc.
As follows from Fig. 5, there is no unambiguous dependence of the share of non-assimilated migrants on the average time required for their assimilation — for the most frequent values of the first indicator (from 7 to 12 years), different values of the second are possible — from 0 to 0.55.
The data shown in Fig. 6 demonstrate an almost linear dependence between the simulated population size (the total number of natives and
% of 'runs' of the simulation
16 -........p1........................................................
14 ............................................................................
12 [Z
10
8 ...........................................'^T^.......
6 .......................................................................
4 -......................................................................
2 ...................._........................................
0
0 2000 4000 6000 8000
Total number of assimilated migrants
Fig. 4. Frequency diagram for the total number of assimilated migrants.
agent-migrants) and the total number of assimilated migrants.
Further, the most important groups of scenarios for the evolutionary development of communities of migrants and indigenous people are considered:
♦ low-intensity and normal migration scenarios;
♦ scenarios of intensive and super-intensive migration.
The main characteristics of the scenarios to be studied are presented in Table 3.
In Figs. 7-10 are shown the model dynamics of the key characteristics of the system under consideration over an 80-year simulation interval which is the result of the behavior of an ensemble of interacting agents-natives and migrants.
Figures 7-8 allow us to make the following important conclusion. With the existing patterns of agent behavior, a significant increase in the population size can be achieved only under conditions of intensive and super-intensive migration. However, such scenarios will cause a significant increase in the share of migrants in the population, which may lead to an increase in social tension.
Share of non-assimilated migrants in population at the end of the simulation
0.5
0.4 -
0.3
0.2
0.1 -
0.0
% of 'runs' of the simulation
- 25
- 20
15
- 10
- 5
5.0 7.5 10.0 12.5 15.0 Average time for assimilation (years)
Fig. 5. Two-dimension frequency diagram for the average time needed for the assimilation and integration and share of non-assimilated migrants.
Table 3.
Studied scenarios and model assumptions
Group of scenarios Scenario number Share of new migrants Share of government expenditure on education and integration
Low-intensity (normal) migration scenarios Scenario 1 0.1 0.1
Scenario 2 0.1 0.25
Scenario 3 0.1 0.5
Intensive migration scenarios Scenario 4 0.2 0.1
Scenario 5 0.2 0.25
Scenario 6 0.2 0.5
Super-intensive migration scenarios Scenario 7 0.3 0.1
Scenario 8 0.3 0.25
Scenario 9 0.3 0.5
0
Total number of assimilated migrants
8000 -
6000 -
4000 -
2000 -
0 -
2000
4000
6000
8000
10000
Population size at the end of the simulation
Fig. 6. Two-dimension frequency diagram for the population size and the total number of assimilated migrants in the model.
- 10
- 8
-6
- 4
Number of agents 10000
8000
6000
4000
2000
10
Scenarios of intensive migration
Scenarios of super-intensive migration
Scenarios of low-intensive migration
T"
T"
20
30
40
50 60 70 Simulation time, years
Scenario 1 Scenario 2 Scenario 3
Scenario 4 Scenario 5 Scenario 6
Scenario 7 Scenario 8 Scenario 9
Fig. 7. Simulated population dynamics.
2
0
0
0
Share of non-assimilated migrants in population
Fig. 8. Simulated dynamics of the share of non-assimilated migrants in the population.
Fig. 9. Simulated dynamics of GDP growth rates.
Figure 9 shows that the highest rates of GDP growth can be achieved under scenarios of intensive migration, however, the subsequent shortage of resources leads to a gradual decrease in the rates of economic growth.
From Fig. 10 it follows that scenarios of intensive and super-intensive migration cause a significant increase in government expenditure, mainly associated with the need to
increase spending on education and integration of migrants, create appropriate jobs, pay unemployment benefits, etc.
Conclusion
This article presents a new approach to modeling migration and demographic processes using the FLAME GPU. The framework is intended
Growth rates of government expenditure 112 -
110 -
108 -
106 -
104 -
102 -
Intensive and super-intensive migration causes significant increase in government expenditure
~~r
10
i
20
r~
30
H-
40
I
50
I
60
70
Scenario 1 Scenario 2 Scenario 3
Scenario 4 Scenario 5 Scenario 6
Scenario 7 Scenario 8 Scenario 9
Simulation time, years
Fig. 10. Simulated dynamics of government expenditure.
0
for supercomputer agent-based modeling and it allows parallelizing the logic of the simulation model at the level of each agent, providing a significant increase in the time efficiency of the corresponding computational procedures.
As a result, using artificial data and methods of the Monte Carlo type, the most important characteristics of the model of interaction between natives and migrants were studied: the population size, average time needed for assimilation, share of non-assimilated migrants in the population, etc. The scenarios that provide a positive contribution to the economic and demographic growth have been found. At the same time, the implementation of such scenarios, based mainly on intensive migration, necessitates a significant increase in government expenditure on education and integration.
The proposed approach can be used to develop decision-making systems for planning hiring new employees based on the forecast dynamics of migration and demographic processes.
Further research will be aimed at complicating and detailing the model of interaction between migrants and indigenous people, using clustering methods for creating jobs, studying the effects of segregation, etc., using the FLAME GPU. ■
Acknowledgments
This study was funded by the Russian Foundation for Basic Research (RFBR) under the research project No. 18-51-14010.
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About the authors
Valery L. Makarov
Dr. Sci. (Phys.-Math.); Academician of Russian Academy of Sciences;
Academic Supervisor, Central Economics and Mathematics Institute, Russian Academy of Sciences, 47, Nakhimovsky Prospect, Moscow 117418, Russia;
E-mail: makarov@cemi.rssi.ru
ORCID: 0000-0002-2802-2100
Albert R. Bakhtizin
Dr. Sci. (Econ.); Corresponding Member of Russian Academy of Sciences;
Director, Central Economics and Mathematics Institute, Russian Academy of Sciences, 47, Nakhimovsky Prospect, Moscow 117418, Russia;
E-mail: albert@cemi.rssi.ru
ORCID: 0000-0002-9649-0168
Gayane L. Beklaryan
Cand. Sci. (Econ.);
Senior Researcher, Laboratory of Computer Modeling of Social and Economic Processes, Central Economics and Mathematics Institute, Russian Academy of Sciences, 47, Nakhimovsky Prospect, Moscow 117418, Russia;
E-mail: glbeklaryan@gmail.com
ORCID: 0000-0002-1286-0345
Andranik S. Akopov
Dr. Sci. (Tech.);
Professor, Department of Business Informatics, Graduate School of Business, National Research University Higher School of Economics, 20, Myasnitskaya Street, Moscow 101000, Russia;
Chief Researcher, Laboratory of Dynamic Models of Economy and Optimization, Central Economics and Mathematics Institute, Russian Academy of Sciences, 47, Nachimovky Prospect, Moscow 117418, Russia;
E-mail: aakopov@hse.ru ORCID: 0000-0003-0627-3037
Nikita V. Strelkovskii
Cand. Sci. (Phys.-Math.);
Research Scholar, International Institute for Applied Systems Analysis, Laxenburg, Austria; E-mail: strelkon@iiasa.ac.at ORCID: 0000-0001-6862-1768
