Evolution of random undirected graphs by the clustering attachment (CA) without node and edge deletion and with uniform node deletion is investigated. The CA causes clusters of consecutive exceedances of the modularity over a sufficiently high threshold. The modularity is a measure that allows us to divide graphs into communities. It shows the connectivity of nodes in the community. An extremal index (a local dependence measure) approximates the mean cluster size of exceedances over a sufficiently high threshold. Considering the change of the modularity at each evolution step, the extremal index of the latter random sequence indicates the consecutive large connectivity of nodes and thus, it reflects the community appearance during the network evolution. This allows to consider the community structure of the network from perspectives of the extreme value analysis. By simulation study we show that estimates of the extremal index of the modularity and the tail index of node degrees depend on the CA parameters. The latter estimates are compared both for evolution without node and edge deletion and with uniform node deletion.

The purpose—The human-made phenomenon of the global computer environment (GCE) has initiated the tectonic processes of the next phenomenon, namely, the all-encompassing digital transformation of the socio-techno-sphere. These historically unprecedented phenomena are changing the fundamental principles of sustainable development of civilizations. The newest problems of controlling the sustainable development of socio-systems and the world socio-system as a whole arise, which bring qualitatively new requirements. These requirements go beyond the historical experience of humankind, modern political and economic views, and general scientific constructive concepts, including the conceptual bases of cybernetic and computer sciences. The work attempts to comprehend the new system-wide situation and the joint fundamental role of cybernetics and computer science in the epoch of all-encompassing digital transformation. For a systemic and holistic substantiation of safe routes to the future, a converging update of the conceptual bases of cybernetic and computer sciences is required, first of all. The work introduces a new research object for cybernetics—the GCE as a whole, which has de facto become the main instrument of global digitalization. Along with this, key system-wide support positions are outlined for such a convergence to form (with an orientation towards implementation in the GCE) promising cybernetic concepts and models of digital control of sustainable development of the entire variety of globally distributed strongly connected sociotechnical systems operating in conditions of global information strongly connectedness. Design/methodology/approach—The spontaneously implemented consolidation in GCE of a growing number of increasingly advanced computer devices with the property of local algorithmic universality does not create qualitatively new prerequisites for the systemically balanced and safe development of either the GCE or the socio-techno-sphere. To achieve the systemic property of emergence, represented by the globally distributed algorithmic universality of GCE (in general), it is necessary to seamlessly extend the property of local universality from intra-computer resources to arbitrarily large networks. This task has not been set before, so there are no methods for solving it. An approach to solving this problem is presented in this work. Findings—The chapter forms and substantiates the conceptual principles of expanding cybernetic issues by including the GCE as a fundamentally new object of scientific knowledge in the scope of its consideration. Cybernetic research was conducted using mathematical methods to study the intra-system patterns of the GCE development and the GCE's influence on social systems. The construction of mathematical models for the sustainable functioning and predictable development of globally distributed sociotechnical systems will allow the formation of fundamental justifications that are missing today for the comprehensive and safe implementation of digital transformation socio-techno-sphere. Originality/value—An original approach to integrating cybernetic and computer science methods to study complementary information/system-forming capabilities of social and computer information environments in the course of their joint functioning and development in the global digital transformation processes is presented. Research/Practical/Social/Environment implications—The proposed concept substantiates the strategic directions of systemically balanced digital transformation, which open the way to the system-holistic integration of the natural ("non-digital") informational universality of Homo Sapiens and algorithmic ("digital") universality of GCE for the sustainable development of the socio-techno-sphere in unprecedented conditions of global information strong connectedness. Research limitations—The results obtained show the ways of further development of research aimed at developing methods, computer-networks architectures, and technologies of new generations aimed at a controlled (transparent to the public) digital transition from the former monopoly of anthropocentric models of sustainable development management to info centric models that will provide a synergetic combination of the advantages of natural ("non-digital") universality of man and algorithmic ("digital") universality of GCE.

A cloud computing system that receives complex user tasks involving several subtasks is studied from the point of view of the response time. In order to reduce the service time, the tasks are divided into smaller components and processed in parallel. As a cloud center model we use a fork-join queuing system with Pareto distribution of the service time on the servers. To analyze the mean response time and its standard deviation, a new approach is used combining simulation modeling with one of the machine learning methods. The estimates obtained are much more accurate than the earlier analytical results on fork-join systems.

The simplest version of the sub-Gramian method is based on the spectral decomposition of a square H2 norm of the transfer function. This case applies when a system can be described as an LTI dynamic one and therefore has a corresponding algebraic Lyapunov equation.

This review is the first to propose the systematic presentation of a new approach to the study of queuing systems and networks. The concept of the new approach is based on a combination of traditional methods of queuing theory with various machine learning algorithms. The detailed description and justification of the possibility of applying the approach are given on the example of a combination of simulation with artificial neural networks. The analysis of publications allows us to conclude that the application of machine learning methods is highly effective, promising for further research, as well as for the possible separation of this new approach into an independent direction in the field of solving complex problems of the theory of queues.