Mathematical models of information dissemination in a population often use the simplifying assumption that all individuals are equally receptive to information. Simply put, if an individual has learned some rumor, then with a probability of, say, 20%, he internalizes the rumor and will relay it to other people. The present work introduces a model in which individuals differ in their receptivity. It is easy to imagine, for example, the indicated probability is 20% for half of the population, 10% for a third of the population, and 15% for the rest. This provision adjusts the model. Thus, the process in question is the spread of a message in a population with differential receptivity. This issue is addressed to clarify whether and to what extent the above simplifying assumption affects the accuracy of the model. We conducted a series of numerical experiments with a mathematical model assuming that the population is composed of three groups with different values of receptivity and a model containing a simplifying assumption for a population with the same parameters. It was found that the simplifying assumption that receptivity is the same for all individuals distorts the description of the dynamic processes of the model.

В статье исследуется надежность привязной беспилотной высотной платформы как единой сложной системы. Разработана структурная схема надежности платформы. Она состоит из основных подсистем и ее элементов, соединенных последовательно. Представлен метод расчета показателей надежности привязной беспилотной высотной платформы, таких как функция надежности и среднее время наработки на отказ. Рассчитаны показатели надежности элементов системы связи. Представлен подход к расчету срока службы привязной беспилотной платформы.

A preferential attachment (PA) has been suggested to model network evolution and to explain conjectured power-law node degree distributions in real-world networks. In Markovich, Ryzhov (2022a,b), the schemes of the linear PA proposed in Wan et al. (2020) for the network evolution were suggested for information spreading. The PA and the well-known algorithm SPREAD proposed in Mosk-Aoyama, Shah (2006) were compared regarding the minimum number of evolution steps K ∗ required to spread a single message among a fixed number of nodes in non-homogeneous directed networks. This comparison was done in Markovich, Ryzhov (2022a,b) without node and edge deletion during the evolution. The objective of the current study is to investigate the AQ3 impact of the PA parameters on spreading of a single message to a fixed number of nodes in the graph when an existing node or edge is uniformly deleted at each step of the PA evolution. The results are provided for simulated and real graphs.

We consider a multiphase queuing system of type M/M/1/k → •/M/1/k → · · · → •/M/1/k with an arbitrary number of nodes and a common retrial queue of type •/M/1/k for other queues in the system. This kind of queuing system can serve as a model for wireless networks of asymmetric nodes, where a node with weak processing power can act as a temporary waiting place for blocked packets. An analytical model of the system is investigated and various performance measures of the system are derived. Comparisons of numerical results from the analytical model with simulation results are also performed. We then utilize the simulation model to explore the impact of the orbit node on system performance. Simulation results point out that in the situation of network saturation, the existence of the orbit queue brings little improvement to the performance of the system. On the other hand, in the case of nearsaturation network and the case of low-utilization network with queues of small buffer size, the orbit node can improve the packet loss rate significantly, with the trade-off of increasing average response time.

A key challenge in computer modeling is obtaining numerical results on large input datasets. For instance, this problem arises when researchers need to produce a visualization of an economic or physical process, as well as during the computation of characteristics of complex mathematical models using the Monte Carlo method. Each problem requires repeating the same program on a large set of inputs, consuming much time, from several hours to days and weeks. Computational algorithms may be implemented in different programming languages and may require various specific tools like GNU Octave, NS-3, or OMNeT++. This article describes a distributed system architecture, which can speed up the process of obtaining results for such problems. The system comprises a backend server, a control service (supervisor), worker nodes, and a database. These algorithms are executed in Docker containers to abstract from particular languages and tools required for computational algorithms. The system supports several strategies for problem prioritization to operate efficiently under heavy loads introduced by multiple users. To use the system, the user only needs to build a Docker image with an encapsulated algorithm, describe the input dataset in a JSON file, and upload them via the web interface. The system can be deployed in any public cloud. In this article, we describe the system architecture and numerical results obtained from computations on various clouds and local platforms. We demonstrate that the computation time for CPU-bound problems in different public clouds varies greatly. Finally, we show the influence of different prioritization strategies on the duration of computations under a moderate workload.