Об эквивалентности операторного и комбинаторного подходов для одношаговых случайных марковских процессов

Herein, for one-step random Markov processes the comparison of the operator and combinatorial methods based on the use of functional integrals is performed. With the combinatorial approach, the transition from the stochastic differential equation to the functional integral is used. This allows us to obtain the expression for the mean population size in terms of the functional integral. With the operator approach, the transition to the functional integral is performed via the creation and annihilation operators. It is shown that the mean values calculated using the functional integrals arising in the combinatorial and operator approaches coincide.Для одношаговых случайных марковских процессов проводится сравнение операторного и комбинаторного методов, основанное на использовании функциональных интегралов. При комбинаторном подходе используется переход от стохастического дифференциального уравнения к функциональному интегралу, с помощью которого получено выражение для среднего размера популяции. При операторном подходе переход к функциональному интегралу осуществляется через операторы рождения и уничтожения. Показано, что средние значения, вычисленные с помощью функциональных интегралов, возникающих при комбинаторном и операторном подходах, совпадают

Вычислительная и имитационная модели системы с управлением на Modelica

When modeling network protocols, the choice of a model approach and a software implementation tool is a problem. The specificity of this subject area is that for the description of protocols usually the discrete-event approach is used. However, the discrete model approach has several disadvantages. It is poorly scalable, not well suited for describing dynamic systems. As an alternative to the discrete approach, a continuous approach is usually considered. But when modeling discrete events, continuous description becomes unnecessarily complicated and heavy. Events take the form of some restrictions on the continuous system, which are often not explicitly included in the continuous model, but have the form of additional semantic descriptions. The authors propose to use a hybrid (continuous-discrete) approach when modeling such systems. In the framework of the hybrid approach, the discrete system is recorded in a continuous form, and the events take the form of discrete transitions inherent in the approach. In addition, if it is based on the description of events, a simulation model can be obtained on the basis of a hybrid approach. This paper demonstrates the use of a hybrid approach to describe systems with control by the example of the interaction of the TCP protocol and the RED algorithm. The simplicity of creating both computational and simulation models of the system is demonstrated. The Modelica language is used as the implementation language.При моделировании сетевых протоколов является проблемой выбор модельного подхода и средства программной реализации. Специфика данной предметной области состоит в том, что для описания протоколов обычно используют дискретно-событийный подход. Однако дискретный модельный подход имеет ряд недостатков. Он плохо масштабируем, недостаточно хорошо подходит для описания динамических систем. Как альтернативу дискретному подходу обычно рассматривают непрерывный подход. Но при моделировании дискретных событий непрерывное описание становится излишне сложным и тяжеловесным. События принимают форму некоторых ограничений на непрерывную систему, которые зачастую не входят явно в непрерывную модель, а имеют форму дополнительных семантических описаний. Авторы предлагают использовать при моделировании подобных систем гибридный (непрерывно-дискретный) подход. В рамках гибридного подхода дискретная система записывается в непрерывном виде, а события принимают вид присущих подходу дискретных переходов. Кроме того, если брать за основу именно описание событий, на основе гибридного подхода можно получить и имитационную модель. В работе демонстрируется применение гибридного подхода для описания системы с управлением на примере взаимодействия протокола TCP и алгоритма RED. Демонстрируется простота создания как вычислительной, так и имитационных моделей системы. В качестве языка реализации используется язык Modelica

Novel Analytical Modelling-based Simulation of Worm Propagation in Unstructured Peer-to-Peer Networks

Millions of users world-wide are sharing content using Peer-to-Peer (P2P) networks, such as Skype and Bit Torrent. While such new innovations undoubtedly bring benefits, there are nevertheless some associated threats. One of the main hazards is that P2P worms can penetrate the network, even from a single node and then spread rapidly. Understanding the propagation process of such worms has always been a challenge for researchers. Different techniques, such as simulations and analytical models, have been adopted in the literature. While simulations provide results for specific input parameter values, analytical models are rather more general and potentially cover the whole spectrum of given parameter values. Many attempts have been made to model the worm propagation process in P2P networks. However, the reported analytical models to-date have failed to cover the whole spectrum of all relevant parameters and have therefore resulted in high false-positives. This consequently affects the immunization and mitigation strategies that are adopted to cope with an outbreak of worms. The first key contribution of this thesis is the development of a susceptible, exposed, infectious, and Recovered (SEIR) analytical model for the worm propagation process in a P2P network, taking into account different factors such as the configuration diversity of nodes, user behaviour and the infection time-lag. These factors have not been considered in an integrated form previously and have been either ignored or partially addressed in state-of-the-art analytical models. Our proposed SEIR analytical model holistically integrates, for the first time, these key factors in order to capture a more realistic representation of the whole worm propagation process. The second key contribution is the extension of the proposed SEIR model to the mobile M-SEIR model by investigating and incorporating the role of node mobility, the size of the worm and the bandwidth of wireless links in the worm propagation process in mobile P2P networks. The model was designed to be flexible and applicable to both wired and wireless nodes. The third contribution is the exploitation of a promising modelling paradigm, Agent-based Modelling (ABM), in the P2P worm modelling context. Specifically, to exploit the synergies between ABM and P2P, an integrated ABM-Based worm propagation model has been built and trialled in this research for the first time. The introduced model combines the implementation of common, complex P2P protocols, such as Gnutella and GIA, along with the aforementioned analytical models. Moreover, a comparative evaluation between ABM and conventional modelling tools has been carried out, to demonstrate the key benefits of ease of real-time analysis and visualisation. As a fourth contribution, the research was further extended by utilizing the proposed SEIR model to examine and evaluate a real-world data set on one of the most recent worms, namely, the Conficker worm. Verification of the model was achieved using ABM and conventional tools and by then comparing the results on the same data set with those derived from developed benchmark models. Finally, the research concludes that the worm propagation process is to a great extent affected by different factors such as configuration diversity, user-behaviour, the infection time lag and the mobility of nodes. It was found that the infection propagation values derived from state-of-the-art mathematical models are hypothetical and do not actually reflect real-world values. In summary, our comparative research study has shown that infection propagation can be reduced due to the natural immunity against worms that can be provided by a holistic exploitation of the range of factors proposed in this work

The method of constructing models of peer to peer protocols

The models of peer to peer protocols are presented with the help of one-step processes. On the basis of this presentation and the method of randomization of one-step processes, it is described method for constructing models of peer to peer protocols. The models of FastTrack and Bittorrent protocols are studied by means of proposed method. © 2014 IEEE

The method of constructing models of peer to peer protocols

The models of peer to peer protocols are presented with the help of one-step processes. On the basis of this presentation and the method of randomization of one-step processes, it is described method for constructing models of peer to peer protocols. The models of FastTrack and Bittorrent protocols are studied by means of proposed method. © 2014 IEEE