Using PDE Model and System Dynamics Model for Describing Multi-operation Production Lines

Two classes of models for describing production flow lines are analyzed. The use of models of these classes for the design of highly efficient control systems of production lines, the technological route of which consists of a large number of technological operations, is analyzed. The division of the technological route into a large number of operations is caused by the development trend of modern production lines. Synchronization of production line equipment performance is provided by an accumulating buffer. A formalized description of the production line was used as a foundation for constructing equations for each models class. The common features of using each models class in the description of production systems, as well as the conditions for their application are shown. The form of the system dynamics model and PDE model equations is substantiated. The assumption about a deterministic rate of processing parts and the absence of a time delay and feedback between the parameters of technological operations was made when deriving the equations. The use of generalized technological operations in the system dynamics model as a way to reduce the number of model equations is discussed. Two limiting transitions from the PDE model equations to the system dynamics equations are demonstrated. It is shown that the system dynamics equations are a special case of the PDE model equations, the result of aggregation of production line parameters within the technological operation. The method for constructing level equations for the system dynamics model is substantiated. For production lines with a different number of operations, the solution to the problem of processing parts along a production line is presented. The comparative analysis of the solutions obtained using the system dynamics and PDE model equations is obtained

Developing A Model of the Dynamics of States of A Recommendation System Under Conditions of Profile Injection Attacks

The recommendation systems used to form a news feed in social networks or to create recommendation lists on content websites or Internet stores are often exposed to information profile injection attacks. These attacks are aimed at changing ratings, and thus at changing the frequency of appearing in recommendations, certain objects of a system. This can lead to threats to users' information security and losses of the system owners. There are methods to detect attacks in recommendation systems, but they require permanent repetitive checks of all users' profiles, which is a rather resource-intensive operation. At the same time, these methods do not contain any proposals as for determining the optimal frequency of attack checks. However, a properly chosen frequency of such checks will not overload a system too much and, at the same time, will provide an adequate level of its operational security.A mathematical model of the dynamics of states of a recommendation system under conditions of an information attack with the use of the mathematical apparatus of Markovian and semi-Markovian processes was developed. The developed model makes it possible to study the influence of profile injection attacks on recommendation systems, in particular, on their operation efficiency and amount of costs to ensure their information security. The practical application of the developed model enables calculating for recommendation systems the optimum frequency of information attack check, taking into consideration the damage from such attacks and costs of permanent inspections.Based on the developed mathematical model, the method for determining total costs of a recommendation system as a result of monitoring its own information security, neutralization of bot-networks activity and as a result of information attacks was proposed.A method for determining the optimal frequency of checking a recommendation system for information attacks to optimize the overall costs of a system was developed. The application of this method will enable the owners of websites with recommendation systems to minimize their financial costs to provide their information securit