Quasi-Linear Differential-Deference Game of Approach

This is a post-peer-review, pre-copyedit version of a book chapter that is part of “V. A. Sadovnichiy, M. Z. Zgurovsky (eds.). Modern Mathematics and Mechanics. Understanding Complex Systems”. The final authenticated version is available online at: https://link.springer.com/chapter/10.1007/978-3-319-96755-4_26The paper is devoted to the games of approach. We consider a controlled object whose dynamics is described by the linear differential system with a pure time delay or the differential-difference system with commutative matrices in Euclidean space. The approaches to the solutions of these problems are proposed which based on the Method of Resolving Functions and the First Direct Method of L.S. Pontryagin. The guaranteed times of the game termination are found, and corresponding control laws are constructed. The results are illustrated by a model example

Methods of limiting decomposition and Markovian summation in queueing system with infinite number of servers

In this paper, we study the process generated by the customers which are serviced in a queueing system with an infinite number of servers. Two methods referred to as the method of limiting decomposition and the method of Markovian summation are proposed, implemented and compared. The characteristic function of the probability distribution for the studied process is obtained. The numerical examples are performed for different values of queueing system characteristics