Transient Phenomena in Information Technology for Branching Processes with an Infinite Set of Types

Abstract

Branching processes as a mathematical concept has applications in various fields, including information technology. In information technology, branching processes can be used to model and analyze various scenarios, such as the propagation of data or information in a network, the growth of computer viruses, the spread of software bugs, and more. Branching processes are particularly useful for understanding the dynamics of systems where events can lead to multiple new events in a probabilistic manner. Overall, branching processes provide a valuable mathematical framework for modeling and analyzing various aspects of information technology, helping to make informed decisions and optimize IT systems and networks. We have studied transient phenomena for branching processes with an infinite number of types close to critical. The analytical apparatus for this study is Markov renewal theorems. Branched processes were used to evaluate the performance of IT systems and predict their behavior under different conditions. This is important for capacity planning and resource allocation.