Institute of Applied Mathematics and Communications Technology Held a Seminar on ‘Mathematical modeling of Queuing systems using Markov counting chains and the presence of a small parameter’

Speaker: Galina Tsareva, post-graduate student of the Department of Applied Computer Science and Probability Theory.

The report examined Queuing systems that consist of an infinite number of identical FCFS servers with a buffer that can store a queue of infinite length, with a Poisson incoming flow of requests to the Queuing system at a constant intensity.

A question of great interest was when each request received by a Queuing system randomly selects and queries two arbitrary servers of this system, and then immediately sends it to one of them, where the queue is shorter. It was discussed in detail that the dynamics of changes in the share of servers in the system can be described using an infinite system of differential equations. For this system of differential equations, a singularly perturbed Cauchy problem of Tychon type with a small parameter is posed. It was emphasized that the presence of a small parameter in the system of differential equations allows describing rapidly changing processes in large-scale Queuing systems, which makes it possible to analyze transients in systems of this type.ф