# Branching Processes and Queueing Systems (Session Two)

#### by Prof. Vladimir A. Vatutin

Institution: Steklov Mathematical Institute (Russia)
Date: Mon 22nd August 2005
Time: 4:15 PM
Location: Room 210, Richard Barry Building

Abstract: A brief description of the course:

The course of lectures is devoted to branching processes and their
applications in queueing theory. Our lectures include:

1. Classification of Markov branching processes; asymptotic behavior of
the survival probability.

2. Branching processes with ordinary or state-dependent immigration.
Queueing systems under heavy traffic: systems with permanent customers or
batch service.

3. Branching processes with final product and queueing system with SIRO
(service in random order) discipline; branching processes with immigration
counted by random characteristics; $M|G|1$ systems with retrials (repeated
calls); regeneration processes and branching processes;
Khintchine-Pollaczek formula.

4. Multitype Markov processes (classification and basic properties);
polling queueing systems with gated and exhaustive disciplines.

5. Crump-Mode-Jagers processes and some related queueing systems.