Seminar: Modelling a polling system with 3 queues and 1 server in an overload regime

• Statistics Seminar
• Abstract:

  We consider a queuing system with three queues and just one server, in the regime when the system overall is eventually overloaded, but yet no individual queue is. The service discipline is as follows. Once the server is at node j, it stays there until it finishes serving all customers present in that queue. After this, the server moves to the "more expensive" of the two remaining queues. We will show that a.s. there will be a periodicity in the order of services, as suggested by the behavior of the corresponding dynamical systems; we also study the cases (of measure zero) when the dynamical system is chaotic, and prove that then the stochastic one cannot be periodic either. These results are quite surprising giving superficial "simplicity" of the model. (Based on a joint work with M.Menshikov, I.MacPhee and S. Popov)

• Date: Friday, 3rd February 2012
• Time: 13:15 to 14:00
• Room: MH:227
• Speaker: Stanislav Volkov