Thu, 17 Feb 2005
16:30
16:30
DH Common Room
Topology and Energy of Nematic Liquid Crystals in Polyhedral Cells
Apala Majumdar
(University of Bristol)
We consider a queuing system with three queues (nodes) and one server.
The arrival and service rates at each node are such that the system overall
is overloaded, while no individual node is. The service discipline is the
following: once the server is at node j, it stays there until it serves all
customers in the queue.
After this, the server moves to the "more expensive" of the two
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 0) when the
dynamical system is chaotic, and prove that then the stochastic one
cannot be periodic either.