Stochastic Networks Part Iii

This course is about the way microscopic laws governing behaviour of individual elements of the system can give rise to macroscopic behaviour in the system. One example of this is the physics of gases: the air in this room is made up of molecules, and you can think of it in terms of molecular movement; however, you can also think about it in terms of Boyle’s Law (relating pressure and volume of a gas). In this course we will mostly consider constructed systems, where if we understand the connection between the microscopic and the macroscopic behaviour, we might be able to change the microscopic laws. Course website: http://www.statslab.cam.ac.uk/~frank/STOCHNET/ Prerequisites: • Basic optimization: at least at the level of Lagrange multipliers. (See Sections 1, 2.1 of Richard Weber’s notes at http://www.statslab.cam.ac.uk/~rrw1/mor/s.pdf.) • Markov Chains: at least the discrete-time theory, although continuous-time will be helpful. (See the book James Norris, Markov Chains, CUP 1998, http://www. statslab.cam.ac.uk/~james/Markov/, sections 1.7 and 2.4 especially; and/or Chapter 1 of Bruce Hajek’s notes http://www.ifp.illinois.edu/~hajek/Papers/networkanalysis. html.) Topics we will cover: Queueing networks: We will first look at a single queue. We will see how to model it as a Markov chain,