** Professor: **
Professor R. J. Williams, AP&M 6121.

** Time: ** Tu, Th 2.30-3.50 p.m.

** Place: ** AP&M 6218.

** Office Hours: ** TBA

**
DESCRIPTION: **
Stochastic networks are used as models for complex manufacturing,
telecommunications and computer systems.
Since the complexity and heterogeneity of these networks usually preclude
exact analysis, approximate models are frequently used.
This course will discuss the mathematics associated with two classes of
approximate models, namely,
first order (functional law of large numbers)
approximations called fluid models,
and second order (functional central limit theorem)
approximations which are frequently diffusion
models.
The interplay between these two levels will be an important subtheme
throughout.
The use of these approximate models for analysis and control of
stochastic networks will also be presented.
Associated mathematical topics that will be covered include
weak convergence of stochastic processes, existence and
uniqueness theory for reflected Brownian motions, positive recurrence
of related processes.

** PREREQUISITES: ** This is not a beginning
graduate course. Knowledge gleaned from a graduate probability course
such as Math 280, and some knowledge of stochastic processes, is advised.
Although this course is labelled (B), there is no (A) course that is a
prerequisite.

** REFERENCES: **

* Background Reference: *

* Journal Articles: *

* Links to Related Sites: *

** QUESTIONS: ** Please direct any questions to
Professor Williams (williams@math.ucsd.edu).