15-858A: Advanced Stochastic Analysis and Applications (SPRING 07)

T 10:30 - 1:30, Room: Tepper 227

(cross-listed as Tepper 47-774 and 47-775)

STARTING DATE: Tuesday, January 23, 2007

Queueing theory is an old area of mathematics which has recently become very hot. The goal of queueing theory has always been to improve the design/performance of systems, e.g. networks, servers, memory, distributed systems, etc., by finding smarter schemes for allocating resources to jobs. This class emphasizes the beautiful mathematical techniques used in queueing theory and throughout stochastic analysis in general. Topics covered include: stochastic orderings of random variables, heavy-tailed workloads, Laplace transforms, z-transforms, scheduling theory analysis using transforms, advanced generalization of Little's Law and other conservation laws, fluid anlaysis, heavy-traffic approximations, delay tail analysis, matrix-geometric methods, and more. Each topic will be presented first be presented in terms of the technique being introduced and then in terms of the application of that technique to solving problems in computer systems and manufacturing systems.

The techniques studied in this class are useful to students in Computer Science, Tepper, Mathematics, ACO, Statistics, and Engineering. This course is packed with open problems -- problems which if solved are not just interesting theoretically, but which have huge applicability to the design of computer systems today.

PREREQUISITES:

It is strongly recommended that you have taken 15-857A or 15-849 before you take this class. I you haven't you should get special permission from one of the instructors.

TEACHING STAFF:

TEXTBOOK:

We will pass out my our own course notes and some supplementary handouts and papers at the end of each class. Some good reference texts are listed here: BOOK LIST. You can borrow most of these books from our offices.

GRADING (preliminary):

ANTICIPATED OUTLINE OF TOPICS FOR THIS CLASS:

  • Stochastic Orderings (2 lectures Alan)
  • Heavy Tailed Workloads (2 lectures Alan)
  • Queueing Theory Laws (1 lecture Mor)
  • Introduction to Transforms (1 lecture Mor)
  • Transform analysis of M/G/1 (1 lecture Mor)
  • Scheduling via Transforms (1-2 lectures Mor)
  • Possible additional applications of transforms (1 lecture Mor, if time)
  • Fluid analysis (2 lectures Alan)
  • Delay Tail (1 lecture Alan)
  • Matrix-Analytic Methods (1 or 2 lectures Mor)