Course AsOR: Asymptotic Methods in Operations Research

Time:	Monday 11.00–12.45
Period:	8 September 2025 – 10 November 2025
Location:	All LNMB courses take place on the Campus Utrecht Science Park. Room HFG 611, Hans-Freudenthal building, Budapestlaan 6, 3584 CD Utrecht
Lecturer:	Prof. Dr. Bert Zwart (CWI and TU/e)

Course description

The goal of this course is to make PhD students familiar with a set of techniques which can be used to simplify the mathematical analysis of models that appear in operations research, by exploiting the fact that some parameter gets very large or very small. Examples are:

stochastic networks in heavy traffic
differential equation approximations of stochastic systems
queues with many servers
games with many agents
large combinatorial optimization problems with some additional random structure

In such problems it is possible to apply techniques from analysis and probability to obtain a better qualitative understanding of stochastic networks, or a better understanding of the empirical performance of algorithms.

Topics which we expect to cover are:

generating functions, Laplace transforms and the Laplace method
fluid and diffusion limits
large deviations for light and heavy-tailed distributions
mean field analysis of large queues and games
asymptotic analysis of algorithms on trees and sparse graphs
applications to algorithms in optimization and machine learning

Literature

Handouts, slides and references to relevant literature will be made available at the lectures.

Prerequisites

This is an advanced course, I expect a good level of mathematical maturity and scholarly interest. A good background in probability theory and stochastic processes will be particularly important.

Examination

Take home problems and short presentations about a research paper of choice.

Address of the lecturer

Prof. Dr. Bert Zwart
CWI, Science Park 123
1098 XG Amsterdam
Phone: 020-5924018
E-mail: Bert.Zwart@cwi.nl