February  3, 2023

Workshop on Large Deviations and Rare Events in Networks
July 4-5, 2005
University of Ottawa,

This workshop will precede the
13th Informs Applied Probability Society Conference
also held in Ottawa on July 6-8, 2005

Supported by
University of Ottawa

Organiser: David McDonald and André Dabrowski,
Department of Mathematics and Statistics,University of Ottawa

Format: 2 days: Invited Talks.

Invited Lecturers

There will be 5 hour long talks on the state of the art of the following subjects all closely related to rare events in networks:

  • Robert Foley, Georgia Institute of Technology
    Doob's h-transform technique, Markov Additive processes and rare events in networks
  • Peter Glynn, Stanford University
    Rare Event Simulation
  • Irina Ignatiouk-Robert, l'Université de Cergy-Pontoise
    Large deviations for Markov jump processes with boundaries
  • Phil Pollett, University of Queensland
    Ratio limit theorems, quasi stationary distributions, the Yaglom limit
  • Marcel Neuts(tentative):
    The Matrix Geometric method

AA, Mogulski, Novosibirsk, Russia
Masakiyo Miyazawa, Science University of Tokyo, Japan
Sean Meyn
, University of Illinois, Urbana
Tomasz Rolski, Mathematical Institute Wroclaw
Hui Wang , Brown

Invited participants:

Atahiru Alfa, University of Manitoba
Doug Down, McMaster University
Winfried Grassman, University of Saskachewan
David Stanford, University of Western Ontario
Yiqiang Zhao, Carleton University

Workshop Description

The subject of queueing networks finds applications in the description of the flow of packets in the internet or in the flow of jobs through the many work stations in a modern factory. The study of congestion and control in such networks drawns on diverse areas of probability. One aspect is the calculation of rare event probabilities like the probability a particular node in a network overflows. Large deviation theory must be adapted to the network context because there are natural boundaries where the queues become empty. Large deviation theory along boundaries has been the subject of research from some time.

At the heart large deviation theory one uses the classical change of measure or h-transform technique due to Doob. In special cases the h-transform technique can even yield sharp asymptotics and a description of the network when the large deviation occurs. Sharp asymptotics are related to strong ratio limit theorems and the study of harmonic functions, quasi-stationary distributions and the Yaglom limit. The latter may be interpreted as the limiting conditional distribution of a Markov chain given the chain has not yet been killed by the nth step. This in turn is related to the literature on random walks conditioned to stay positive. In some sense the Yaglom limit is a more practical and fundamental concept than the traditional equilibrium limit since, as Keynes said, “in the long run we are all dead”. In other words most equilibrium states we may identify are more likely to be quasi-stationary distributions.

There is also recent work on determining the steady state and hence the large deviation probabilities using the Matrix Geometric method with infinite phase.

The aim of the workshop is to connect all these different threads.

Summer School (June 27th to June 30th)

The Rare Events Summer School will be held in room STE C0136 starting 9am on Monday June 27th.
This room is in the SITE (School of Information Technology and Engineering) building at the
extreme south end of the University of Ottawa Campus.
(This building is located on the South of the Campus).See:

For emergencies on arrival please call David McDonald at (613) 236 5893.

Professors Foley, McDonald, and Rolski will give a series of lectures on this theme. We also hope to have a couple of guest lecturers. The aim is to prepare the participants for the following rare events workshop and the Informs meeting.

There was some financial assistance for local expenses for qualified graduate students.
First round deadline is May 1 with notification of funding by May 9th.

We have arranged space in residence at the University of Ottawa for students attending the summer school, right in the city center.
Note: Classes will be cut short on Friday July 1st due to Canada Day celebrations.


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