Ted Hill

Georgia Tech

**October 2, 1997**

Jim Dai

Georgia Tech

A fundamental question is: When can one approximate the normalized vector process of inventory levels for various customer classes by a multi-dimensional reflected Brownian motion under heavy traffic conditions? This talk will survey the latest developments in the area, including recent work of Bramson and Williams. No prior knowledge of queueing networks is needed.

**October 9, 1997**

Rafal Latala

Georgia Tech and Warsaw University

**October 16, 1997**

Miguel Arcones

University of Texas, Austin

We also give some sufficient conditions for the compact law of the iterated logarithm for $$(n2 \log \log n)^{-1/2}\sum_{j=1}^{n}(G(X_{j})-E[G(X_{j})]).\leqno{(2)}$$ Our result builds on Ho (1995), who proved an upper--half of the law of iterated logarithm for (2).

**October 23, 1997**

Michael Maxwell

Georgia Tech

**October 30, 1997**

Don McNickle

University of Canterbury

The Kinleith Weighbridge

Every year some 2.5 million of wood are transported to the Carter Holt
Harvey complex at Kinleith. More than 400 truck-loads per day pass over a
single lane weighbridge. Waiting times had been observed to sometimes
reach 20 minutes per truck. A second weighbridge in parallel was under
consideration. The queueing model had to deal with non-stationary
behaviour and a move-up effect as the trucks moved on to the bridge.

Revising G1/AS1

Works Consultancy Services was contracted by the Buildings Industry
Authority to undertake a study of the number of sanitary facilities to be
provided in buildings, leading to revision of the G1/AS1 tables in the New
Zealand Building Code. A very extensive data-gathering exercise to predict
demand and occupancy times for various kinds of buildings was carried out.
Simple queueing models proved to be adequate for predicting the waiting
time distributions that the new standards would produce. The potential
savings of the new standards were surprising.

**November 6, 1997**

Presad Tetali

Georgia Tech

In graph-theoretic terms, such valid configurations correspond to independent sets (a.k.a. stable sets). Given a finite (or countably infinite) graph, and an arbitray real $\lambda$, the model associates a weight $\lambda^{|I|}$ to each independent set $I$ of the graph. This model is of interest and significance in statistical physics, theory of computing, and communication networks. The speaker intends to review some of the recent results and open problems concerning the hard-core model.

In particular, the notions of Dobrushin-Shlosman (spatial) mixing conditions and rapid mixing of certain reversible dynamics and other mixing conditions which guarantee the uniqueness of a hard-core infinite-volume (Gibbs) distribution will be explained.

**November 13, 1997**

Bob Foley

Georgia Tech

**November 20, 1997**

Ron Fox

Physics, Georgia Tech

**December 4, 1997**

Christian Houdre

Math, Georgia Tech

Bartek Blaszczyszyn

University of Wroclaw

We use this result as a basis for a new approach to light traffic approximations of stochastic systems, which can be viewed as being driven by a simple marked point process.

In a special case of thinning a point process, we obtain Taylor approximations. Particular results for Petri nets, ruin functions of risk models, workload vectors of many-server queues in a Markov modulated environment and the clump size i the Boolean model are presented.

The talk is based on the Ph.D. thesis of the author and some complementary studies.

**January 22, 1998**

David McDonald

University of Ottawa

We propose a test for Poissoness which involves a characterization of Poisson processes and Cramer-Von Mises statistics. We also discuss extensions of these ideas to nonparametrique quality control and nonparametrique regression.

**January 29, 1998**

John Elton

Georgia Tech

**February 5, 1998**

Y. L. Tong

Georgia Tech

**February 12, 1998**

Carlangelo Liverani

University of Rome, Italy

**February 19, 1998**

Philippe Barbe

Math, Georgia Tech and CNRS, France

The talk is based on a joint work with Michel Broniatowski (Universit\'e de Reims).

**February 26, 1998**

Tito Manlio Homem de Mello

ISyE, Georgia Tech

**March 5, 1998**

Sergey Bobkov

Math, Georgia Tech

**March 12, 1998**

Soren Asmussen

Lund University

For a random walk or Levy process, we identify the large deviations path leading to exceedance of a large level. In particular, it is shown that the time of exceedance, when properly normalized, has a limit which is either Pareto or exponential.

For a reflected random walk, we find the tail asymptotics of the maximum during the cycle. This determines the extreme value behaviour of the process as a whole. The results yield as a corollary similar results for storage processes with state dependent release and asymptotics for their stationary distribution. By sample path duality, this extends to approximations for finite or infinite horizon ruin probabilities in insurance risk models with compounding assets or a more general state--dependent premium rule.

**March 19, 1998**

Sabine Schlegel

University of Ulm

**April 2, 1998**

Daryl J. Dayley

School of Math Sciences, Australian National University

The transformation of one point process into another is examined. Any LRcD property is shown to be invariant under the independent translation of points. Such a transformation is equivalent to feeding a point process through an infinite server queue. Other queueing transformations are examined and shown to be capable of preserving LRcD properties, and of introducing them.

(Includes joint work with Rein Vesilo of Macquarie University, Sydney.)

**April 9, 1998**

Dick Serfozo

ISyE, Georgia Tech

**April 16, 1998**

Carl Spruill

Math, Georgia Tech

**April 23, 1998**

Otis Jennings

ISyE, Georgia Tech

**April 30, 1998**

Lisa Bloomer

Math, Georgia Tech

*Last updated: April 27, 1998 by J. Hasenbein
( johnny@isye.gatech.edu)*