D. Nualart

University of Barcelona

**January 18, 1996**

Jim Dai

Math/ISyE

Georgia Institute of Technology

**January 25, 1996**

Dan Mauldin

Department of Mathematics

University of North Texas

**February 2, 1996**

David McDonald

Department of Mathematics

University of Ottawa

Here we consider one node in a queueing network whose transitions may be represented by an Markov additive process which recurs to a reflection point at zero. The steady state pi is not known so the clumping heuristic doesn't work. Nevertheless it is possible to perform an h-transformation or {twist} which turns the additive process around much like the one dimensional associated random walk described in Feller Volume II. This twist automatically yields the rough asymptotics of the mean excursion length. The exact asymptotics are given by probabilistic expression involving the twisted Markov additive process. The steady state of the network conditioned on the specified node being in F also follows. The twisted process is transient to F so a computer simulation of the rare event is very quick. The hitting distribution of the twisted process on F immediately yields that of the original Markov chain.

**February 8, 1996**

M. Borodovsky

Department of Mathematics

Georgia Tech

** February 14, 1996**

Gideon Weiss

Haifa
A process of zigzag lines with Poisson breakpoints

**February 22, 1996**

Michael Monticino

Department of Mathematics

University of North Texas

**March 1, 1996**

Richard Durrett

Department of Mathematics

Cornell University

From the voter model to species area curves

**March 8, 1996**

Jianqing Fan

Department of Statistics

University of North Carolina

The talk will be based on a recent work with Haerdle and Mammen.

**April 4, 1996**

Jin Feng

Department of Statistics

University of Wisconsin-Madison

The usual linear martingale problems (a probabilistic approach for studying contraction linear semigroups) provide a powerful tool for characterizing Markov processes, especially in addressing convergence issues: convergence of generators implies the weak convergence of processes.

In this research, parallel results for large deviations will be established. A class of nonlinear martingale problems will be introduced (which corresponds to a class of nonlinear semigroups named after Nisio). The principal result says if the nonlinear generators converge in a sense, then large deviation principle will follow.

It is hoped that this approach will provide a useful tool for answering probabilistic questions using available nonlinear analytical results, as well as providing tools for studying the large deviation princinple for general processes - measure valued, for example.

**May 9, 1996**

Sigrun Andradottir

Industrial and Systems Engineering

Georgia Tech

This is joint work with James M. Calvin and Peter W. Glynn.

**May 14, 1996**

IC 215, 11 am

Sandy Stidham

Industrial and Systems Engineering

University of North Carolina-Chapel Hill

1) We show exact conditions under which it will be optimal to accept a
lower-fare class and simultaneously reject a higher-fare class. (A
possible scenario which can cause this phenomenon is if the full-fare
class is fully refundable and a lower-fareclass is non-refundable.) In
this case it does not make sense to have nested booking limits based on
fares alone.

2) The booking limits may not be monotonically increasing in the time
remaining until the flight.

3) With the possibility of cancellations, an optimal policy may depend on
the total capacity as well as the capacity remaining. In fact, for a
given capacity remaining the booking limits are monotone
(non-decreasing) in the total capacity.

Finally, by pointing out the connection between yield management and queueing control we hope to stimulate further research that exploits this connection to solve additional problems in yield management.

Unless otherwise noted, the seminar meets Thursdays at 3 PM in 269
Skiles. For further
information, contact Ted Hill (hill@math.gatech.edu,
(404)853-9111)

*Last updated: May 13, 1996 by J. Shear ( joannas@isye.gatech.edu)*