Christian Gromoll
Associate Professor of Mathematics


Department of Mathematics
University of Virginia
Charlottesville, VA 22903

Tel: (434) 924 4152
Fax: (434) 982 3084



UVA Probability Seminar

Teaching (previous courses are here)


Fall 2011
MATH 7310 Real Analysis I

Spring 2012
MATH 5110 Introduction to Stochastic Processes
MATH 7370 Probability Theory II



Research


I work in probability, stochastic processes, and their applications. I've been focusing on proving scaling limit theorems for classes of stochastic networks, using measure-valued processes to deal with complex state spaces. Recently, I've also become interested in models of social networks, and certain mathematical questions arising in ecology.

Publications
The fluid limit of a heavily loaded processor sharing queue (PDF)
(with A.L. Puha and R.J. Williams). Annals of Applied Probability 12 797-859 2002.
Diffusion approximation of a processor sharing queue in heavy traffic (PDF)
Annals of Applied Probability 14 555-611 2004.
The impact of reneging in processor sharing queues (PDF)
(with Ph. Robert, B. Zwart, and R. Bakker). In ACM-Sigmetrics, Saint Malo, June 2006. ACM/IFIP WG 7.3.
Heavy traffic limit for a processor sharing queue with soft deadlines (PDF)
(with L. Kruk). Annals of Applied Probability 17 1049-1101 2007.
Fluid limits for processor sharing queues with impatience (PDF)
(with Ph. Robert, and B. Zwart). Mathematics of Operations Research. 33 375-402 2008.
Fluid model for a data network with alpha-fair bandwidth sharing and general document size distributions: two examples of stability (PDF)
(with R.J. Williams). IMS Collections - Markov Processes and Related Topics: A Festschrift for Thomas G. Kurtz 4 253-265 2008.
Fluid limits for shortest remaining processing time queues (PDF)
(with D.G. Down and A.L. Puha). Mathematics of Operations Research 34 880-911 2009.
State-dependent response times via fluid limits for shortest remaining processing time queues (PDF)
(with D.G. Down and A.L. Puha). SIGMETRICS Performance Evaluation Review 37 75-76 2009.
Fluid limits for networks with bandwidth sharing and general document size distributions (PDF)
(with R.J. Williams). Annals of Applied Probability. 19 243-280 2009
Invariance of fluid limits for the shortest remaining processing time and shortest job first policies (PDF)
(with M. Keutel). Submitted.
Diffusion limits for shortest remaining processing time queues (PDF)
(with L. Kruk and A. Puha). Stochastic Systems. To appear