Current Research Publications/Recent Talks Teaching Education/Work Home

Robert T. Buche, Current Research

Heavy traffic limit models and control: incorporating long range dependence and heavy tailed behavior

Multimedia traffic, (for example, in movies and gaming) in both wireline and wireless systems has lead to a new paradigm for traffic modeling capturing heavy tailed and long range dependent behavior. Heavy traffic methods for queueing systems under such models is in its infancy. Based on recent works analyzing the arrival processes, one expects the heavy traffic limit models for these multimedia applications to include (but not limited to) those driven by stable Levy motion or fractional Brownian motion. We are interested in deriving heavy traffic limit models in this framework.

Support for this work in this area:

  • Grant from the NSF Division of Mathmatical Sciences, (Fall 2006-2009). Co-PIs are Arka Ghosh (Department of Statistics, Iowa State University) and Vladas Pipiras (Statistics and Operations Research, UNC, Chapel Hill).
    • Conference Paper: Proceedings of the 46th IEEE Conference on Decision and Control 2007, here
    • Research Paper: Under review in Queueing Systems, here

Numerical methods for stochastic control

We have implemented continuous-time methods for stochastic control for wireless queueing systems. The method is being applied to stochatic control problems for the queueing models obtained from heavy traffic methods. The numerical techniques applied were developed by Harold J. Kushner and Paul Dupuis (Division of Applied Math, Brown University; see their book Numerical Methods for Stochastic Control Problems in Continuous Time, Springer, second edition, 2002).

We are also applying extensions of the method developed in Numerical approximations for nonlinear stochastic systems with delays, by H.J. Kushner, Stochastics, Vol.77, No. 3, 2005, to incorporate models with delay along with further modifications for including a prediction component over the delay interval.

Support for this work in this area:

  • Grants (SBIR, Phase I and II) from Intelligent Automation, Inc. (Rockville, MD) and the Army Research Office (2004-2006).