RESEARCH IN PROBABILITY: R. J. WILLIAMS
LIST OF PUBLICATIONS
ABSTRACTS AND PREPRINTS OF RECENT RESEARCH
  • Diffusion approximation for a heavily loaded multi-user wireless communication system with cooperation
  • Homotopy methods for counting reaction network equilibria
  • State space collapse and diffusion approximation for a network operating under a fair bandwidth sharing policy
  • HJB equations for certain singularly controlled diffusions
  • Fluid model for a data network with alpha fair bandwidth sharing and general document size distributions: two examples of stability.
  • On the performance of a two-user downlink system in heavy traffic.
  • Fluid limits for networks with bandwidth sharing and general document size distributions.
  • An invariance principle for semimartingale reflecting Brownian motions in domains with piecewise smooth boundaries.
  • Workload interpretation for Brownian models of stochastic processing networks.
  • The fluid limit of an overloaded processor sharing queue.
  • Product form stationary distributions for diffusion approximations to a flow level model operating under a proportional fair sharing policy (MAMA 07 - to appear in Performance Evaluation Review)
  • On fluid and Brownian approximations for an Internet congestion control model.
  • Dynamic scheduling of a parallel server system in heavy traffic with complete resource pooling: asymptotic optimality of a threshold policy.
  • Workload reduction of a generalized Brownian network.
  • Fluid model for a network operating under a fair bandwidth-sharing policy.
  • Two workload properties for Brownian networks.
  • Diffusion approximation for a processor sharing queue in heavy traffic by H. C. Gromoll.
  • Invariant states and rates of convergence for a critical fluid model of a processor sharing queue.
  • The fluid limit of a heavily loaded processor sharing queue
  • On dynamic scheduling of a parallel server system with complete resource pooling
  • Dynamic scheduling of a system with two parallel servers in heavy traffic with complete resource pooling: asymptotic optimality of a continuous review threshold policy
  • Stabilization of stochastic nonlinear systems driven by noise of unknown covariance
  • Reflecting diffusions and queueing networks
  • Heavy traffic limits for open multiclass queueing networks
  • On K. L. Chung's Research on Stopped Feynman-Kac Functionals and the Schrodinger Equation.
    SNAPSHOTS: Some selected snapshots of recent research
  • Dynamic Scheduling for Parallel Server Systems
    TALKS
  • Diffusion approximation for a heavily loaded multi-user wireless communication system with cooperation, Stochastic Networks meeting, Paris, June 2008.
  • Markov Lecture, Annual INFORMS meeting, Seattle, November 2007. For a pdf copy of this talk, click here. For a recent paper related to this talk, click here.
  • 3rd Cornell Probability Summer School, June 2007: Reflecting Brownian motions.
    Lecture 1: Multiclass Queueing Networks and Semimartingale Reflecting Brownian Motions in the Orthant.
    Click here for a copy with white background and 6 to a page for easy printing.
    Lecture 2: Stochastic Processing Networks and Semimartingale Reflecting Brownian Motions in Piecewise Smooth Domains.
    Click here for a copy with 6 to a page for easy printing.
    (Copyright Ruth Williams 2007.)
  • Stochastic Processing Networks, a lecture series at the University of Melbourne, September 4-6, 2006. Jointly sponsored by the Maurice H. Belz trust and MASCOS. (Copyright Ruth Williams 2006. All print and electronic rights and use rights reserved. Personal, non-co mmerical use only, for individuals with permission from author --- write to williams@math.ucsd.edu for this.)
  • A measure-valued process in a bandwidth sharing model with general document size distributions, Madison, WI, July 2006. (Copyright Ruth Williams 2006. All print and electronic rights and use rights reserved. Personal, non-commerical use only, for ind ividuals with permission from author --- write to williams@math.ucsd.edu for this.)
  • Input Queued Crossbar Switch Operating under a Maximum Weight MatchingPolicy in Heavy Traffic, Stochastic Networks meeting, Urbana, June 2006. (Copyright Ruth Williams 2006. All print and electronic rights and use rights reserved. Personal, non-commerical use only, for individuals with permission from author --- write to williams@math.ucsd.edu for this.)
  • Hotelling Lecture Series, University of North Carolina, Chapel Hill, November 1-5, 2004. (Copyright Ruth Williams 2004. All print and electronic rights and use rights reserved. Personal, non-commerical use only, for individuals with permission from author --- write to williams@math.ucsd.edu for this.)
  • Transparencies from talk given at IMA Workshop on Control and Pricing in Communication and Power Networks, March 8-13, 2004. (Copyright Ruth Williams 2004. All print and electronic rights and use rights reserved. Personal, non-commerical use only, for individuals with permission from author --- write to williams@math.ucsd.edu for this.)
    Fluid and Brownian Models of Congestion at Flow Level.

  • Transparencies from tutorial given at SAMSI Workshop, October 31, 2003. (Copyright Ruth Williams 2003. All print and electronic rights and use rights reserved. Personal, non-commerical use only, for individuals with permission from author --- write to williams@math.ucsd.edu for this.)
    Fluid and diffusion approximations for stochastic processing networks, and a flow level model of congestion control.

  • Transparencies from lectures given at the Eight Summer Workshop of the New Zealand Mathematics Research Institute, Napier, January 6-11, 2002. (Copyright Ruth Williams 2002. All print and electronic rights and use rights reserved. Personal, non-commerical use only, for individuals with permission from author --- write to williams@math.ucsd.edu for this.)
    -Performance analysis for multiclass queueing networks via reflecting diffusions.
    -Dynamic scheduling for stochastic networks in heavy traffic.

  • La Trobe University, Bendigo, G.S. Watson Annual Lecture, 1999
    "From Queueing Networks to Reflecting Diffusions", by Professor Ruth     Williams,
    July 19, 1999, 4pm to 5pm, Education Lecture Theatre, La Trobe University, Bendigo, Australia.

  • Transparencies from talk at the Applied Probability Day, Columbia University, April 23, 1999. Multiclass queueing networks and reflecting diffusion processes.
    (Copyright Ruth Williams 1999. All print and electronic rights and use rights reserved. Personal, non-commerical use only, for individuals with permission from author --- write to williams@math.ucsd.edu for this.)
    ACKNOWLEDGEMENT
    The research of Ruth Williams is supported in part by the National Science Foundation. Any opinions, findings and conclusions or recomendations expressed in the material found on these web pages are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF). Some of the research of Ruth Williams has also been partially supported by a gift from the David and Holly Mendel Fund and a John Simon Guggenheim Fellowship.
    MATHEMATICS GENEALOGY PROJECT
    Includes a list of Ph.D. students of R. J. Williams.
    NEWS ITEMS RELATED TO RESEARCH IN PROBABILITY AND STOCHASTIC PROCESSES
  • Article on the use of queueing models in manufacturing (Stanford online report, May 19, 1999).
    USEFUL INFORMATIONAL LINKS
  • Maury Bramson's homepage with access to his 2006 Saint Flour lecture notes on stability of queueing networks. For a direct link to the notes, click here.
  • Avi Mandelbaum's site on Service Engineering, with particular emphasis on call centers.
  • Ward Whitt's page with links to Call Center related websites, including Avi Mandelbaum's Research Bibliography on Call Centers.
  • Nosokinetics - The mathematics of patient flow through health and social care systems.
  • Student's 1927 paper entitled "Errors of Routine Analysis" (see especially page 10 for a memory aid concerning kurtosis).
  • Systems and Synthetic Biology - links to some researcher web pages.
  • Brownian motion: a description of aspects of this process and some of its applications
  • Links to some web sites of researchers in Stochastic Networks
  • Ernst Hairer's website with links to code for numerical approximation of ordinary differential equations with delay.
    Last updated: July 26, 2004