144 citations · 308 across the 6 of their papers we have counts for
6 papers
State space collapse and diffusion approximation for a network operating under a fair bandwidth sharing policy
W. N. Kang, F. P. Kelly, N. H. Lee +1
We consider a connection-level model of Internet congestion control, introduced by Massoulié and Roberts [Telecommunication Systems 15 (2000) 185--201], that represents the randoml…
HJB equations for certain singularly controlled diffusions
Rami Atar, Amarjit Budhiraja, Ruth J. Williams
Given a closed, bounded convex set with nonempty interior, we consider a control problem in which the state process and the control process…
Homotopy methods for counting reaction network equilibria
Gheorghe Craciun, J. William Helton, Ruth J. Williams
Dynamical system models of complex biochemical reaction networks are usually high-dimensional, nonlinear, and contain many unknown parameters. In some cases the reaction network st…
Fluid model for a network operating under a fair bandwidth-sharing policy
F. P. Kelly, R. J. Williams
We consider a model of Internet congestion control that represents the randomly varying number of flows present in a network where bandwidth is shared fairly between document trans…
Invariant states and rates of Convergence for a critical fluid model of a processor sharing queue
Amber L. Puha, Ruth J. Williams
This paper contains an asymptotic analysis of a fluid model for a heavily loaded processor sharing queue. Specifically, we consider the behavior of solutions of critical fluid mode…
Transition operators of diffusions reduce zero-crossing
Steven N. Evans, Ruth J. Williams
If is a solution of a one--dimensional, parabolic, second--order, linear partial differential equation (PDE), then it is known that, under suitable conditions, the number…