Fluid and Brownian Models of Congestion at Flow Level

Abstract-IMA March 2004

 Flow Level Model of Congestion Control
(Roberts-Massoulie ‘00)

Flow Level Model
(Roberts and Massoulie, ‘00)

 Stochastic Processing Network with Simultaneous Resource Possession

Flow Level Model with Bandwidth Sharing
(cf. Roberts & Massoulie ‘00)

Bandwidth Allocations

Examples of    -fair allocations

Example: linear network

Stochastic Assumptions for Flow Level Model
(cf. Roberts & Massoulie ‘00)

Outline of rest of talk

 Stochastic Network Model

Fluid model
(formal functional law of large numbers limit)

 Stability

Balanced Fluid Model

Asymptotic Behavior of Balanced Fluid Model

(Multiplicative) State Space Collapse

Diffusion Scaling in Heavy Traffic

Diffusion Approximation in Heavy Traffic

Diffusion Approximation in Heavy Traffic

Example:  Linear Network

Future Work