Brownian network models of ramp metering

Frank Kelly
Conference on Stochastic Processing Networks, in Honor of J. Michael Harrison,
Stanford, August 2009.

Unlimited access to a highway network can, in overloaded conditions, cause a loss of capacity. Ramp metering can help avoid this loss of capacity. The design of ramp metering strategies has several features in common with the design of access control mechanisms in communication networks.

In this talk we describe an approach to the design of ramp metering flow rates informed by results developed for models of Internet congestion control. Our approach is based on Brownian network models that exploit simplifications arising in heavy traffic.



Data, modelling and inference in road traffic networks
R.J. Gibbens and Y. Saatci
Phil. Trans. R. Soc. A366 (2008), 1907-1919.

Brownian models of open processing networks: canonical representation of workload
J.M. Harrison
Annals of Applied Probability 10 (2000), 75-103.

A broader view of Brownian networks
J.M. Harrison
Annals of Applied Probability 13 (2003), 1119-1150.

State space collapse and diffusion approximation for a network operating under a proportional fair sharing policy
W. Kang, F. P. Kelly, N. H. Lee and R. J. Williams
Annals of Applied Probability, to appear.

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F. P. Kelly and R.J. Williams

What we've learned about highway congestion
P. Varaiya
Access 27, Fall 2005, 2-9.