NDLI: Stability of a dynamic model for traffic networks

Content Provider	IEEE Xplore Digital Library
Author	Mounce, R.
Copyright Year	2002
Description	Author affiliation: Dept. of Math., York Univ., UK (Mounce, R.)
Abstract	The dynamic assignment model assumes flow moves towards cheaper routes at each time at a rate proportional to the product of the flow along the more expensive route and the cost difference. Therefore, it is important for the cost function to be monotone so that convergence to equilibrium will occur. Conditions on the bottleneck output function are given for the bottleneck delay function to be monotone, which will imply monotonicity of the route cost function in the single bottleneck per route case. It is shown that for reasonable bottleneck output functions, we have monotonicity of the product of link cost with a decaying exponential. This decay-monotonicity transfers to the route cost in certain given circumstances. This will in turn imply convergence of the dynamical system by applying Lyapunov's theorem using the appropriate Lyapunov function. It is then important to note that monotonicity of the route cost function implies decay-monotonicity of the route cost function and hence the convergence result is valid for the single bottleneck per route case with monotone link cost functions.
Starting Page	795
Ending Page	800
File Size	356835
Page Count	6
File Format	PDF
ISBN	0780373898
DOI	10.1109/ITSC.2002.1041321
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2002-09-06
Publisher Place	Singapore
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Stability Telecommunication traffic Traffic control Cost function Convergence Mathematics Mathematical model Vehicle dynamics Vehicles Time measurement
Content Type	Text
Resource Type	Article

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