User-equilibrium properties of fixed points in dynamic traffic assignment
✍ Scribed by David E. Kaufman; Robert L. Smith; Karl E. Wunderlich
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 183 KB
- Volume
- 6
- Category
- Article
- ISSN
- 0968-090X
No coin nor oath required. For personal study only.
✦ Synopsis
This paper considers the problem of dynamic trac assignment under the principle that individual drivers will choose fastest paths, in the dynamic situation where path durations consist of time-dependent link travel times. Rather than constructing a uni®ed model encompassing trac dynamics and route choice, we decompose the model into an assignment mapping, which identi®es the link travel times resulting from an input routing policy, and a routing mapping, which yields fastest-path routings associated with input link travel times. Since time-dynamic link travel times are in¯uenced by route choice, this dynamic situation therefore encompasses predictive routing strategies. We establish that user-equilibrium routing policies are ®xed points of the composition of the routing and assignment functions. After discussing diculties associated with establishing existence of ®xed points under discrete-time modeling and all-or-nothing routing, we present instead new iterative routing mappings for continuous-time multipath routing (the splitting of a single-class ¯ow onto multiple paths), which adjust routing policies more incrementally. We provide sucient conditions for existence of ®xed points in various routing policy domains and oer some suggestions on the computation of these ®xed-point policies.