Traffic Equilibria Analysed via Geometric Programming.
Abstract
The 'traffic-assignment problem' consists of predicting 'Wardrop-equilibrium flows' on a roadway network when origin-to-destination 'input flows' are specified. The 'demand-equilibrium problem' consists of predicting those input flows that place the network in a state of 'economic equilibrium' when the input flows are related via given travel-demand (feedback) curves to the resulting Wardrop-equilibrium origin-to-destination 'travel costs'. The traffic-assignment problem is treated as a special cast of the demand-equilibrium (the case in which the travel-demand curves are graphs of constant functions); and the demand-equilibrium problem is formulated and studied in the context of (generalized) 'geometric programming'. In particular, existence, uniqueness and characterization theorems are obtained via the duality theory of geometric programming by introducing appropriate extremality conditions and their corresponding dual variational principles (sometimes called complementary variational principles). These dual variational principles and extremality conditions also lead to new computational algorithms that show promise in the analysis of relatively large networks (such as those in relatively large urban or metropolitan areas).
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1975
- Accession Number
- ADA008819
Entities
People
- Elmor L. Peterson
- Michael A. Hall
Organizations
- Northwestern University