DYNAMIC EQUILIBRIUM NETWORK DESIGN

摘要

The present work shows how the continuous equilibrium network design problem can be formulated to incorporate elastic dynamic assignment with departure time choice. First-order optimality conditions for the network design problem are established in a manner that corresponds to the static counterpart. Expressions for components of the optimality conditions are then derived by sensitivity analysis of the dynamic equilibrium process. The present analysis applies to free-flow travel times on all links but is restricted to capacities only where they each affect traffic on a single route. An indication is given of how these formulae can be extended by further analysis to apply to capacity restrictions that affect several routes. They can also be extended to other elements of the design of road networks and their usage such as departure and arrival time costs, and time-varying road tolls. Application of the present analysis to a small example network has shown how improvements to elements of a network design can affect the usage of the network, and can interact with each other. In particular, we note that the magnitude of traffic attracted to an improved route through reassignment from other routes can be substantially greater than that due to traffic generation. Whether or not increases to the capacity of a link are worthwhile depends on the volume of traffic that uses it, and can vary according to the free-flow travel times of that link and of others in the network. The results presented here illustrate how reductions in free-flow travel time have a direct effect on the travel costs incurred, whilst increases in capacity have one that depends on the elasticity of demand and so is indirect.