Programmability of continuous and discrete network equilibria
Programming formulations of the continuous network equilibrium problem are known to exist whenever the link cost functions are differentiable and symmetric. In this dissertation several aspects of these programming formulations are considered. First, more general conditions under which network equilibrium problems are programmable are developed. In particular, it is demonstrated that the cost functions need not be differentiable, but need only satisfy certain strong forms of continuity. Second, the stability of the solutions of programming formulations of the problem are considered, in an attempt to justify the study and use of these formulations. These results are developed using a behaviorally meaningful class of adjustment processes. Finally, a discrete version of the network equilibrium problem (with symmetric, non-separable cost functions) is developed in order to motivate the use of the continuous problem.
Area planning & development;
0999: Area planning & development
0796: Operations research