IMPLEMENTATION OF OPERATIONAL NETWORK EQUILIBRIUM PROCEDURES

Abstract

Operational network equilibrium procedures are being developed for the fixed-demand single-mode case. The basis of these procedures is described in the light of the historical development of approaches to the problem of predicting equilibrium flows in transportation networks. The procedures are described as capacity restraint methods that have the following advantages overtraditional approaches: On each iteration, improvement of the solution is ensured; and following each iteration, a measure that indicates the maximum amount of error remaining can be calculated. This paper describes network equilibrium procedures being made operational as a part of the UMTA Transportation Planning System. These procecures are described in light of their theoretical and mathematical background. Although significant theoretical work has been done on the variable-demand network equilibrium problem, the first developmental step being taken is to provide an efficient fixed-demand equilibrium procedure. It is expected, however, that expansion to the variable-demand case will be possible within the general algorithmic framework being developed. The paper begins by stating the general (variable-demand) network equilibrium problem. This problem is then formulated mathematically, and the nature of its solution is discussed. Previous work to develop efficient solution techniques is discussed. The results of much of the previous work are summarized as a general equilibrium algorithm for the fixed-demand problem. Finally, based on this general algorithm, current development work is described.

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