Traffic flows in networks are approached in terms of two basic problems: (1) how can the optimum utilization of a transportation network be characterized? (2) how can individual traveler behavior be described, and how can the resulting equilibrium in a network be characterized? Finally, when is a system equilibrium a system optimum? If individual traveler behavior is described as individual maximization of utility functions the question assumes this form: when does individual optimization generate a systems optimum? In the presence of delays through congestion and/or capacity constraints, individual optimization results in a systems optimum only when certain corrections are made. These are expressible in terms of lagrangian multipliers which can be interpreted as tolls. These tolls, added to time and money costs as experienced by the traveler, make individual optimization conform to a systems optimum. Special assumptions are needed, however, in order that these tolls be uniform for all users. Other questions examined include when is a shortest path to a destination from an intermediate point independent of the origin of the trip? When does a shortest path vary with the type of traveler? When can individual traffic flow variables be aggregated into total flows of one type of traveler on a link to a destination? The utility approach serves to relate traffic flow theory to welfare economics and to point out the various restrictive assumptions underlying more conventional network models. (a). For the covering abstract of the symposium, please see irrd abstract no. 224453.
Abstract