The application of origin-based assignment to SATURN networks with asymmetric cost functions.

Origin-based traffic assignment techniques (OBA) have removed a long-standing impediment in traffic assignment by producing Wardrop Equilibrium solutions whose accuracy is effectively limited only by the numerical precision of the computer. All previous algorithms (e.g., Frank-Wolfe) produce solutions which may, in theory, be converging towards the correct solution but, in practice, stall. OBA has been extended to more complex problems such as the combined solution of traffic assignment with variable demand trip matrices. However all these applications have been based on networks in which the cost-flow functions are separable, i.e., the cost of travel on link a is a function of the flow on link a only. More realistic network models allow for "interactions" between links so that the non-separable effects of, e.g., lane-sharing or give ways at priority junctions may be modelled. For example these effects are modelled within the widely used SATURN simulation sub-model. This paper describes the integration of OBA techniques into the SATURN Suite of programs and demonstrates that the numerical accuracy of OBA solutions may also be obtained by networks which incorporate a simulation component. More importantly these solutions are obtained with comparable cpu times as the more conventional SATURN assignment techniques. Numerical results for a range of real-life networks are presented. The question of whether and/or when multiple equilibrium solutions are possible (with or without OBA) will be addressed. For the covering abstract see ITRD E126595.