Solving the Sequential Travel Forecasting Procedure with Feedback

Travel forecasters generally understand that an iterative solution of the sequential travel forecasting procedure is required to bring specific model inputs and outputs into consistent agreement. In particular, the congested interzonal travel time inputs to the trip distribution and mode choice steps should equal the user-equilibrium travel times obtained from the assignment step. The process of achieving consistency is called solving the sequential procedure with feedback. The Capital District Transportation Committee of Albany, New York, maintains a travel forecasting model with 1,000 traffic analysis zones. This model was used to evaluate feedback procedures for three applications drawn from its planning activities. Three alternative feedback solution procedures were applied to the model: (a) naïve or direct feedback (no averaging of trip matrices or link flows), (b) averaging of trip matrices with constant weights, and (c) the method of successive averages (MSA) applied to trip matrices. The convergence of the feedback procedures was measured by comparing the results as follows: total misplaced flow (trip matrices), relative gap (route-based user-equilibrium traffic assignments), and root squared error (travel cost matrices). The test results showed that (a) averaging of trip matrices by using constant weights converges to a single, stable solution with consistent travel costs; (b) a single pair of weights is most effective for all three applications; (c) neither naïve feedback nor MSA is as effective as use of constant weights; and (d) the relative gaps of the traffic assignment reach values of less than 10-7. Tests with different models and software systems are needed to generalize the findings.