Calibration Procedure for Traffic Flow Models of Merge Bottlenecks

Abstract

Travel times and delays on freeways are highly dependent on the discharge rate of the bottlenecks. Consequently, it is important to model the traffic flow at bottlenecks as accurate as possible. However this is not straightforward in merge bottlenecks as the traffic flow is impacted by the acceleration, deceleration, and lane changing maneuvers induced by the merging vehicles. The interaction of these factors results in a reduced discharge rate when the bottleneck is congested compared to the discharge rate observed when the bottleneck is uncongested. This phenomenon is often referred to as capacity drop. Therefore, a traffic flow model of merge areas must reproduce the capacity drop phenomenon features including: (i) magnitude of drop in the outflow, (ii) when and how the capacity drop occurs, and (iii) how and when the bottleneck can recover nominal capacity. This can be achieved by a model able to reproduce capacity drop and the correct imputation of its parameters. Here we tackle the imputation of parameters aspect by proposing a calibration procedure that ensures the aforementioned aspects of capacity drop are captured. The procedure, based on the Multi-Objective Differential Evolution (MODE), does not require any information about the calibrated model and therefore is applicable to different models. The output contains multiple solutions in contrast to the usual single solution in single-objective optimization. Therefore, it returns multiple combinations of parameters that can reproduce the field measurements with similar level of accuracy. Unlike single objective approach, defining weights is not necessary. This is beneficial even when the ultimate goal is to find a single solution. The practitioner can inspect the model outputs of each parameter set and pick the one that suits better. Also, the multiple solutions can be used for further analysis and applications such as parameter and output uncertainty. The procedure is tested against field data of a bottleneck in which capacity drop is consistently observed based on data of 16 days. The following implementations of link transmission model (LTM) are calibrated: (a) standard LTM with no extension (capacity drop is not captured), (b) LTM with outflow reduction based on the upstream queue (density); (c) LTM with outflow reduction based on on-ramp flow, and (d) LTM with outflow reduction based on on-ramp flow and queue. In all cases the algorithm output approximate the Pareto Frontier or trade-off curve between downstream outflow and density errors. As expected, the errors are smaller as additional features are added to the model (from case (a) - no feature - to case (d) - two features); however, among the models with one additional feature ((b) and (c)), considering ramp flows had lead to smaller errors. With the multiple solutions, time-dependent upper and lower bounds of density, outflow, and travel times can be obtained by applying the model for all solutions given expected demands. Therefore a possible application is the estimation of lower and upper bounds of travel times.