Piecewise-Linearized Cell Transmission Model and Parameter Calibration Methodology

Abstract

This paper concerns the development of macroscopic freeway traffic models and parameter calibration methodologies that are computationally efficient and suitable for use in real-time traffic monitoring and control applications. Toward the fulfillment of these objectives, a macroscopic traffic model, the Switching-Mode Model (SMM), is presented, which is a piecewise linearized version of Daganzo's Cell Transmission Model (CTM). The observability and controllability properties of the SMM modes are reviewed, since these properties are of fundamental importance in the design of traffic estimators and on-ramp metering controllers. A semi-automated method has been developed for calibrating the CTM and SMM parameters. In this method, a least-squares data fitting approach is applied to loop detector data to determine free-flow speeds, congestion-wave speeds, and jam densities for specified subsections of a freeway. Bottleneck capacities are estimated from measured mainline and onramp flows. The calibration method was tested using loop detector data from an approximately 14-mile (23 km) section of Interstate 210 West (I-210W) in southern California. Traffic data sources were the Performance Measurement System (PeMS), and a set of manually-counted ramp volumes provided by Caltrans District 7. Parameters were first calibrated for a short (2 mi (3 km)) subsection of I-210W and tested on both the SMM and CTM, which were shown to perform similarly to one another. The calibration method was then extended to the full 14-mi section, and the parameters were tested with the CTM. The CTM was able to reproduce observed bottleneck locations and the general behavior of traffic congestion, yielding approximately 2% average error in predicted total travel time.

Calibration and validation of a switched linear macroscopic traffic model

“…7. Note also that the calculation of the mean error percentage (10), indicates that the M.E for the three cells are respectively 3.64%, 5.39% and 6.19%. Finally, the mean error percentage over the portion is around of 5%.…”

“…Among the first order traffic models, a switched Mode model (SMM) has been proposed more recently [10]. This latter is a piecewise linearization of the cell transmission model (CTM), which has been currently used in intelligent transportation systems, like as in traffic dynamic assignment [11], optimization [12], traffic network design applications [13], estimation [14], and ramp metering control [15].…”

Offline Calibration of Dynamic Traffic Assignment

“…Each of estimator is generally associated with prohibitively high running times (7). Further, studies focusing on the separate calibration of demand-and-supply models (10)(11)(12)(13)(14)(15) keep the other parameters fixed, thus ignoring the critical interactions between different types of variables.…”

Modeling and Density Estimation of an Urban Freeway Network Based on Dynamic Graph Hybrid Automata

“…Moreover, the nonlinear relationship between traffic flow and density results in study difficulty. Although Mu$\stackrel{false˜}{n}$oz and Sun et al [17,18] presented the Switching Mode Model (SMM) which is a piecewise linearized version of the CTM, this model may be improved further by introducing some modeling tools as solid theoretical basis. Hence, in the previous work [19,20,21] we proposed a model framework by introducing dynamic digraph and hybrid automata.…”