Ajith Muralidharan

Optimal control of freeway networks based on the Link Node Cell transmission model

We present an optimal control approach to freeway traffic congestion control. A Link-Node Cell transmission model (LN-CTM) is used to represent the freeway traffic dynamics. The approach searches for solutions represented by a combination of ramp metering and variable speed control. The optimization problem corresponding to the optimal control problem based on the LN-CTM is non-convex and nonlinear. We relax the problem to a linear optimization problem, and propose an approach to map the solution of the linear optimization algorithm to the solution of the original optimal control problem. We prove that the solution derived from this approach is optimal for the original optimal control algorithm. Finally, we use a model predictive framework to demonstrate the optimal control formulation presented in this paper and discuss its potential use.

Imputation of Ramp Flow Data for Freeway Traffic Simulation

The Tools for Operational Planning is a suite of tools that uses the link–node cell transmission model for macroscopic freeway traffic simulations for specifying operational strategies such as ramp metering and demand and incident management. Traffic flow and occupancy data from loop detectors are used for calibrating these models and specifying the inputs to the simulation. Flow data from ramps, however, are often found to be missing or incorrect. This paper elaborates an imputation procedure used to determine these ramp flows. This automated imputation procedure is based on an adaptive identification technique that attempts to minimize the error between the simulated and the measured densities. Simulation results using the imputed flow data indicate good conformation with loop detector measurements.

TOPL: TOOLS FOR OPERATIONAL PLANNING OF TRANSPORTATION NETWORKS

TOPL is a suite of software tools for specifying freeway operational improvement strategies, such as ramp metering, demand and incident management, and for quickly estimating the benefits of such improvements. TOPL is based on the macroscopic cell transmission model. The paper summarizes the theory of the cell transmission model and describes the procedure to carry out a TOPL application. The procedure is illustrated for the 26-mile long I-210W freeway in California, whose model is calibrated using loop detector measurements of volume and speed. The measurements show that congestion originates in a bottleneck and moves upstream, as predicted by the theory. The simulations show that appropriate ramp metering can dramatically reduce total congestion delay and mainline travel time.Copyright

Freeway traffic flow simulation using the Link Node Cell transmission model

This paper illustrates the calibration and imputation procedure implemented to specify the inputs to the Link-Node Cell Transmission model used for simulating traffic flow in freeways. Traffic flow and occupancy data from loop detectors is used for calibrating these models and specifying the inputs to the simulation. In addition, flow data from ramps are often found to be missing or incorrect. A model based iterative learning technique is used to impute these ramp flows by minimizing the error between simulated and measured densities. The simulation results using the calibrated parameters and imputed flows indicate good conformation with loop detector measurements.

Probabilistic Graphical Models of Fundamental Diagram Parameters for Simulations of Freeway Traffic

Freeway traffic simulations must account for the probabilistic nature of model parameters to capture observed variations in traffic behavior. Fundamental diagrams specify freeway section parameters describing the flow–density relationship in macroscopic simulation models. A triangular fundamental diagram—specified with the free-flow speed, congestion wave speed, and capacity—is commonly adopted in first-order cell transmission models. Capacity (defined as the maximum flow observed in a given freeway section over a particular day) exhibits significant day-today variation, and capacity variations across different sections of the freeway are significantly correlated. Free-flow speeds do not exhibit significant variation, but congestion wave speeds exhibit variation uncorrelated with section capacities or parameters from other sections. A probabilistic graphical approach is presented to model the probabilistic distribution of fundamental diagram parameters of an entire freeway section chosen for simulation. More than 1 year of data from dozens of loop detectors along a 25-mi section of the I-210 freeway westbound in Los Angeles, California, are used for demonstration. The parameters of the distribution are estimated with the expectation–maximization algorithm to account for missing observations. Model selection from among plausible models indicates that a first-order spatial Markov model is appropriate to capture the capacity distribution, which is the joint probability distribution of freeway section capacities. Stochastic simulations with sampled parameters demonstrate that capacity variations can lead to significant variations in congestion patterns and freeway performance.

MODEL PREDICTIVE CONTROL OF A FREEWAY NETWORK WITH CAPACITY DROPS

In this paper, we present a model predictive controller to reduce road traffic congestion in freeway networks. The model predictive controller regulates traffic in the freeway through the use of ramp metering and variable speed limits. The controller uses a Link-Node Cell transmission model (LN-CTM) to represent freeway dynamics. We modify the standard LN-CTM to account for the capacity drop phenomenon, which is observed as a discontinuous decrease in flow throughput when traffic density exceeds a critical value. The resulting optimal control problem with a modified model, which accounts for the capacity flow phenomenon, is non-convex. We present heuristic restrictions on the solution trajectories, which allow us to solve the problem efficiently. This enables us to obtain the solution of the actual optimal control problem by solving a sequence of relaxed linear programs. We describe the procedure which can be used to map the optimal solution of this relaxed problem to the solution of the actual optimal control problem. Finally, we demonstrate the application of the model predictive controller on a simulated example, and discuss the characteristics of the controller.

Macroscopic Modeling and Simulation of Freeway Traffic Flow

Abstract This paper illustrates the macroscopic modeling and simulation of Interstate 80 Eastbound Freeway in the Bay Area. Traffic flow and occupancy data from loop detectors are used for calibrating the model and specifying the inputs to the simulation. The freeway is calibrated based on the Link-Node Cell Transmission Model and missing ramp flow data are estimated using an iterative learning-based imputation scheme. An ad-hoc, graphical comparison-based fault detection scheme is used to identify faulty measurements. The simulation results using the calibrated model exhibit good agreement with loop detector measurements with total density error of 3.3% and total flow error of 7.1% over the 23 mile stretch of the freeway under investigation and the particular day for which the ramp flows were imputed.

Imputation of Ramp Flow Data Using the Asymmetric Cell Transmission Traffic Flow Model

The Asymmetric Cell Transmission model can be used to simulate traffic flows in freeway sections. The model is specified by fundamental diagram parameters—determined from mainline data, and on-ramp and off-ramp flows. The mainline flow/density data are efficiently archived and readily available, but the ramp flow data are generally found missing. This paper presents an imputation technique based on iterative learning control to determine these flows. The imputation technique is applied sequentially on all the segments of the freeway, and the ramp flows, which minimize the error between the model calculated densities/flows and measurements are investigated. The stability and convergence of the density and flow errors using the imputation updates is also presented. Finally an example is shown to illustrate its use in a practical scenario.Copyright

High-resolution Sensing of Urban Traffic

Cities do not collect the high-resolution (HR) traffic data needed to evaluate and improve roadway operation. This paper describes a HR system called SAMS (Safety and Mobility System) that detects and records the lane, speed, signal phase and time when each vehicle enters and leaves the intersection; fuses these sensor events to estimate the intersection traffic state in real time for use by signal controllers; and archives the time series of traffic states to produce reports of vehicle counts and turn ratios, saturation rates, queues, waiting times, Purdue Coordination Diagram, and level of service (LOS); red light, speed, and right-turn-on-red (RTOR) violations, and vehicle-vehicle conflicts. The reports can be used to evaluate the performance of the current road operation and to improve traffic control.

ANALYSIS OF AN ADAPTIVE ITERATIVE LEARNING ALGORITHM FOR FREEWAY RAMP FLOW IMPUTATION

We present an adaptive iterative learning based flow imputation algorithm, to estimate missing flow profiles in on ramps and off ramps using a freeway traffic flow model. We use the LinkNode Cell transmission model to describe the traffic state evolution in freeways, with on ramp demand profiles and off ramp split ratios (which are derived from flows) as inputs. The model based imputation algorithm estimates the missing flow profiles that match observed freeway mainline detector data. It is carried out in two steps: (1) adaptive iterative learning of an ”effective demand” parameter, which is a function of ramp demands and off ramp flows/ split ratios; (2) estimation of on ramp demands/ off ramp split ratios from the effective demand profile using a linear program. This paper concentrates on the design and analysis of the adaptive iterative learning algorithm. The adaptive iterative learning algorithm is based on a multi-mode (piecewise non-linear)equivalentmodel of the Link-NodeCell transmission model. The parameter learning update procedure is decentralized, with different update equations depending on the local apriori state estimate and demand estimate. We present a detailed convergence analysis of our approach and finally demonstrate some examples of its application.