Shaurya Agarwal

A Dynamic Network Modeling-Based Approach for Traffic Observability Problem

This paper presents a novel approach for studying the observability problem on a general topology of a traffic freeway network. We develop a new framework, which investigates observability in terms of flow and routing information on the network arcs. We utilize lumped-parameter-based ordinary differential equation (ODE) setting to model traffic (ρ) dynamics on a network arc and then combine it with the ODE model of routing (π) dynamics to develop a state-space model for the network. We then linearize the network dynamics about steady-state flow, calculate the observability matrix, and apply the rank condition test on it. Some of the problems addressed in the paper include the following: identification of essential and redundant measurements in the context of observability, and verification of the sufficiency of a given set of states for the observability of the system. In particular, three different observability problems are formulated and solved using the proposed framework. The methodology is then illustrated by its application on carefully chosen network examples from the commonly encountered traffic freeway scenarios. A theorem and a corollary providing a necessary condition for observability are also proved. Finally, a conjecture based on the observations from the solved network examples is provided.

Observability and Sensor Placement Problem on Highway Segments: A Traffic Dynamics-Based Approach

Traffic congestion is a major problem on highways. To analyze this problem and then design different ways of reducing congestion, researchers need to observe traffic conditions on highways. Sensors are used to record and collect traffic data on highways. However, sensors must be placed efficiently to maximize the information collected and minimize monetary cost. This paper presents a novel approach for studying the observability problem on highway segments by utilizing linearized traffic dynamics about steady-state flows. First, we analyze the observability problem in terms of sensor placement and then present a method for comparing scenarios having different sensor placements along a highway. Different sensor placement scenarios are compared using the condition number of the observability matrix for the modeled system. Simulations are performed for various different numbers of highway cells, and then, generalized results are provided. We also discuss steps needed to extend this methodology to a general traffic network system.

Feedback-Coordinated Ramp Control of Consecutive On-Ramps Using Distributed Modeling and Godunov-Based Satisfiable Allocation

This paper presents a feedback control design for a coordinated ramp metering problem for two consecutive on-ramps. We design a traffic allocation scheme for ramps based on Godunovs numerical method and using a distributive model. Most of the previous work for designing feedback control for ramp metering is based on either the discretized linear methods or nonlinear methods based on the traffic ordinary differential equations (ODEs). We utilize the distributive model to construct a control condition for regulating the traffic density at critical density. Then, we design a Godunov-method-based satisfiable allocation scheme that gives us the actual control for each ramp individually. We show the stability properties of the closed-loop system and validate the effectiveness of the feedback control law by running a simulation using real traffic flow measurements with parameter estimation.

Is having accurate knowledge necessary for implementing safe practices?: A consumer folk theories-of-mind perspective on the impact of price

Purpose The purpose of this research is to increase consumer safety by providing insights about the linkage between consumer knowledge, price perception and safety intentions. Drawing from the expanded societal view of marketing, this model aims to further understanding of the connection between consumer education and safety from a folk theories-of-mind perspective. Design/methodology/approach This paper utilizes a phased, mixed-methods and interdisciplinary approach which blends transportation research and marketing. First, a qualitative inquiry of 151 comments regarding child safety seats was conducted. Next, using the key themes and concepts, a quantitative model was derived and a proposed structural equation model on a sample of 217 respondents was tested. Findings Although consumers understand the importance of child safety seats and the ample potential harms associated with their misuse, this paper contributes to existing literature by showing that a high perceived price can offset potential experience with them, attitude toward them and future use of them. Practical implications Integrated marketing campaigns to increase safety practices regarding child safety can be framed from a “cost of a life” rather than a “cost of a seat” perspective. Originality/value This research contributes by highlighting the importance of perceived price as it weighs against safety in a quantitative model, showing that consumer education can increase usage intentions for critical products and offering a mixed-methods, interdisciplinary approach to reduce framing biases and address a topic of significant societal concern.

Inverse Problem for Non-Viscous Mean Field Control: Example From Traffic

This paper presents an inverse problem for mean field games where we find the mean field problem statement for which the given dynamics is the solution. We use distributed traffic as an example and derive the classic Lighthill Whitham Richards (LWR) model as a solution of the non-viscous mean field game. We also derive the same model by choosing a different problem where we use travel time, which is a distributed parameter, as the cost for the optimal control. We then study the stationary versions of these two problems and provide numerical solutions for the same.

Quality of Traffic Observability on Highways With Lagrangian Sensors

Observability is essential to estimate the states of a system from sensor measurements. Observability indicates the sufficiency of the sensors for state estimation. In a highway traffic setting, using global positioning system-enabled smartphones as sensors sets this observability problem in the Lagrangian dynamics framework, in which the moving vehicle that follows the microscopic dynamics of the system senses its own current state. This paper addresses the question of how different numbers of sensor vehicles in the traffic stream affect the observability of the system. This was accomplished by performing spatiotemporal discretization of the traffic hydrodynamics to obtain a system on which the rank observability condition was applied. Then, the observability problem for a generic system was studied in terms of the average penetration of these mobile devices in the traffic stream. Simulation results are provided to support the developments in this paper.Note to Practitioners—This paper is motivated by the problem of observing the state of traffic in a highway setting from Lagrangian sensors. These are sensors that travel with individual vehicles rather than the traditional sensors that remain at fixed positions. There is much literature written on traditional sensors, but currently, there is development on what additional value Lagrangian sensors can provide. Lagrangian sensors recently became plausible, and readily available with the growth of smartphones. The problem that is studied is how much of the traffic behavior can be inferred from different numbers of the Lagrangian sensors. A traditional mathematical model for traffic flow is studied in the Lagrangian coordinates. The concept of observability and condition number is used to analyze how much and how well the sensors can capture traffic information. This problem is studied with idealized vehicle behavior, but this paper will be extended to cope with more realistic driving behaviors in the future.

Optimal Control for Congestion Pricing: Theory, Simulation, and Evaluation

This paper presents a mathematical framework for dynamic congestion pricing. The objective is to calculate an optimal toll using the optimal control theory. The problem consists of tolled lanes or routes and alternate non-tolled lanes or routes. The model is developed using a traffic conservation law, the queuing theory, and fundamental macroscopic relationships. A logit model is used for establishing the relationship between the price and the drivers choice behavior. We design a cost function and then use Hamilton–Jacobi–Bellman equation to derive an optimal control law that uses real-time information to determine an optimal tolling price. Simulations are performed to demonstrate the performance of this optimal control congestion-pricing algorithm.

Modeling and Estimation of the Vehicle-Miles Traveled Tax Rate Using Stochastic Differential Equations

The mismatch in demand and supply of the revenue for improving highway infrastructure and maintenance is an area of growing concern. In various studies, it has been found that the existing revenue collection system based on gas/fuel tax is not an appropriate model for highway funding. Some of the main drawbacks of the current system include no effective tax process for vehicles based on alternative fuel, no effective changes to the tax rate due to economic inflation, and more highway expenditure than generated revenue. A revenue model based on vehicle-miles traveled (VMT) has been identified as a potential alternative by various studies. For this new revenue model, it is extremely important to develop the required mathematical framework and estimate an effective VMT tax rate that addresses the current gap between generated and required revenue. The main objective of this paper was to estimate what VMT tax rate should be charged in order to generate the same amount of revenue that is being generated by the gas tax or to generate some specific required revenue. To this purpose, mathematical models for motor gasoline (gas) prices, gas consumption, and VMT based on stochastic differential equations were developed. Parameters for all the developed models then were estimated based on the maximum likelihood principle (maximum likelihood estimation) technique using relevant past data for each variable. The validity of the models was analyzed using the mean square errors which were found to be low. Numerical simulations were performed, and the effective VMT tax rate was estimated. To the best knowledge of authors this is the first attempt to model VMT and the VMT tax rate using stochastic dynamical models hence this is a novel contribution to the field.

Multiscale Modeling and Control Architecture for V2X Enabled Traffic Streams

In this paper, we propose a multiscale modeling framework, which is appropriate for analyzing the heterogeneous traffic streams involving connected vehicles as well as normal vehicles. In this framework connected vehicles are treated as discreet entities, which can be controlled microscopically so that they can then influence and control overall traffic streams in a macroscopic sense. To establish the connection between the individual vehicle behavior (microscopic entities) and overall macroscopic traffic streams, we propose to use Mean Field Games theory. We then highlight the formulation and design of control objectives using the proposed mathematical framework. Following that, we study the effect of varying penetration levels of V2X communication enabled vehicles on the efficiency of traffic flow. We use total entropy of the system as a measure of traffic flow efficiency. We also design control of traffic network via controlling the connected vehicles microscopically. A microscopic simulation is also performed in the end to validate the proposed framework and control algorithm.

Multidimensional Compression of ITS Data Using Wavelet-Based Compression Techniques

This paper explores the use of wavelet transform-based methods for ITS data compression. A methodology for structuring data and applying wavelet transform-based algorithms is proposed. The methodology provides the option of controlling the compression ratio at the cost of an acceptable distortion, visualizing data at different detail levels. With proper database management, this methodology will also allow faster data access without fully decompressing them. Given a high correlation of traffic data and knowing that the image data are compressed very well due to the inherent correlation of image pixels, the idea here is to restructure the traffic data, such that efficient image compression methods underlying modern image compression standards can be used. Three data structures are discussed: 1-D, 2-D, and 3-D. For a 1-D arrangement, different wavelets and decomposition levels were tested and analyzed for distortion levels in the data after decompression. The 2-D and 3-D data arrangements were compressed using embedded zero-tree wavelet and set partitioning in hierarchical trees algorithms, which are well-proved algorithms for compressing image data. A case study was performed using the traffic flow data from freeways in Las Vegas, Nevada. As could be expected, the compression ratio under the 3-D scheme has shown the best results. The 2-D and 3-D approaches yielded a 91% and 95.2% reduction ratios, respectively.