Traffic Theory

Arriving on Time: Estimating Travel Time Distributions on Large-scale Road Networks

Hunter, Timothy
Hofleitner, Aude
Reilly, Jack
Krichene, Walid
Bayen, Alexandre
2013

Most optimal routing problems focus on minimizing travel time or distance traveled. Oftentimes, a more useful objective is to maximize the probability of on-time arrival, which requires statistical distributions of travel times, rather than just mean values. We propose a method to estimate travel time distributions on large-scale road networks, using probe vehicle data collected from GPS. We present a framework that works with large input of data, and scales linearly with the size of the network. Leveraging the planar topology of the graph, the method computes efficiently the time...

State Estimation for Polyhedral Hybrid Systems and Applications to the Godunov Scheme

Thai, Jérôme
Bayen, Alexandre
2013

In this article, the problem of estimating the state of a discretized hyperbolic scalar partial differential equation is studied. The discretization of the Lighthill-Whitham-Richards equation with a triangular flux function using the Godunov scheme is shown to lead to a hybrid linear system or Switched Linear Systems (SLS) with a number of modes exponential in the size of the discretized model. Some geometric properties of the partition of the space into polyhedra (in which a mode is active) are exploited to find heuristics to reduce the number of modes to a representative set. This...

Phase Transition Model of Non-Stationary Traffic Flow: Definition, Properties and Solution Method

Blandin, Sébastien
Argote, Juan
Bayen, Alexandre M.
2013

We consider the problem of modeling traffic phenomena at a macroscopic level. Increasing availability of streaming probe data allowing the observation of non-stationary traffic motivates the development of models capable of leveraging this information. We propose a phase transition model of non-stationary traffic in conservation form, capable of propagating joint measurements from fixed and mobile sensors, to model complex traffic phenomena such as hysteresis and phantom jams, and to account for forward propagation of information in congested traffic. The model is shown to reduce to the...

A Diffusion Approximation to a Single Airport Queue

Lovell, David
Vlachou, Kleoniki
Rabbani, Tarek
Bayen, Alexandre M.
2013

This paper illustrates a continuum approximation to queuing problems at a single airport, adapted from the well-known diffusion approximation, as encapsulated in the Kolmogorov forward equation of stochastic processes or the Fokker–Planck equation of physics. The continuum model is derived using special artifacts of the airport problem context, and a numerical solution scheme based on the finite element method is presented. The results are compared against known stationary results from the M/M/1 process, as well as against airport scenarios generated from real demand and supply data. In...

A Heterogeneous Routing Game

Farokhi, Farhad
Krichene, Walid
Bayen, Alexandre
2013

Most literature on routing games make the assumption that drivers or vehicles are of the same type and, hence, experience the same latency or cost when traveling along the edges of the network. In contrast, in this article, we propose a heterogeneous routing game in which each driver or vehicle belongs to a certain type. The type determines the cost of traveling along an edge as a function of the flow of all types of drivers or vehicles over that edge. We examine the existence of a Nash equilibrium in this heterogeneous routing game. We study the conditions for which the problem of finding...

Large-Scale Estimation in Cyberphysical Systems Using Streaming Data: A Case Study With Arterial Traffic Estimation

Hunter, Timothy
Das, Tathagata
Zaharia, Matei
Abbeel, Pieter
Bayen, Alexandre M.
2013

Controlling and analyzing cyberphysical and robotics systems is increasingly becoming a Big Data challenge. We study the case of predicting drivers' travel times in a large urban area from sparse GPS traces. We present a framework that can accommodate a wide variety of traffic distributions and spread all the computations on a cluster to achieve small latencies. Our framework is built on Discretized Streams, a recently proposed approach to stream processing at scale. We demonstrate the usefulness of Discretized Streams with a novel algorithm to estimate vehicular traffic in urban networks...

Special Issue on Mathematics of Traffic Flow Modeling, Estimation and Control

Bayen, Alexandre M.
Frankowska, Hélène
Lebacque, Jean-Patrick
Piccoli, Benedetto
2013

This Special Issue gathers contributions, most of which were presented atthe Workshop ``Mathematics of Traffic Flow Modeling, Estimation and Control', organized at the Institute for Pure and Applied Mathematicsof the University of California Los Angeles on December 7--9 2011.For more information please click the “Full Text” above.

Hybrid Traffic Data Collection Roadmap: Objectives and Methods

Bayen, Alexandre
Sharafsaleh, Mohammad
Patire, Anthony D.
2013

Traffic data is used to estimate current traffic conditions so that travelers and agencies can make better decisions about how to use and manage the transportation network. This research explores the fusion of probe data (vehicle speed and direction) with loop data (density, speed, and count) in the context of producing overall network speed and travel time estimates. Speed and travel time estimates are useful in many circumstances, but current system control strategies (ramp metering, for example) require density data. While it is difficult to significantly increase the quantity of loop...

Stackelberg Thresholds on Parallel Networks with Horizontal Queues

Jebbari, Yasser
Krichene, Walid
Reilly, J.
Bayen, Alexandre M.
2013

We study Stackelberg routing games on parallel networks with horizontal queues, in which a coordinator (leader) controls a fraction α of the total flow on the network, and the remaining players (followers) choose their routes selfishly. The objective of the coordinator is to minimize a system-wide cost function, the total travel-time, while anticipating the response of the followers. Nash equilibria of the routing game (with zero control) are known to be inefficient in the sense that the total travel-time is sub-optimal. Increasing the compliance rate α improves the cost of the equilibrium...

Optimization-Based Queue Estimation on an Arterial Traffic Link with Measurement Uncertainties

Anderson, Leah
Canepa, Edward
Horowitz, Roberto
Claudel, Christian G.
Bayen, Alexandre
2014

Advanced monitoring and control of arterial road traffic network operations requires accurate knowledge of current and predicted performance measures on the network. Recently studied signal control algorithms, for example, use the lengths of vehicle queues for each turning movement to determine how subsequent signal cycles should be distributed into phases. This article presents a queue estimation procedure that can integrate measurements from classical count or occupancy sensors into a single physical model of general link state and queue length in particular. The authors show how...