Traffic State Estimation in Heterogeneous Networks with Stochastic Demand and Supply: Mixed Lagrangian–Eulerian Approach

Abstract

A network fundamental diagram (NFD) represents the relationship between network-wide average flow and average density. Network traffic state estimation to observe NFD when congestion is heterogeneously distributed, as a result of a time-varying and asymmetric demand matrix, is a challenging problem. Recent studies have formulated the NFD estimation problem using both fixed measurements and probe trajectories. They are often based on a given ground-truth NFD for a single day demand. Stochastic variations in network demand and supply may significantly affect the approximation of an NFD. This study proposes a modified framework to estimate network traffic states to observe NFD while capturing the stochasticity in transportation networks. A mixed integer problem with non-linear constraints is formulated to address stochasticity in the NFD estimation problem. To solve this Nondeterministic Polynomial-hard (NP-hard) problem, a solution algorithm based on the simulated annealing method is applied. The problem is formulated and the solution algorithm is implemented to find an optimal configuration of loop detectors and probe vehicles to estimate the NFD of the Chicago downtown network and capture its day-to-day variations, considering a given available budget. Ground-truth NFDs and estimated NFDs based on a subset of loop detectors and probe vehicles are calculated using a simulation-based dynamic traffic assignment model, which is the best surrogate available to replicate real-world conditions. The main contribution of this study is to capture stochasticity in the demand and supply sides to find a more robust subset of links and trajectories to be acquired for the NFD estimation.

Impacts of Connected and Autonomous Vehicles on Traffic Flow with Heterogeneous Drivers Spatially Distributed over Large-Scale Networks

“…A relationship between the network-wide weighted average of traffic flow and density is used to define the NFD. These variables are calculated as the space-mean weighted averages of the link flows and densities, with link weights equal to the product of link length and number of lanes ( 33 , 36 – 38 ).…”

“…The simulation horizon is the morning peak period between 5:00 and 10:00 a.m. The static hourly demand, provided by the Chicago Metropolitan Agency for Planning, is transformed into a time-dependent origin–destination (OD) demand table with an OD estimation technique ( 37 ). The number of vehicles, simulated in the network during the morning peak period, is about 760,000.…”

Comparison of Support Vector and Non-Linear Regression Models for Estimating Large-Scale Vehicular Emissions, Incorporating Network-Wide Fundamental Diagram for Heterogeneous Vehicles

“…NFD can also be expressed as relations between network-wide averages of link flow and density ( 26 ). Researchers have proposed different methods to estimate NFD, such as the use of space-time three-dimensional vehicle trajectories ( 27 ) and formulating a resource allocation problem to account for limited resources in real networks for data collection, traffic heterogeneity, and asymmetry in origin-destination demand ( 28 , 29 ).…”

“…Unlike the micro-emission model, however, once it is calibrated, it does not require detailed trajectories of all traveling vehicles. It only incorporates the network-wide average flow and density given by an available NFD, and the traffic composition, which can be estimated for any given network with various approaches (e.g., see 28, 29, 44 ). This makes the proposed model a perfect tool for real-time control of emissions, unlike the micro model.…”

Empirical Validation of Bimodal MFD Models

“…The existence of empirical MFD was shown a not long time ago by Geroliminis and Daganzo (2008) for the city of Yokohama, Japan. Ever since, there had been several applications like traffic state estimation (Yildirimoglu and Geroliminis, 2014;Kavianipour et al, 2019), perimeter control (Keyvan-Ekbatani et al, 2012;Ampountolas et al, 2017;Haddad and Mirkin, 2017;Mohajerpoor et al, 2020), route guidance (Genser and Kouvelas, 2020), congestion pricing (Gu et al, 2018), and cruising for parking (Cao and Menendez, 2015;Leclercq et al, 2017), etc. proposed based on MFD approach at the network level.…”