•A series of methods are proposed for queue length and traffic volume estimation.•Only a few assumpitions are imposed and only probe vehicle data are needed.•The methods work well even when the ...penetration rate of probe vehicles is low.•Test results show the methods are useful for signal control and performance measures.
The rapid development of connected vehicle technology and the emergence of ride-hailing services have enabled the collection of a tremendous amount of probe vehicle trajectory data. Due to the large scale, the trajectory data have become a potential substitute for the widely used fixed-location sensors in terms of the performance measures of transportation networks. Specifically, for traffic volume and queue length estimation, most of the trajectory data based methods in the existing literature either require high market penetration of the probe vehicles to identify the shockwave or require the prior information about the queue length distribution and the penetration rate, which may not be feasible in the real world. To overcome the limitations of the existing methods, this paper proposes a series of novel methods based on probability theory. By exploiting the stopping positions of the probe vehicles in the queues, the proposed methods try to establish and solve a single-variable equation for the penetration rate of the probe vehicles. Once the penetration rate is obtained, it can be used to project the total queue length and the total traffic volume. The validation results using both simulation data and real-world data show that the methods would be accurate enough for assistance in performance measures and traffic signal control at intersections, even when the penetration rate of the probe vehicles is very low.
Although stochastic user equilibrium (SUE) problem has been studied extensively in the past decades, the solution convergence of SUE is generally quite slow because of the use of the method of ...successive averages (MSA), in which the auxiliary flow pattern generated at each iteration contributes equally to the final solution. Realizing that the auxiliary flow pattern is in fact approaching to the solution point when the iteration number is large, in this paper, we introduce the method of successive weighted averages (MSWA) that includes a new step size sequence giving higher weights to the auxiliary flow patterns from the later iterations. We further develop a self-regulated averaging method, in which the step sizes are varying, rather than fixed, depending on the distance between intermediate solution and auxiliary point. The proposed step size sequences in both MSWA and self-regulated averaging method satisfy the Blum theorem, which guarantees the convergence of SUE problem. Computational results demonstrate that convergence speeds of MSWA and self-regulated averaging method are much faster than those of MSA and the speedup factors are in a manner of magnitude for high accuracy solutions. Besides SUE problem, the proposed methods can also be applied to other fixed-point problems where MSA is applicable, which have wide-range applications in the area of transportation networks.
► We develop a boundedly rational (BR) day-to-day dynamical system. ► The BR system is used to model an irreversible network change. ► A network change is said to be irreversible if the traffic state ...cannot be restored by revoking the change. ► The BR system is applied to model the network changes after the I-35
W Bridge collapse and reopening.
A network change is said to be irreversible if the initial network equilibrium cannot be restored by revoking the change. The phenomenon of irreversible network change has been observed in reality. To model this phenomenon, we develop a day-to-day dynamic model whose fixed point is a boundedly rational user equilibrium (BRUE) flow. Our BRUE based approach to modeling irreversible network change has two advantages over other methods based on Wardrop user equilibrium (UE) or stochastic user equilibrium (SUE). First, the existence of multiple network equilibria is necessary for modeling irreversible network change. Unlike UE or SUE, the BRUE multiple equilibria do not rely on non-separable link cost functions, which makes our model applicable to real-world large-scale networks, where well-calibrated non-separable link cost functions are generally not available. Second, travelers’ boundedly rational behavior in route choice is explicitly considered in our model. The proposed model is applied to the Twin Cities network to model the flow evolution during the collapse and reopening of the I-35
W Bridge. The results show that our model can to a reasonable level reproduce the observed phenomenon of irreversible network change.
Anderson and Renault (1999) show that when search cost is needed to evaluate any product, a U-shaped relationship exists between equilibrium price and product differentiation. This paper revisits ...this relationship by incorporating partial-depth search in a sequential search process which allows consumers to evaluate a subset of product attributes. We show that, when search depth is endogenous, the relationship is either always positive or N-shaped, depending on the elasticity of the hazard rate function of utility distribution.
•The relationship between equilibrium price and product differentiation is explored under a partial sequential search model.•The relationship is always positive with an inelastic hazard rate function of utility distribution.•However, the relationship is N-shaped with an elastic hazard rate function of utility distribution.
On August 1, 2007, the collapse of the I-35W bridge over the Mississippi River in Minneapolis abruptly interrupted the usual route of about 140,000 daily vehicle trips, which substantially disturbed ...regular traffic flow patterns on the network. It took several weeks for the network to re-equilibrate, during which period travelers continued to learn and adjust their travel decisions. A good understanding of this process is crucial for traffic management and the design of mitigation schemes. Data from loop-detectors, bus ridership statistics, and a survey are analyzed and compared, revealing the evolving traffic reactions to the bridge collapse and how individual choices could help to explain such dynamics. Findings on short-term traffic dynamics and behavioral reactions to this major network disruption have important implications for traffic management in response to future scenarios.
•MCross is a new intersection operation scheme for connected and automated vehicles.•This new scheme maximizes intersection capacity by utilizing all lanes of a road simultaneously.•Numerical ...examples show that MCross can almost double the intersection capacity.
With the advent of connected and automated vehicle technology, in this paper, we propose an innovative intersection operation scheme named as MCross: Maximum Capacity inteRsection Operation Scheme with Signals. This new scheme maximizes intersection capacity by utilizing all lanes of a road simultaneously. Lane assignment and green durations are dynamically optimized by solving a multi-objective mixed-integer non-linear programming problem. The demand conditions under which full capacity can be achieved in MCross are derived analytically. Numerical examples show that MCross can almost double the intersection capacity (increase by as high as 99.51% in comparison to that in conventional signal operation scheme).
Traffic light optimization is known to be a cost-effective method for reducing congestion and energy consumption in urban areas without changing physical road infrastructure. However, due to the high ...installation and maintenance costs of vehicle detectors, most intersections are controlled by fixed-time traffic signals that are not regularly optimized. To alleviate traffic congestion at intersections, we present a large-scale traffic signal re-timing system that uses a small percentage of vehicle trajectories as the only input without reliance on any detectors. We develop the probabilistic time-space diagram, which establishes the connection between a stochastic point-queue model and vehicle trajectories under the proposed Newellian coordinates. This model enables us to reconstruct the recurrent spatial-temporal traffic state by aggregating sufficient historical data. Optimization algorithms are then developed to update traffic signal parameters for intersections with optimality gaps. A real-world citywide test of the system was conducted in Birmingham, Michigan, and demonstrated that it decreased the delay and number of stops at signalized intersections by up to 20% and 30%, respectively. This system provides a scalable, sustainable, and efficient solution to traffic light optimization and can potentially be applied to every fixed-time signalized intersection in the world.
This paper compares consumers' optimal search behaviors and firms' strategic reactions in prices under two modes of search: parallel search and sequential search, with the incorporation of partial ...search depth that measures the amount of information to evaluate a product. Our analysis shows a series of new results: when products are partially evaluated, search depth is greater under sequential search than under parallel search; consumers search for (on average) more products either under parallel search or sequential search, depending on whether partial‐depth search is chosen; the equilibrium price is higher under parallel (sequential) search when search costs are high (low). Interestingly, parallel search might yield higher equilibrium prices with more products searched, compared with sequential search. This challenges the conventional wisdom in the search literature that more products searched lower prices because of the intensified competition.
For uninterrupted traffic flow, it is well-known that the fundamental diagram (FD) describes the relationship between traffic flow and density under steady state. For interrupted traffic flow on a ...signalized road, it has been recognized that the arterial fundamental diagram (AFD) is significantly affected by signal operations. But little research up to date has discussed in detail how signal operations impact the AFD. In this paper, based upon empirical observations from high-resolution event-based traffic signal data collected from a major arterial in the Twin Cities area, we study the impacts of
g/
C ratio, signal coordination, and turning movements on the cycle-based AFD, which describes the relationship between traffic flow and occupancy in a signal cycle. By microscopically investigating individual vehicle trajectories from event-based data, we demonstrate that not only
g/
C ratio constrains the capacity of a signalized approach, poor signal coordination and turning movements from upstream intersections also have significant impact on the capacity. We show that an arterial link may not be congested even with high occupancy values. Such high values could result from queue build-up during red light that occupies the detector,
i.e. the Queue-Over-Detector (QOD) phenomenon discussed in this paper. More importantly, by removing the impact of QOD, a stable form of AFD is revealed, and one can use that to identify three different regimes including under-saturation, saturation, and over-saturation with queue spillovers. We believe the stable form of AFD is of great importance for traffic signal control because of its ability to identify traffic states on a signal link.
► An analytically tractable Gaussian model of (stochastic) first-order traffic flow. ► Analysis of Lipschitz continuity and (weak-sense) differentiability of disjunctive flux functions. ► A recipe ...for computing large state covariance matrices using few parameters and discussion of their properties. ► A preliminary validation of the model using Kalman filtering in a real-world setting.
A Gaussian approximation of the stochastic traffic flow model of Jabari and Liu (2012) is proposed. The Gaussian approximation is characterized by deterministic mean and covariance dynamics; the mean dynamics are those of the Godunov scheme. By deriving the Gaussian model, as opposed to assuming Gaussian noise arbitrarily, covariance matrices of traffic variables follow from the physics of traffic flow and can be computed using only few parameters, regardless of system size or how finely the system is discretized. Stationary behavior of the covariance dynamics is analyzed and it is shown that the covariance matrices are bounded. Consequently, Kalman filters that use the proposed model are stochastically observable, which is a critical issue in real time estimation of traffic dynamics. Model validation was carried out in a real-world signalized arterial setting, where cycle-by-cycle maximum queue sizes were estimated using the Gaussian model as a description of state dynamics. The estimated queue sizes were compared to observed maximum queue sizes and the results indicate very good agreement between estimated and observed queue sizes.
PDF
