Optimizing the trajectory of connected automated vehicles (CAVs) through cooperation with signal controllers can smoothen the traffic flow and reduce energy consumption. However, most existing research efforts in this domain do not consider the effect of stochastic disturbances generated by exogenous systems. Ignoring these stochasticities may cause a mismatch between the estimated and real vehicle dynamics, which may result in a deviation among implemented and optimized trajectories, inefficient operational performance, and even collisions in the worst-case condition. This paper introduces a two-stage optimization model for CAVs trajectory and signal timing control that considers and responds to uncertainty in vehicle dynamics. The signal controller receives the speed, acceleration, and position of incoming CAVs within the communication range and identifies incoming platoons based on vehicle headways. At the upper stage, a mixed-integer linear program within the signal controller optimizes the trajectories of the platoon leaders and signal timing parameters. At the lower stage, platoon leaders optimize the trajectories of all other vehicles within the platoon based on a chance-constrained concept to consider uncertainties involved in implementing optimized trajectories. We utilize a sample-based approximation of the collision probabilities to formulate constraints to control vehicle trajectory. The resulting formulation ensures that the probability of satisfying inter-vehicle safety distance is above a certain threshold and reduces the probability of longitudinal crashes between vehicles. The proposed framework shows a 48%-67% reduction in travel delays in comparison with optimized fixed-time signal timing plans in a simulated signalized intersection under different levels of uncertainty in vehicle dynamics.

This study presents a vehicle-level distributed coordination strategy to control a mixed traffic stream of connected automated vehicles (CAVs) and connected human-driven vehicles (CHVs) through signalized intersections. We use CAVs as mobile traffic controllers during a newly introduced “white phase”, during which CAVs will negotiate the right-of-way to lead a group of CHVs while CHVs must follow their immediate front vehicle. The white phase will not be activated under low CAV penetration rates, where vehicles must wait for green signals. We have formulated this problem as a distributed mixed-integer non-linear program and developed a methodology to form an agreement among all vehicles on their trajectories and signal timing parameters. The agreement on trajectories is reached through an iterative process, where CAVs update their trajectory based on shared trajectory of other vehicles to avoid collisions and share their trajectory with other vehicles. Additionally, the agreement on signal timing parameters is formed through a voting process where the most voted feasible signal timing parameters are selected. The numerical experiments indicate that the proposed methodology can efficiently control vehicle movements at signalized intersections under various CAV market shares. The introduced white phase reduces the total delay by 3.2% to 94.06% compared to cooperative trajectory and signal optimization under different CAV market shares in our tests. In addition, our numerical results show that the proposed technique yields reductions in total delay, ranging from 40.2% – 98.9%, compared to those of a fully-actuated signal control obtained from a state-of-practice traffic signal optimization software.

Existing multi-class cell transmission model (CTM) based methodologies for signal timing or traffic assignment may transfer prioritized transit vehicles from one cell to the next one before processing their preceding passenger cars. In addition, existing CTM-based methodologies process a proportion of a slow-moving transit vehicle in each time step. As such a portion of each transit vehicle remains in each cell and it never clears them. This paper presents constraints to project the position of transit vehicles based on the speed and cell occupancy variations between different classes of vehicles and incorporates them into the CTM. The resulting optimization program is a mixed-integer nonlinear problem. We used a distributed receding horizon control framework to solve it in real-time. The proposed formulation is executed in a simulated arterial street with four signalized intersections in Springfield, IL with different traffic volume levels and transit vehicle frequencies. The results showed that the proposed algorithm addressed the mentioned issues of the existing multi-class CTM, and yielded more efficient network performance than the conventional transit signal priority-based (CTSP) systems. The proposed formulation reduced average bus delay by 1% to 70% and car delay by 52% to 76% compared to CTSP.

This study presents a distributed gradient-based approach to solve system optimal dynamic traffic assignment (SODTA) formulated based on the cell transmission model. The algorithm distributes SODTA into local sub-problems, who find optimal values for their decision variables within an intersection. Each sub-problem communicates with its immediate neighbors to reach a consensus on the values of common decision variables. A sub-problem receives proposed values for common decision variables from all adjacent sub-problems and incorporates them into its own offered values by weighted averaging and enforcing a gradient step to minimize its objective function. Then, the updated values are projected onto the feasible region of the sub-problems. The algorithm finds high quality solutions in all tested scenarios with a finite number of iterations. The algorithm is tested on a case study network under different demand levels and finds solutions with at most a 5% optimality gap.

This study introduces a methodology for cooperative signal timing and trajectory optimization at intersections with a mix of connected automated vehicles (CAVs) and human-driven vehicles (HVs). We represent joint signal timing and trajectory control as a mixed-integer non-linear program, which is computationally complex. The developed methodology provides a balance between computational efficiency and solution quality by (a) linearizing the nonlinear constraints and reformulating the problem with a tight convex hull of the mixed-integer solutions and (b) decomposing the intersection-level program into several lane-level programs. Hence, a unique controller jointly optimizes the trajectories of CAVs on a lane and the signal timing parameters associated with that lane. This setting will allow finding near-optimal solutions with small duality gaps for complex intersections with different demand levels. Case study results show that the proposed methodology finds solutions efficiently with at most 0.1% duality gap. We compared the developed methodology with an existing signal timing and trajectory control approach and found 13% to 41% reduction in average travel time and 1% to 31% reduction in fuel consumption under different scenarios.

This paper develops a stochastic gradient-based optimization model for traffic signal control with bounds on network-level vehicular energy consumption. The signal control problem is formulated as a mixed-integer linear mathematical program, which incorporates inequality constraints to limit the total energy consumption in the network. The developed stochastic gradient approximation algorithm provides a near-optimal solution to the non-convex optimization problem. To account for the energy consumption constraints, a penalty function method leveraging the pseudo gradient estimation technique is developed. Empirical results from a signalized arterial street show that it is possible to achieve optimized signal settings at the desired energy consumption bound without compromising delay. Further, we report the sensitivity of the energy bounds to the mobility metrics-system delay. Our novel gradient-approximation-based solution technique offers a functional and feasible way to accommodate non-convex energy consumption bounds within a signal control optimization model to achieve maximal mobility with minimal energy consumption.

This study develops a methodology for coordinated speed optimization and traffic light control in urban street networks. We assume that all vehicles are connected and automated. The signal controllers collect vehicle data through vehicle to infrastructure communications and find optimal signal timing parameters and vehicle speeds to maximize network throughput while harmonizing speeds. Connected and automated vehicles receive these dynamically assigned speeds, accept them, and implement them. The problem is formulated as a mixed-integer non-linear program and accounts for the trade-offs between maximizing the network throughput and minimizing speed variations in the network to improve the network operational performance and at the same time smoothen the traffic flow by harmonizing the speed and reducing the number of stops at signalized intersections. A distributed optimization scheme is developed to reduce the computational complexity of the proposed program, and effective coordination ensures near-optimality of the solutions. The case study results show that the proposed algorithm works in real-time and provides near-optimal solutions with a maximum optimality gap of 5.4%. The proposed algorithm is implemented in Vissim. The results show that coordinated signal timing and speed optimization improved network performance in comparison with cases that either signal timing parameters or average speed of vehicles are optimized. The coordinated approach reduced the travel time, average delay, average number of stops, and average delay at stops by 1.9%, 5.3%, 28.5%, and 5.4%, respectively compared to the case that only signal timing parameters are optimized.

Previous research has shown that proper metering of entry traffic to urban street networks, similar to metering traffic on on-ramps in freeway facilities, reduces traffic congestion, especially in oversaturated flow conditions. Building on the previous research, this paper presents a real-time and scalable methodology for finding near-optimal metering rates dynamically in urban street networks. The problem is formulated into a mixed-integer linear program (MILP) based on the cell transmission model. We propose a distributed optimization scheme that decomposes the network level MILP into several link-level MILPs to reduce the complexity of the problem. We convert the link-level MILPs to linear programs to reduce the computational complexity further. Moreover, we create distributed coordination between the link-level linear programs to push the solutions toward optimality. The distributed optimization and coordination solution algorithm is incorporated into a rolling horizon technique to account for the time-varying demand and capacity and to reduce the computational complexity further. We applied the proposed solution technique to a number of case studies and observed that it was scalable and real time and found solutions that were at most 2.2% different from the optimal solution of the problem. Like the previous studies, we found significant improvements in network operations as a result of traffic metering.

This study formulates a program for simultaneous traffic signal optimization and system optimal traffic assignment for urban transportation networks with added degree of realism. The formulation presents a new objective function, i.e., weighted trip maximization, and explicit constraints that are specifically designed to address oversaturated conditions. This formulation improves system-wise performance while locally prevents queue spillovers, de-facto reds, and gridlocks. A meta-heuristic algorithm is developed that incorporates microscopic traffic flow models and system optimal traffic assignment in genetic algorithms. This solution technique efficiently optimizes signal timing parameters, at the same time solves system optimal traffic assignment, and accounts for oversaturated conditions and different driver's behaviors. This study also proposes a framework to calculate an upper bound on the value of the objective function by solving the problem while several constraints (i.e., network loading and traffic assignment) are relaxed. An empirical case study for a portion of downtown Springfield, Illinois has been conducted under four demand patterns. Findings indicate that our solution approach can solve the problem effectively. Several managerial insights have also been drawn.