Stability-based analysis of autonomous intersection management with pedestrians
Introduction
Intersections are important components of urban traffic networks. They connect vehicle and pedestrian flows between network links and are also the main bottlenecks that contribute to most of the delays for vehicles and pedestrians. Consequently, intersection control plays an important role in improving traffic efficiency, enhancing the road safety level, and mitigating traffic congestion. Current intersection control is based on traffic signals. Vehicle movements in different directions are categorized into signal groups and vehicles whose trajectories are not conflicting or partially conflicting with other vehicles are allowed to move in the same time interval, which is called a phase. Fixed signal controls use different signal timing plans for multiple periods of a day based on historical traffic data. Typically, intersection control gives a phase that includes vehicle movements with larger volumes longer activation time. In contrast, adaptive signal controls use traffic data collected by detectors at the upstream or downstream of an intersection to flexibly adjust the duration of predefined phases aiming to reduce vehicle delay at the intersection. There are some widely used adaptive signal control system applied to a city-wide area, such as SCOOT (Bing and Carter, 1995), SCATS (Sims and Dobinson, 1980), RHODES (Mirchandani and Head, 2001), OPAC (Gartner, 1983), and etc.
With the advances in vehicle-to-infrastructure (V2I) and vehicle-to-vehicle (V2V) communications, it is easier to collect real-time traffic data for adjusting the signal or calculating the optimal control. There are studies that optimize phase-based intersection controls (Priemer and Friedrich, 2009, He et al., 2012, Goodall et al., 2013, Feng et al., 2015). The phase order or the phase time of the intersection signal is optimized with data collected by V2I and V2V devices and only vehicles that are not conflicting with each other are allowed to move in a specific phase. As autonomous vehicle technology develops, vehicles can be precisely controlled by computers. Some studies designed algorithms for vehicles to adjust their driving speeds or accelerations based on existing traffic signals so that vehicles can pass the intersection smoothly and avoid stopping for the red light (Kamalanathsharma and Rakha, 2013, Ma et al., 2017). Some other studies proposed signal-free intersection control algorithms to coordinate non-conflicting trajectories at the intersection. Once vehicle trajectories are determined, vehicles can follow these assigned trajectories and avoid collisions without the safety buffers of traffic signal phases. Autonomous intersection management (AIM), which was proposed by Dresner and Stone (2004), is an intersection control mechanism in which all vehicles that approach an intersection send their information to the controller at the intersection and follow its instructions.
Most AIM models do not consider pedestrian access for intersections. In the future, for a traffic network with autonomous vehicles, pedestrians will still require intersection access due to the costs of constructing separate right-of-way for pedestrians (e.g. tunnels or bridges). However, having pedestrians at an intersection controlled by AIM introduces a lot of unpredictable risks to the intersection. An AIM-controlled intersection calculates the trajectories of approaching vehicles based on their position and speed information and does not consider pedestrians so the calculated vehicle trajectories only service the condition when there is no pedestrian crossing the street. To minimize the vehicle delay at the intersection, AIM models often leave small gaps between vehicles. It is hard for pedestrians to find a safe gap for them to cross the street under the control of AIM as they typically cross with traffic signal phases. The detectors on autonomous vehicles enable vehicles to react to jaywalking pedestrians, but the resulting unplanned stop causes the temporary breakdown of the intersection traffic. Therefore, AIM needs significant modification to include pedestrian movements.
In traditional phase-based intersection control, crosswalks are activated with signal phases which significantly reduce the number of conflict points between the trajectories of pedestrians and vehicles. However, in AIM, phases that align with crosswalk activation do not exist. This study incorporates pedestrians into intersection control by adding crosswalk activation to a reservation-based algorithm. When one or multiple crosswalks are activated, vehicles whose trajectories do not intersect with the activated crosswalks are allowed to move.
Activating crosswalks in AIM reduces the throughput of vehicles at the intersection because it blocks vehicles with conflicting trajectories. However, using the conventional objective of AIM, which is to maximize the total throughput or reduce the total delay of vehicles, the efficiency of pedestrians will not be carefully considered. It is also hard to determine the weights assigned to vehicles and pedestrians respectively as there is a subtle trade-off between these two components. Therefore, we apply max-pressure control to the intersection control, which is able to maximize the network throughput of the total combined vehicle and pedestrian flow.
Max-pressure control was originally used as a scheduling policy in communication and power networks (Tassiulas, 1992). Max-pressure control defines weights and pressures of turning movements and uses a mathematical program to get the optimal control strategy which maximizes the total weight of the intersection. Most intersection control algorithms do not have network-level properties that max-pressure control algorithms have, including the stability of the total queue length. Besides, it is also a distributed algorithm with the controller at each intersection in a network calculating the control strategy by itself. The max-pressure control algorithm needs input data, normally the queue length, to calculate the weight of each turning movement, but pedestrians are not connected to the intersection controller. Therefore, a model is needed to estimate the queue length of pedestrians at the intersection.
The contributions of this study are: (1) proposing a max-pressure policy based on the conflict region model of AIM to address vehicles and the pedestrians at an intersection (2) designing a queue length estimation method for pedestrians. (3) proving the proposed algorithm can achieve optimal throughput of the network. (4) integrating the max-pressure control with an existing AIM algorithm. The new algorithm can calculate the optimal vehicle trajectory at the intersection under the max-pressure control. (5) testing the effects of the pedestrian demand on the efficiency of vehicles using the conflict-point model of AIM.
This paper is organized as follows: Section 2 summarizes the relevant studies about AIM and max-pressure control. Section 3 introduces the network model used to represent the flow propagation on the network. Section 3.3 proposes the modified max-pressure algorithm that integrates the pedestrian flow on the network. Section 3.4 formulates the stability region of the demand and proves the stability properties of the control algorithm. Section 4 formulates a mixed-integer program that integrates an existing trajectory planning algorithm with the max-pressure control. Section 5 presents the simulation experiment and simulation results.
Section snippets
Literature review
This section introduces the existing literature related to AIM and max-pressure control.
Network model
Consider a traffic network consisting of a road network for vehicles and a sidewalk network for pedestrians . These networks interact at intersections where crosswalks and vehicles can conflict. For both networks, denotes the node set and denotes the link set. The link set can be classified into three subsets , and representing the entry, interval, and exiting links respectively. The entry link set includes links that bring
Intersection control: AIM-ped
In Section 3.3, the max-pressure algorithm is proposed based on the conflict region model of AIM (Levin and Boyles, 2015) and the proposed stability properties are also based on this model. When applied to microscopic simulation, the conflict region model of AIM has some limitations. This model only considers the capacity constraint at each conflict region but does not consider the order of arriving vehicles at the intersection. Therefore, the vehicle behavior in this model may violate the
Numerical experiments
To test the effects of the pedestrian demand on the efficiency of the vehicle network, simulations with different pedestrian and vehicle demands are conducted. A multi-layer network is used in the simulation, as shown in Fig. 5.
Conclusion
This study proposes an autonomous intersection management algorithm based on max-pressure control considering both vehicles and pedestrians. This study defines the stability region of the traffic demand and proves that this algorithm can produce throughput-optimal intersection control at network level. To apply this algorithm in simulation, this study combines an existing trajectory optimizing algorithm with max-pressure control and formulates a mixed-integer program model to calculate the
CRediT authorship contribution statement
Rongsheng Chen: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Writing - original draft, Writing - review & editing, Visualization. Jeffrey Hu: Methodology, Software, Investigation, Writing - original draft, Visualization. Michael W. Levin: Conceptualization, Methodology, Software, Resources, Writing - review & editing, Supervision, Project administration, Funding acquisition. David Rey: Conceptualization, Writing - review & editing.
Acknowledgements
The authors gratefully acknowledge the support of the National Science Foundation, Award No. 1935514.
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