Optimal traffic control at smart intersections: Automated network fundamental diagram

https://doi.org/10.1016/j.trb.2019.10.001Get rights and content

Highlights

  • We eliminate delay by coordinating the approach of CAV platoons at smart intersections.

  • We formulate the synchronization success probability for a general distribution of error.

  • We maximize the network capacity by optimizing the platoon size and marginal gap length.

  • We present the ANFD as a macro-level analytical tool for modeling the traffic dynamics.

  • We evaluate the accuracy of the analytical model using our simulation results.

Abstract

Recent advances in artificial intelligence and wireless communication technologies have created great potential to reduce congestion in urban networks. In this research, we develop a stochastic analytical model for optimal control of communicant autonomous vehicles (CAVs) at smart intersections. We present the automated network fundamental diagram (ANFD) as a macro-level modeling tool for urban networks with smart intersections. In the proposed cooperative control strategy, we make use of the headway between the CAV platoons in each direction for consecutive passage of the platoons in the crossing direction through non-signalized intersections with no delay. For this to happen, the arrival and departure of platoons in crossing directions need to be synchronized. To improve system robustness (synchronization success probability), we allow a marginal gap between arrival and departure of the consecutive platoons in crossing directions to make up for operational error in the synchronization process. We then develop a stochastic traffic model for the smart intersections. Our results show that the effects of increasing the platoon size and the marginal gap length on the network capacity are not always positive. In fact, the capacity can be maximized by optimizing these cooperative control variables. We analytically solve the traffic optimization problem for the platoon size and marginal gap length and derive a closed-form solution for a normal distribution of the operational error. The performance of the network with smart intersections is presented by a stochastic ANFD, derived analytically and verified numerically using the results of a simulation model. The simulation results show that optimizing the control variables increases the capacity by 138% when the error standard deviation is 0.1 s.

Introduction

Autonomous vehicles are expected to be introduced to the consumer market in the near future. The artificial intelligence and wireless communication technologies embedded in these vehicles make “driving” more convenient and roads safer (Zhang and Ioannou, 2004; Van Arem et al., 2006; Fernandes and Nunes, 2011, 2012; Aria et al., 2016; Shabanpour et al., 2018). Improvement in the traffic condition, however, would be trivial in urban networks without upgrading conventional traffic control systems (Mahmassani, 2016). In this research, we propose a cooperative traffic control strategy for smart intersections to reduce congestion in urban networks.

The concept of self-driving vehicles was introduced in the 1930s. However, only recent advances in computation, communication, and automation technologies have made it feasible to realize the dream of autonomous vehicles. Currently, major car manufacturers, along with high technology companies, are making prototypes to be introduced by 2025 (Shi and Prevedouros, 2016; Kockelman et al., 2017). The radar-based autopilot technology of autonomous vehicles enables real-time monitoring of the environment and automatic independent actions on roads (Bose and Ioannou, 2003; Ni et al., 2010; Zohdy et al., 2015; Aria et al., 2016; Kockelman et al., 2017). In addition to autopilot technology, the capability of communicant autonomous vehicles (CAVs) to exchange information with both predecessors and infrastructure, through vehicle-to-vehicle (V2V) and vehicle-to-infrastructure (V2I) communication technologies, respectively, enables cooperative traffic control in automated highways and networks (Bekiaris-Liberis et al., 2016; Shi and Prevedouros, 2016; Ghiasi et al., 2017; Lioris et al., 2017).

Cooperative traffic control can substantially increase the throughput of automated highways by safely increasing speed and decreasing the headway between the CAVs moving in platoons. (Fernandes and Nunes, 2011, 2012; Lam and Katupitiya, 2013; Roncoli et al., 2014; Ghiasi et al., 2017). Improving highway throughputs, however, increases network inflow as well, which can worsen the traffic condition in urban regions by overloading the network over the peaks, ultimately causing a complete gridlock (hypercongestion phenomenon). Hence, the overall performance of the integrated system of highways and urban networks can be improved by dynamically controlling the speed and size of CAV platoons in highways to keep network inflow optimized over time (Amirgholy et al., 2020). Overall, the limited capacity of urban networks is the main barrier to improving the traffic condition, even in interregional highways. In this research, we aim to improve network capacity by enabling cooperative traffic control at smart urban intersections.

For automated networks, we coordinate CAV platoons to safely pass through each other at non-signalized intersections with no interruption. For this to happen, the inter-platoon headway (the time gap between the passage of the rear bumper of the last vehicle in a platoon and the front bumper of the leader of the next platoon, from a reference point) in each direction needs to be sufficient for the safe passage of the consecutive platoons in the crossing direction. Thus, the effect of increasing the size of the platoons on the capacity of the network is not always positive, as opposed to the case in automated highways.1 In this research, we maximize network capacity by optimizing platoon size (number of vehicles in each platoon) as one of the primary cooperative control variables of the system.

Network capacity largely depends on the precision and speed of sensors, computation processing, vehicle-to-vehicle and vehicle-to-infrastructure communication technology, and the actuation system. Operational error in coordinating the arrival and departure of the platoons at an intersection can cause a failure (interruption) in the synchronization process. For resynchronization, the approaching platoon stops at the intersection upon an early/late arrival and waits for the next upcoming spacing between the successive platoons (spacing between the rear bumper of the last vehicle in a platoon and the front bumper of the leader of the next platoon) in the crossing direction to pass through the intersection. In this case, the inter-platoon headway also needs to be adjusted for the safe passage of the stopped platoon through the intersection. When the synchronization process fails repeatedly, the capacity significantly drops. Hence, we maximize the network capacity by allowing a marginal gap (extra time gap) of an optimal length between the arrival and departure of the consecutive platoons in crossing directions.

In this research, we develop a stochastic analytical model for optimal traffic control at smart intersections. We formulate synchronization failure probability as a function of marginal gap length for a general statistical distribution of the operational error. We then derive the intersection capacity by accounting for the probabilistic impacts of synchronization failure. Our analytical results show that the intersection capacity can be maximized by optimizing the size of platoons and the length of the marginal gap. We analytically solve the optimal control problem for the platoon size and the marginal gap length and derive a closed-form solution for a general (bell-shaped) statistical distribution of the operational error. To show the generality of the analytical derivations, we also reformulate the closed-form solution for a normal distribution of the operation error. The performance of the network with smart intersections is also presented by the automated network fundamental diagram (ANFD). The stochastic ANFD reveals that the performance of the network in the “highly hypercongested” state can be improved by altering the pattern of the synchronized operation from approach-and-pass to stop-and-pass in one of the directions. In the end, we verify the analytical results using a double-ring simulation model. The simulation results show that optimizing the control variables increases the capacity by 138% when the error standard deviation is 0.1 s.

The remainder of the paper is organized as follows: Section 2 develops a stochastic traffic model for the smart intersections. Section 3 formulates the optimal control problem. Section 4 presents the analytical ANFD. In Section 5, we evaluate the analytical model with the results of a simulation model. Lastly, conclusions of the paper are summarized in Section 6.

Section snippets

Cooperative traffic control in automated networks

Cooperative traffic control can substantially improve the performance of urban networks. On the link level, it improves capacity by safely increasing the speed and decreasing the headway between the CAVs moving in platoons. At intersections, the delay can be entirely eliminated by coordinating arrival and departure of platoons in crossing directions, as illustrated in Fig. 1.

In the proposed cooperative control strategy, we make use of the spacing between successive platoons in each direction

Optimal platoon control problem

Besides the physical and technological characteristics of the vehicles, infrastructure, and the control system, the intersection capacity largely depends on adjustments of the control system settings. To achieve the highest performance of the system, we maximize the expected capacity of the intersection by solving the following optimization problem for the platoon size, n, and the marginal gap mean length, G¯:maxn,G¯q=nτS(1+Ps(G¯))+τAPA(G¯)+G¯,where PA(G¯)=1PS(G¯), and τS and τA can be plugged

Automated network fundamental diagram

In this section, we present the automated network fundamental diagram (ANFD) as an analytical tool for modeling the dynamics of traffic in networks with smart intersections. In conventional networks, the macroscopic fundamental diagram (MFD) approximates the interrelationship between traffic variables in large urban regions. Observed traffic data from the city of Yokohama (Geroliminis and Daganzo, 2008) and the results of the traffic simulation of the downtown network of San Francisco (

Simulation and numerical analysis

In this section, we evaluate the analytical model with the results of a simulation model. We also numerically evaluate the effects of adjusting the control system settings on the performance of the automated network. In this simulation, we use the double-ring concept developed by Daganzo et al. (2011). In this example, the average vehicle length is lv, the maximum allowable acceleration rate is av = 16m/s2, and the intersection width is w = 3m. In the absence of automation technology, the

Conclusion

Automation technology is more effective when infrastructure is integrated with traffic. In this research, we propose an optimal traffic control strategy to entirely eliminate the queue at urban intersections by making use of the headway between CAV platoons in each direction for consecutive passage of platoons in the crossing direction through the non-signalized intersection with no delay. However, the operational error in coordinating the arrivals and departures of the consecutive platoons can

Acknowledgments

This work was supported in part by the United States Department of Transportation (USDOT) Center for Transportation, Environment, and Community Health (CTECH), the National Science Foundation (project CMMI-1462289), and the Lloyd's Register Foundation, UK. The authors are grateful to the two anonymous reviewers for their valuable comments.

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