Researchers from IIT Bombay propose a computationally efficient, network theory-based mathematical framework to test decentralised traffic control systems.

Have you ever wondered how city traffic would look without traffic control? Traffic control systems, such as the traffic lights at intersections, play a crucial role in bringing order to what would otherwise be chaotic streets. The better these systems are at managing vehicle movement, the smoother our drives and the shorter our wait times.

Thanks to ongoing research, these systems are getting smarter. New algorithms, including those based on machine learning as well as improved traditional methods, are being developed to tackle the growing challenge of urban congestion. However, it is important to test and validate the performance of these newer algorithms before deploying them in the real world. Poorly designed or malfunctioning traffic signals could create more problems than having no signals at all, making careful evaluation essential to ensure safer and more efficient traffic flow.

In one such effort, a recent study by Dr. Namrata Gupta and Prof. Gopal R. Patil from the Indian Institute of Technology Bombay (IIT Bombay), in collaboration with Prof. Hai L. Vu from Monash University, Australia, introduces a new framework to evaluate certain traffic control systems. The framework does not rely heavily on expensive simulations and uses fewer computational resources.

Traffic across a city could be controlled centrally, through a single control centre, or a decentralised system could be used, where traffic at each intersection is controlled locally. Centralised systems that make decisions using data from the entire road network can potentially yield shorter travel times and reduced congestion. However, they demand significant resources, and any system-wide failure can bring city traffic to a halt. In contrast, decentralised systems use local cues and feedback, making them cheaper, easier to implement and less likely to cause large-scale disruptions.

Computer simulations of traffic are often employed to test traffic control systems. However, detailed computer simulations of traffic are often costly and time-consuming. Even if one employs very resource-intensive simulations, it may not be possible to anticipate and model all possible real-world scenarios. The approach developed by IIT Bombay researchers tries to address this challenge by using mathematical models from network theory.

This novel approach introduces two metrics to evaluate traffic control policies. Both metrics can be computed by simulating the policy on what are known as two-bin network systems. The simulation requires much less computing power and time. The first metric measures how effectively a policy can avoid gridlock, where traffic in any direction comes to a halt. It indicates the ability of a policy to evenly spread vehicles across different directions and ensure smooth flow. The second metric captures how quickly a policy can clear traffic jams. “ Our proposed metrics can be applied to any traffic control policy, including those based on machine learning, provided the policy can be adapted to the structure of the two-bin model ,” says Prof. Patil.

Traffic policies, whether traditional algorithm-based or AI-driven, that aim to balance vehicle volumes and flows between two main directions can be modelled using the two-bin approach. The approach treats each direction as a separate ‘bin’ and a change in direction of vehicles as a flow from one bin to another.

In the current study, the researchers consider road networks that are structured as rectangular grids, similar to those seen in planned cities like Chandigarh. The streets are grouped in two different bins: those running along the north-south direction (N-S) in one bin and those running along the east-west direction (E-W) in another. The change of direction of vehicles from N-S to E-W is represented as a flow from the N-S bin to the E-W bin and vice versa. This two-bin approach helps translate the road network and traffic flow into mathematical equations, namely ordinary differential equations. By solving these, researchers determine the best-possible flow conditions, and also obtain what is known as the macroscopic fundamental diagram (MFD) of traffic flow. The MFD describes relationships between average vehicle speed, average density, and average traffic flow at the network level, helping us understand traffic behaviour and congestion under different vehicular loads.

The theoretical results from this analysis set a benchmark, the best results possible for traffic flow within a two-bin system. Any traffic policy, then, can be simulated within the two-bin model and compared to this theoretical maximum. Policies that come closer to this ideal are considered more effective. The proposed metrics measure how close a given policy is to this maximum.

A major advantage of this framework is its efficiency. Network performance can be calculated based on just a few simple equations, without laboriously modelling every single car and intersection. “ The two-bin model is a macroscopic abstraction, governed by two simple ordinary differential equations. We can obtain network optimal performance theoretically. Further, this model requires much less computation, enabling rapid evaluation of multiple traffic scenarios, ” explains Dr. Gupta. The researchers also validated their method by simulating traffic policies using the commonly used traffic simulator PTV VISSIM.

Even though the method appears robust, it cannot simulate every possible traffic state. “ While it is impossible to simulate all possible traffic states, we incorporate such theoretical results to design diverse scenarios that include variations in congestion levels, demand patterns, and network configurations, which are chosen to reflect diverse operating conditions, ” clarifies Prof. Patil.

Another limitation of the framework is that it cannot be applied effectively to complex road networks. More complex abstractions like four-bin systems can potentially model complex road networks. In another work , the same team has extended this framework to three-bin models. Incorporating pedestrians is another challenge. “Extending these bin-based models to capture pedestrians is not straightforward. Pedestrian movement is governed by different dynamics and constraints compared to vehicular flow,” explains Dr. Gupta.

Looking forward, the researchers hope to link their new performance metrics to familiar quantities such as travel time and waiting time, making the findings even more practical. They are also exploring whether the theoretical insights from the two-bin model can encourage new machine learning approaches for traffic management, including signal controllers based on physics-inspired reinforcement learning.

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