Throughput and Delay Tradeoff Management for Partially Connected Networks

Report, 2024

Traffic congestion is a major issue in cities worldwide, causing significant economic and environmental impacts. For instance, in the United States, congestion costs commuters over 8 billion hours and $1337 per person annually. In the UK, by 2030, it will cost each driver £1317 per year, totaling £4.4 billion nationwide. In China, urban congestion contributed to 30% of overall fuel consumption in 2020. These problems worsen air pollution and greenhouse gas emissions. Network-level signal control is an effective method to improve road capacity and alleviate congestion.

Current traffic signal control methods are predominantly centralized, facing scalability challenges in large networks. Distributed control strategies, including Max-pressure (MP) signal control, have gained attention. MP signal control relies on queue length information from adjacent links and average turn ratios for real-time signal phase updates. It is analytically proven to ensure network stability when demand is within capacity. However, these enhancements typically depend on accurate average turn ratio estimates, often requiring extensive historical data.

MP signal control's benefits have led to its expansion in various directions, such as addressing waiting delays, reducing phase switching losses, and integrating transit lines. However, these improvements rely on precise queue length information, feasible mainly in fully connected environments. As networks blend connected vehicles (CVs) and regular vehicles (RVs), accurate queue length and turn ratio estimations become challenging. Existing studies have not thoroughly analyzed the impact of estimation errors on network stability, throughput, and delays.

Most studies assume infinite queue capacity, but this is unrealistic. Networks with finite queue capacity cannot achieve stability solely with MP signal control. To address this, capacity-aware algorithms have been proposed but lack analytical proof of network stability. Current studies extending MP signal control have not integrated traffic control to ensure that demand arrival rates fall within the network’s capacity region. According to the macroscopic fundamental diagram (MFD) theory, trip completion rates initially rise with demand until reaching a critical density point, beyond which they decline with further demand increase. This theory suggests that in oversaturated networks, no signal control method can effectively alleviate congestion or improve network throughput. Recent studies have combined MFD-based perimeter control with MP signal control to adjust inflows and outflows between regions, preventing oversaturation and enhancing overall network performance. However, these studies fail to dynamically address evolving congestion and local congestion issues.

To address these limitations, this paper explores network-level admission and signal control, retaining the benefits of MP control such as distributed control, no need for prior knowledge of demand arrival rates, and analytically provable network performance. The contributions of this paper can be summarized as follows: 1) This paper develops algorithms for estimating queue lengths and turn rates using only the speed and turning information provided by connected vehicles; 2) This study develops a distributed, micro-level joint admission and signal control algorithm for networks with finite queue capacity to adaptively adjust demand input rates at entry nodes and update signal phases at intersections in real time; and 3) This paper develops a Lyapunov drift optimization algorithm to analytically prove the [O(1/V), O(V)] tradeoff between throughput and delay for this joint control, and to evaluate performance degradation bounds due to estimation errors in queue lengths and turn ratios, with the control parameter V adjustable based on finite queue capacity.

Extensive simulations in a network with 256 origin-destination pairs under diverse traffic scenarios demonstrate significant improvements in traffic efficiency, with reduced travel delay and up to a 17.54% increase in throughput, particularly in high-demand urban settings. Additionally, the joint control algorithm shows strong robustness in responding to sudden demand and incidents, enabling quick network recovery.