Enlarging Stability Region of Urban Networks with Imminent Supply Prediction

TL;DR

The paper addresses how knowledge about imminent saturation flow rate (I-SFR) impacts the stability region of urban traffic networks under BackPressure (BP) control. It develops a formal stability-region framework $\mathcal{D}$, introducing levels of SFR knowledge: M-SFR ($\mathcal{D}_0$), full I-SFR ($\mathcal{D}_1$), and partial I-SFR with a prediction parameter $\theta$ yielding $\mathcal{D}_\theta$, and proves that better I-SFR knowledge enlarges the precision upper frontier of the region. It then shows that BP with predicted I-SFR can stabilize networks within the enlarged region, provided the I-SFR predictions are unbiased, and corroborates the theory with calibrated simulations on a real corridor. Simulation results indicate that higher I-SFR prediction accuracy significantly increases the reserve demand margin $\epsilon_{max}$ and reduces average delays, demonstrating practical benefits for real-time traffic operations. Overall, the work highlights the value of incorporating accurate real-time supply predictions into decentralized BP controls to improve stability and mobility in urban networks.

Abstract

Stability region is a key index to characterize a dynamic processing system's ability to handle incoming demands. It is a multidimensional space when the system has multiple OD pairs where their service rates interact. Urban traffic network is such a system. Traffic congestion appears when its demand approaches or exceeds the upper frontier of its stability region. In this decade, with the rapid development of traffic sense technology, real-time traffic operations, e.g., BackPressure (BP) control, have gained lots of research attention. Urban network's mobility could be further improved with these timely demand-responding strategies. However, most studies on real-time controls continue with traditional supply assumptions and ignore an important fact -- imminent saturation flow rate (I-SFR), i.e., the system's real-time service rate under green, is neither fixed nor given, but hard to be precisely known. It is unknown how the knowledge level of I-SFR would influence the stability region. This paper proves that knowing more accurate I-SFR can enlarge the upper frontier of the network's stability region. Furthermore, BP policy with predicted I-SFR can stabilize the network within the enlarged stability region and relieve the congestion level of the traffic network. Therefore, improving the I-SFR's prediction accuracy is meaningful for traffic operations.

Figures (21)

• Figure 1: Two types of "supply ability" for the northbound automobiles in real time
• Figure 2: Movement $m$'s upstream and downstream movements
• Figure 3: An example of a four-legged intersection and its allowable phase set
• Figure 4: Stability regions, $\mathcal{D}_0$'s hull: orange, $\mathcal{D}_1$'s hull: green.
• Figure 5: Change from $\bm{c}$ to $\bm{c}^{\mathrm{new}}$ in Example 2.

Theorems & Definitions (20)

• Definition 1: Rate stability
• Proposition 1
• Definition 2: Stability Region
• Proposition 2
• Definition 3: dominating point
• Definition 4: Precise Upper Frontier
• Example 1
• Lemma 1
• Example 2
• Example 3