Potential detrimental effects of real-time route recommendations in traffic networks

TL;DR

This paper tackles how real-time route recommendations shape traffic performance in a two-route network by embedding a dynamical network-flow model with a fraction $α$ of app-informed drivers and a supply–demand mechanism on each link. It employs a logit-based routing rule and analyzes both high and low user compliance, proving global stability and elucidating the link between app penetration, equilibrium behavior, and efficiency losses. The key contributions are the explicit demonstration of partial demand transfer arising from routing decisions, a Wardrop-equilibrium-based characterization of the high-compliance regime, and a convexity-driven analysis of PoA across penetration levels, with validation through macroscopic and microscopic simulations. The results show that more information can paradoxically worsen network performance under certain conditions, providing insights for the design and management of real-time routing recommendations in practice.

Abstract

Navigation apps have become pervasive in providing real-time route recommendations to travelers willing to minimize their travel times. However, such technologies introduce new complexities, raising concerns about their overall impact on traffic networks. This paper focuses on evaluating the effect of navigation apps on traffic flows, particularly examining how real-time route recommendations influence network efficiency and congestion. Using a dynamical network flow model, we study traffic dynamics between an origin-destination pair, where a fraction of drivers follow app recommendations while others rely on fixed route preferences. By incorporating supply-demand mechanisms to account for capacity and volume constraints on routes, we uncover partial demand transfer, i.e., only a portion of the traffic demand is able to traverse the network, while the rest builds up congestion at the origin. We prove that the dynamics converges to a globally stable equilibrium and we provide a detailed analysis of this equilibrium when the choices of the informed drivers follow a logit model, correlating the emergence of partial demand transfer to the penetration rate of navigation apps among users.

Figures (6)

• Figure 1: The origin-destination pair $\mathcal{G}$.
• Figure 2: Simulations for $\Phi=1500$. The three plots respectively show the demand directed toward Route $1$ (left), average travel time $T$ (middle) and route travel times (right) at equilibrium, as functions of penetration rate $\alpha$. The diamond-marked lines are the logit routing ratios, while the dashed lines correspond to the linearized model. We draw the curves for $1/\eta=10$ in orange, for $1/\eta=100$ in light-blue, and for $1/\eta=500$ in green. The limit Wardrop equilibrium $\mathrm{WE}(\alpha)$ is drawn as solid violet lines. In the left-most plot, the area highlighted in red identifies the cases in which the demand toward Route $1$ is unsatisfied. In the right-most plot, the increasing travel time refers to Route $1$, the decreasing one to Route $2$.
• Figure 3: Simulations for $\Phi=2100$. The three plots respectively show the demand directed toward Route $1$ (left), average travel time $T$ (middle) and route travel times (right) at equilibrium, as functions of the penetration rate $\alpha$. The diamond-marked lines are the logit routing ratios, while the dashed lines correspond to the linearized model. We draw the curves for $1/\eta=10$ in orange, for $1/\eta=100$ in light-blue, and for $1/\eta=500$ in green. The limit Wardrop equilibrium $\mathrm{WE}(\alpha)$ is drawn as solid violet lines. In the left-most plot, the area highlighted in red identifies the cases in which the demand toward Route $1$ is unsatisfied. In the middle plot, the lines are truncated at the value of $\alpha$ at which unsatisfied demand emerges. In the right-most plot, the increasing travel time refers to Route $1$, the decreasing one to Route $2$.
• Figure 4: Network used for the Aimsun simulation.
• Figure 5: First line: time-averaged inflow to the two routes and time-averaged travel times on each route, each expressed as a function of the penetration rate, $\alpha$. Blue lines indicate the slow, high-capacity route, while orange lines represent the fast, small-capacity route. Data is derived from micro-simulations. Second line: time-averaged flow supplied to the two-route subsystem, time-averaged density on the access road/buffer, and total travel time across the two-route subsystem, all shown as functions of the penetration rate, $\alpha.$

Theorems & Definitions (24)

• Definition 1: Monotone ratios
• Lemma 1: Properties of region $P$
• proof
• Remark 1: Traffic interpretation of the properties of region $P$
• Definition 2: Monotone system
• Proposition 1: Monotonicity
• proof
• Theorem 1: Global Asymptotic Stability
• proof
• Remark 2: Beyond piece-wise linear supply and demand functions