Macroscopic pricing schemes for the utilization of pool ride-hailing vehicles in bus lanes

TL;DR

This paper addresses how to allocate space between vehicle and bus networks to leverage pool ride-hailing in bus lanes, with the goal of reducing total travel delays in a multi-modal urban system. It develops a macroscopic delay model that separates vehicle and bus networks via a space split and an endogenous pooling split, and analyzes both system optimum and Wardrop equilibria, proposing a tolling scheme to reconcile potential inefficiencies when needed. The results show conditions under which bus-lane pooling improves total delays and provide an additive toll formulation to align user choices with the social optimum, illustrated through numerical examples aligned with Macroscopic Fundamental Diagram theory. The work offers a policy-relevant framework for integrating pooling ride-hailing into dedicated-lane networks and informs toll design for maintaining efficiency in multi-modal urban traffic.

Abstract

With the increasing popularity of ride-hailing services, new modes of transportation are having a significant impact on the overall performance of transportation networks. As a result, there is a need to ensure that both the various transportation alternatives and the spatial network resources are used efficiently. In this work, we analyze a network configuration where part of the urban transportation network is devoted to dedicated bus lanes. Apart from buses, we let pool ride-hailing trips use the dedicated bus lanes which, contingent upon the demand for the remaining modes, may result in faster trips for users opting for the pooling alternative. Under an aggregated modelling framework, we characterize the spatial configuration and the multi-modal demand split for which this strategy achieves a system optimum. For these specific scenarios, we compute the equilibrium when ride-hailing users can choose between solo and pool services, and we provide a pricing scheme for mitigating the gap between total user delays of the system optimum and user equilibrium solutions, when needed.

Figures (4)

• Figure 1: Schematic sketch of the problem structure. Users travel by private vehicle, ride-hailing, or buses whose demand rates we denote as $x^{pv}$, $x^{rs}$, and $x^b$ respectively. The network space is partitioned into two parts, with a portion $\alpha \in (0,1)$ assigned to the vehicle network $\mathcal{V}$, and the remaining portion assigned to the bus network $\mathcal{B}$. Private vehicles and solo trip users utilize the vehicle network $\mathcal{V}$ with an average trip time of $t_{\mathcal{V}}$ whereas buses and pool ride-hailing vehicles travel exclusively in the bus network $\mathcal{B}$ with a travel time of $t_{\mathcal{B}}$ and $t_b$ respectively. The demand rates are exogenous but the split between solo and pool ride-hailing trips $\beta$ is endogenous.
• Figure 2: The Macroscopic Fundamental Diagrams (MFDs) in Example \ref{['ex:MFD']}.
• Figure 3: Comparison of PHT and $\beta$ for $x^{pv} = 80000$, $x^{rs} = 35000$, and $x^b = 100000$.
• Figure 4: Tolls for the different values of $\alpha$

Theorems & Definitions (20)

• Theorem 1
• proof
• Remark 1
• Example 1
• Proposition 1
• Proposition 2
• Proposition 3
• Proposition 4
• Proposition 5
• Remark 2