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How Will the Presence of Autonomous Vehicles Affect the Equilibrium State of Traffic Networks?

Negar Mehr, Roberto Horowitz

TL;DR

The paper investigates how introducing autonomous vehicles into traffic networks with mixed autonomy affects equilibrium outcomes under selfish routing. It develops a nonatomic routing game with inelastic demands and Wardrop equilibrium, using BPR-like delay models that incorporate mixed vehicle classes and a capacity function $C_l(\alpha_l)$. The main findings show that equilibrium may be nonunique in mixed autonomy, but social delay is unique under homogeneous capacity asymmetry and nonincreasing with autonomy in single-origin-destination networks; with heterogeneous asymmetry or multiple O/D pairs, autonomy can paradoxically increase total delay, a Braess-like effect. A universal bound $J(\alpha) \le (1-\lambda(\mathcal{E}))^{-1} J^o$ quantifies worst-case delay degradation, highlighting the need for control strategies to steer the system toward beneficial equilibria in the presence of autonomy.

Abstract

It is known that connected and autonomous vehicles are capable of maintaining shorter headways and distances when they form platoons of vehicles. Thus, such technologies can result in increases in the capacities of traffic networks. Consequently, it is envisioned that their deployment will boost the network mobility. In this paper, we verify the validity of this impact under selfish routing behavior of drivers in traffic networks with mixed autonomy, i.e. traffic networks with both regular and autonomous vehicles. We consider a nonatomic routing game on a network with inelastic (fixed) demands for the set of network O/D pairs, and study how replacing a fraction of regular vehicles by autonomous vehicles will affect the mobility of the network. Using the well known US bureau of public roads (BPR) traffic delay models, we show that the resulting Wardrop equilibrium is not necessarily unique even in its weak sense for networks with mixed autonomy. We state the conditions under which the total network delay is guaranteed not to increase as a result of autonomy increase. However, we show that when these conditions do not hold, counter intuitive behaviors may occur: the total delay can grow by increasing the network autonomy. In particular, we prove that for networks with a single O/D pair, if the road degrees of asymmetry are homogeneous, the total delay is 1) unique, and 2) a nonincreasing continuous function of network autonomy fraction. We show that for heterogeneous degrees of asymmetry, the total delay is not unique, and it can further grow with autonomy increase. We demonstrate that similar behaviors may be observed in networks with multiple O/D pairs. We further bound such performance degradations due to the introduction of autonomy in homogeneous networks.

How Will the Presence of Autonomous Vehicles Affect the Equilibrium State of Traffic Networks?

TL;DR

The paper investigates how introducing autonomous vehicles into traffic networks with mixed autonomy affects equilibrium outcomes under selfish routing. It develops a nonatomic routing game with inelastic demands and Wardrop equilibrium, using BPR-like delay models that incorporate mixed vehicle classes and a capacity function . The main findings show that equilibrium may be nonunique in mixed autonomy, but social delay is unique under homogeneous capacity asymmetry and nonincreasing with autonomy in single-origin-destination networks; with heterogeneous asymmetry or multiple O/D pairs, autonomy can paradoxically increase total delay, a Braess-like effect. A universal bound quantifies worst-case delay degradation, highlighting the need for control strategies to steer the system toward beneficial equilibria in the presence of autonomy.

Abstract

It is known that connected and autonomous vehicles are capable of maintaining shorter headways and distances when they form platoons of vehicles. Thus, such technologies can result in increases in the capacities of traffic networks. Consequently, it is envisioned that their deployment will boost the network mobility. In this paper, we verify the validity of this impact under selfish routing behavior of drivers in traffic networks with mixed autonomy, i.e. traffic networks with both regular and autonomous vehicles. We consider a nonatomic routing game on a network with inelastic (fixed) demands for the set of network O/D pairs, and study how replacing a fraction of regular vehicles by autonomous vehicles will affect the mobility of the network. Using the well known US bureau of public roads (BPR) traffic delay models, we show that the resulting Wardrop equilibrium is not necessarily unique even in its weak sense for networks with mixed autonomy. We state the conditions under which the total network delay is guaranteed not to increase as a result of autonomy increase. However, we show that when these conditions do not hold, counter intuitive behaviors may occur: the total delay can grow by increasing the network autonomy. In particular, we prove that for networks with a single O/D pair, if the road degrees of asymmetry are homogeneous, the total delay is 1) unique, and 2) a nonincreasing continuous function of network autonomy fraction. We show that for heterogeneous degrees of asymmetry, the total delay is not unique, and it can further grow with autonomy increase. We demonstrate that similar behaviors may be observed in networks with multiple O/D pairs. We further bound such performance degradations due to the introduction of autonomy in homogeneous networks.

Paper Structure

This paper contains 14 sections, 6 theorems, 38 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Nonatomic Selfish Routing
  3. Wardrop Equilibrium
  4. Delay Characterization
  5. Prior Work
  6. Existence of Equilibrium
  7. Uniqueness of Equilibrium
  8. Monotonicity of Social Delay
  9. Uniqueness in the Mixed-Autonomy Setting
  10. Networks with a Single O/D Pair
  11. Homogeneous Degrees of Capacity Asymmetry
  12. Heterogeneous Degrees of Capacity Asymmetry
  13. Networks with Multiple O/D Pairs
  14. Conclusion and Future Work

Key Result

Proposition 1

Given a network $G = (N,L,W)$, if the link delay functions are continuous and monotone in the link flow of each class; then, there exists at least one Wardrop equilibrium.

Figures (6)

  • Figure 1: A network with a single O/D pair and two paths.
  • Figure 2: A network with a single O/D pair and three paths from A to D.
  • Figure 3: Maximum and minimum social delay for Example \ref{['ex:non_unique_delay']}.
  • Figure 4: Maximum and minimum social delays for the Example \ref{['ex:counter_intuitive']}.
  • Figure 5: A network with three O/D pairs.
  • ...and 1 more figures

Theorems & Definitions (18)

  • Definition 1
  • Definition 2
  • Proposition 1
  • Remark 1
  • Proposition 2
  • Remark 2
  • Proposition 3
  • Example 1
  • Theorem 1
  • proof
  • ...and 8 more