Steady-state models and multiple equilibria in transportation: theory and evidence

Pandey, Ayush

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https://hdl.handle.net/2142/130171 Copy

Description

Title

Steady-state models and multiple equilibria in transportation: theory and evidence

Author(s)

Pandey, Ayush

Issue Date

2025-07-15

Director of Research (if dissertation) or Advisor (if thesis)

Lehe, Lewis J.

Doctoral Committee Chair(s)

Lehe, Lewis J.

Committee Member(s)

• Ouyang, Yanfeng
• Dall’Erba, Sandy
• Gayah, Vikash V.

Department of Study

Civil & Environmental Eng

Discipline

Civil Engineering

Degree Granting Institution

University of Illinois Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• Transportation
• transportation economics
• multiple equilibria
• stability analysis
• ride-hailing
• ride-pooling
• hyper-congestion
• scale economies
• economies of scale
• transit

Abstract

Predicting the effects of major transportation system changes presents a unique challenge. This challenge arises from the dual nature of all transportation systems: they comprise both an engineering-based aspect (focusing on network design, scheduling, facility location, and optimization) and a human-centric aspect (involving countless individuals making diverse, self-interested travel decisions). These aspects continuously interact: engineering decisions shape people's choices, while those collective choices redefine what constitutes optimal design. Effective policy interventions therefore require a thorough understanding of both dimensions and their dynamic interplay. This dissertation studies stylized, steady-state models with simplified representations of the human (demand side) and engineering (supply side) aspects of transportation systems. Even these simplified models can exhibit interesting behavior, such as circular causation, and can admit multiple equilibria. In a system with multiple equilibria, different equilibria have different comparative statics, i.e., they respond differently to a policy change. A key shortcoming of steady-state models is that they give us no information about how the system behaves when it is not in equilibrium. What happens if a random shock moves the system out of equilibrium? Will the system return to the same equilibrium, or will it transition to a different one? Which equilibria are actually stable and can actually persist? These questions of stability are particularly relevant for transportation systems, as they are subject to frequent random perturbations. The first part of this dissertation studies the local stability of traffic equilibria in an isotropic urban zone when density, speed, and demand evolve gradually and simultaneously. Drawing parallels between traffic systems and market economics, I propose a system of ordinary differential equations that describes the evolution of density, speed, and demand over time. Possible equilibria are classified into three types, by whether traffic is hypercongested and by the relative slopes of ``supply'' and ``demand'' curves. The analysis shows that some hypercongested equilibria may be stable when demand adjusts quickly enough to congestion, while hypercongested equilibria with counterintuitive comparative statics are never stable. The formal analysis is supported by a discrete event simulation with a dynamic Poisson arrival process that validates the theoretical results. Next, I study circular causation: a phenomenon wherein a sequence of causes and effects leads back to the initial cause. I introduce a novel mechanism of circular causation called Congestive Mode-Switching (CMS), which arises when increasing congestion penalizes high-occupancy modes (such as transit) more than driving. As congestion rises, some transit riders switch to driving, which further increases congestion, reinforcing the cycle. I develop a steady-state model of a bus route in mixed traffic and show that CMS can give rise to multiple stable equilibria with varying levels of congestion and transit ridership. When fleet size is fixed, CMS is the only mode of circular causation. When fleet size increases with ridership, economies of scale emerge as a second feedback mechanism. The comparative statics of a road improvement reveal that first-order effects can be either amplified or dampened, depending on the relative slopes of the ``supply'' and ``demand'' curves. Finally, I empirically validate the presence of scale economies in ride-pooling using data from New York City. Ride-pooling was already in decline prior to COVID-19, with the share of matched trips falling from 25\% in February 2019 to 10\% in February 2020, due in part to reduced subsidies from Transportation Network Companies (TNCs). After pandemic-related suspensions, ride-pooling failed to rebound, with only 1\% of all trips (solo and pooled) being matched in October 2023. The match rate (the ratio of matched to requested trips) also declined from 60\% pre-COVID to 30\% post-COVID. I hypothesize that this persistent decline can be explained by the fact that ride-pooling gets more efficient as more passengers request pooled rides, i.e, it exhibits scale economies. Statistically estimating scale economies in ride-pooling is challenging because both the quality of matching and the demand for ride-pooling are endogenous: as more passengers request pooled rides, it becomes more efficient, and as pooled rides become more efficient, more passengers request them. I use instrumental variables analysis with two sources of exogenous variation---precipitation patterns and stadium events---to provide empirical evidence that ride-pooling exhibits scale economies. Scale economies act as a mechanism of circular causation and can admit multiple stable equilibria; the lockdowns may have shifted the system from a high-matching equilibrium to a new, lower-demand and lower-matching equilibrium.

Graduation Semester

2025-08

Type of Resource

Thesis

Handle URL

https://hdl.handle.net/2142/130171

Copyright and License Information

Copyright 2025 Ayush Pandey

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