Parameter Estimation in Optimal Tolling for Traffic Networks Under the Markovian Traffic Equilibrium

TL;DR

This paper introduces an online learning algorithm for optimal tolling in traffic networks that estimates latency and entropy parameters simultaneously, aiming to minimize congestion without requiring prior parameter knowledge.

Contribution

It proposes a novel arc-based traffic assignment model with an online algorithm that adaptively learns parameters and sets tolls, backed by theoretical regret bounds and simulation validation.

Findings

Regret bounded by $O(\

Algorithm effectively estimates parameters in real-time.

Numerical results validate theoretical guarantees.

Abstract

Tolling, or congestion pricing, has emerged as an effective tool for preventing gridlock in traffic systems. However, tolls are currently mostly designed on route-based traffic assignment models (TAM), which may be unrealistic and computationally expensive. Existing approaches also impractically assume that the central tolling authority can access latency function parameters that characterize the time required to traverse each network arc (edge), as well as the entropy parameter $\beta$ that characterizes commuters' stochastic arc-selection decisions on the network. To address these issues, this work formulates an online learning algorithm that simultaneously refines estimates of linear arc latency functions and entropy parameters in an arc-based TAM, while implementing tolls on each arc to induce equilibrium flows that minimize overall congestion on the network. We prove that our algorithm incurs regret upper bounded by $O(\sqrt{T} \ln(T) |\arcsMod| \max\{|\nodesMod| \ln(|\arcsMod|/|\nodesMod|), B \})$, where $T$ denotes the total iteration count, $|\arcsMod|$ and $|\nodesMod|$ denote the total number of arcs and nodes in the network, respectively, and $B$ describes the number of arcs required to construct an estimate of $\beta$ (usually $\ll |I|$). Finally, we present numerical results on simulated traffic networks that validate our theoretical contributions.