A Combinatorial Approach for Nonparametric Short-Term Estimation of Queue Lengths using Probe Vehicles

TL;DR

This paper introduces a nonparametric, combinatorial method for short-term queue length estimation using probe vehicles, which does not rely on assumptions of random arrivals or parameter estimation, and matches the accuracy of traditional parametric methods.

Contribution

It develops a novel algebraic approach based on the Negative Hypergeometric distribution for queue estimation from probe vehicle data without needing prior parameters.

Findings

Nonparametric method matches parametric accuracy in field tests.

Method does not assume random arrivals or require parameter estimation.

Uses simple algebraic expressions based on signal timing.

Abstract

Traffic state estimation plays an important role in facilitating effective traffic management. This study develops a combinatorial approach for nonparametric short-term queue length estimation in terms of cycle-by-cycle partially observed queues from probe vehicles. The method does not assume random arrivals and does not assume any primary parameters or estimation of any parameters but uses simple algebraic expressions that only depend on signal timing. For an approach lane at a traffic intersection, the conditional queue lengths given probe vehicle location, count, time, and analysis interval (e.g., at the end of red signal phase) are represented by a Negative Hypergeometric distribution. The estimators obtained are compared with parametric methods and simple highway capacity manual methods using field test data involving probe vehicles. The analysis indicates that the nonparametric methods presented in this paper match the accuracy of parametric methods used in the field test data for estimating queue lengths.