Rakha, Kang, and Dion 1 Estimating Vehicle Stops at Under-Saturated and Over-Saturated Fixed-Time Signalized Intersections by Hesham Rakha, Youn-Soo Kang, and François Dion Virginia Tech Transportation Institute 3500 Transportation Research Plaza, Blacksburg, VA 24061 ABSTRACT This paper first reviews state-of-practice models for estimating vehicle stops at signalized intersections and then introduces two approaches for computing vehicle stops at under-saturated and over-saturated signalized intersections. The first approach that is introduced is a microscopic model that computes instantaneous partial and full stops for under-saturated and over-saturated conditions using second-by-second speed measurements. This model, in particular, has been introduced in the INTEGRATION traffic simulation software. The second model that is introduced is an analytical formulation derived from the proposed microscopic model that computes the number of vehicle stops for over-saturated approaches over a given analysis period. Finally, comparisons of the stop estimates produced by the two proposed models to estimates obtained from current state-of-practice analytical models demonstrate both their validity in their respective domains of application. INTRODUCTION The measurement of the level of performance of signalized intersections has been an area of interest for traffic engineers since the birth of the profession. For many years, this interest has primarily focused solely on vehicle delay. Besides delay, other performance measures such as the number of vehicle stops and the spatial extent of queues on intersection approaches have also been found to play an important role in the evaluation of signalized intersections. These measures not only relate to the level of service that is provided to the drivers, but also to the level of fuel consumption and air pollution that is generated by the vehicles traversing the signalized intersections. In particular, while vehicle stop estimates play an important role in determining vehicle fuel consumption and emissions on intersection approaches, queue length estimates are important not only for the design of pocket lanes, but also to ensure that traffic signal operations do not result in vehicle queues that spillback onto upstream intersections. Background Numerous researchers have dealt with the problem of estimating vehicle stops at signalized intersections. An important early contribution is attributed to Webster (1), who generated stop and delay relationships by simulating uniform traffic flows on a single-lane approach to an isolated intersection. These relationships have been fundamental to traffic signal setting procedures since their development. Later, Webster and Cobbe (2) developed a formula for estimating vehicle stops at under-saturated intersections assuming random vehicle arrivals. In another effort, Catling (3) adapted equations of classical queuing theory to over-saturated traffic conditions and developed a comprehensive queue length estimation procedure that captured the time-dependent nature of queues and that can be applied to both under-saturated and over-saturated conditions. In a last effort, Cronje (4-7) developed stop and delay equations by treating traffic flow through a fixed-time signal as a Markov process. The approach assumed that the number of queued vehicles at the beginning of a cycle could be expressed by a geometric distribution. Although a number of stop estimation models have been developed, the majority of these models have not been designed to account for the partial stops that vehicles may incur on intersection approaches. Furthermore, the models that currently account for partial stops do not estimate them for over-saturated conditions. In many instances, it has been observed that vehicles approaching an over-saturated intersection incur a series of partial