Using Input-Output Diagram To Determine Spatial and Temporal Extents of a Queue Upstream of a Bottleneck

Abstract

A simple approach is described for modifying an input-output (or queue-ing) diagram to measure the time and distance spent by vehicles in a queue in a much simpler and self-serving manner than a time-space diagram. The graphic technique requires construction of a curve depicting the cumulative number of vehicles to have reached the back of the queue as a function of time, but, as indicated here, the technique can be easily automated with a spreadsheet. The technique is applied to the simple case of a constant departure rate from a bottleneck and to the slightly more general case of a bottleneck capacity that changes once, which is demonstrated to be applicable to the study of an undersaturated traffic signal. In the course of describing the usefulness of this technique for estimating several measures, including the maximum length of a physical queue and the time when this maximum occurs, the difference between “delay” at a bottleneck and the “time spent in queue,” which appears to have been confused in some of the literature, is clarified.