Using the Input-Output Diagram to Determine the Spatial and Temporal Extents of a Queue Upstream of a Bottleneck
Tim W. Lawson, David J. Lovell, and Carlos F. Daganzo
Transportation Research Record 1572, Transportation Research Board, pp. 140-147.
ABSTRACT
This paper describes a simple approach for modifying an input-output (or queueing) diagram to measure the time and distance spent by vehicles in a queue in a much
simpler and self-serving manner than using a time-space diagram. The graphical 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 shown herein, the technique can be easily automated with a spreadsheet. Application of
the technique is shown for the simple case of a constant departure rate from a bottleneck, and for the slightly more general case of a bottleneck capacity which
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 at which this maximum occurs, the paper clarifies the difference between
"delay" at a bottleneck and the "time spent in queue," which appear to have been confused in some of the literature.