Using the event-based data, a set of arterial performance measures, especially intersection queue length and arterial travel time, can be estimated. Queue length is unarguably the most important performance measure at a signalized intersection, since other performance measures such as average delay and level of services can be easily derived from queue length information. A major shortcoming of traditional input-output models for estimating queue length has been their inability to determine queue length under saturated conditions—i.e., when the queue of cars waiting to pass through an intersection extends beyond the upstream vehicle detector. Under saturated conditions, data on incoming traffic flow are no longer available and the input side of the input-output model breaks down. The SMART-Signal developers overcame this limitation by developing a new algorithmic approach to queue length estimation based on traffic shockwave theory.

    This approach first utilizes the high-resolution data collected by the SMART-Signal to identify the changes of traffic states, and then applies Lighthill-Whitham-Richards (LWR) shockwave theory to construct shockwave profiles. The figure below demonstrates the shockwave profile within a cycle. This profile consists of four shockwaves and the shockwave motion will repeat from cycle to cycle. Using the high-resolution data, the changes of traffic states, i.e. the “break points” (A, B, and C), can be identified. The time-dependent queue length including the maximum and minimum queue (if existing) can then be easily derived from the constructed shockwave profile.

    A Minneapolis-based Transportation Consulting firm, Alliant Engineering, Inc., conducted an independent evaluation of the queue length estimation algorithm. To observe the queue length, Alliant sent observers to the field (the Rhode Island intersection on TH55) during the morning peaks (7:00am-9:00am) on three randomly selected days in 2008: Jul. 23rd, Occ. 29th, and Dec. 10th. These observers manually counted the vehicles as they entered the queue (they were instructed to count a stopped vehicle as one that was traveling at less than 5 mph), and recorded the time when queue was maximum. The following figure compares the measured and estimated times and lengths of maximum queues. As indicated in the figure, the proposed model tracks the trend of cycle-based queue dynamics successfully.