User:Jingchengwu/Queue Length at Metered On-Ramps

The ability to accurately monitor vehicle queue lengths at a metered on-ramp and adjust the metering rate correspondingly could allow control of the on-ramp delay in real time and improve ramp metering performance at the system level. Queues that back up onto adjacent arterial streets from entrance ramps can adversely affect the surface roadway network. Drivers may occasionally divert from freeways to adjacent arterial streets to avoid queues at ramp meters. Local emissions near ramps may increase due to stop-and-go conditions and vehicles idling within a queue.

Introduction
In order to collect on-ramp queue information useful for freeway traffic operations, traffic professionals have been researching two categories of methods, physically directly measuring queues through detection technologies or estimating queues through various models based on detector data.

Queue Detection
Video image detection is one method to directly monitor queues and deliver vehicle queue length. Another approach is to install many detectors at close spacings along the on-ramp, which helps to improve the accuracy of queue length estimation to a certain degree.

Queue Estimation
Queue lengths at a metered on-ramp can be estimated through various models using detector data as inputs.

Queue Estimation
===Original Kalman Filter Algorithm ===
 * $$\textbf{Q}_{n} = \textbf{Q}_{n-1} + T(\textbf{V}_{in} - \textbf{V}_{out}) + K(\textbf{q}_{n-1} - \textbf{Q}_{n-1}) $$

where $${Q}_{n}$$ = predicted number of on-ramp queued vehicles in the next time period (veh), $${Q}_{n-1}$$ = number of on-ramp queued vehicles in the current time period (veh), $$T$$ = time interval for number of queued vehicles calculation (second), $${V}_{in}$$ = flow rate entering the on-ramp (veh/h), $${V}_{out}$$ = flow rate exiting the on-ramp (veh/h), $$K$$ = 0.22 recommended for one detector and 0.5 recommended for all other detector numbers, generally, $$0 <= K <= 1$$, and $${q}_{n-1}$$ = number of on-ramp queued vehicles calculated from detector time occupancy data (veh).


 * $$\textbf{q}_{n-1} = \frac{\textbf{L} \textbf{N}}{\textbf{l} + \textbf{D}} \textbf{O}_{n-1} $$

where $${q}_{n-1}$$ = number of on-ramp queued vehicles calculated from detector time occupancy data (veh), $$L$$ = length of the on-ramp (ft), $$n$$ = number of lanes, $$l$$ = average physical vehicle length (ft), $$D$$ = safety distance between vehicles (ft), and, $${O}_{n-1}$$ = time occupancy collected by loop detectors.

===Kalman Filter Algorithm with Volume Balancing Ratio ===
 * $$\textbf{Q}_{n} = \textbf{Q}_{n-1} + T(\textbf{C}\textbf{V}_{in} - \textbf{V}_{out}) + K(\textbf{q}_{n-1} - \textbf{Q}_{n-1}) $$

where $$C$$ = adjustment factor to account for the miscounting of the detectors.

Conservation Model

 * $$\textbf{Q}_{n} = \textbf{Q}_{n-1} + \textbf{N}_{in} - \textbf{N}_{out} $$

where $${Q}_{n}$$ = predicted number of on-ramp queued vehicles in the next time period (veh), $${Q}_{n-1}$$ = number of on-ramp queued vehicles in the current time period (veh), $${N}_{in}$$ = vehicle counts entering the on-ramp during a data collection time interval like 20 seconds, which can be from queue loop detectors or entrance reporting loop detectors (veh), and, $${N}_{out}$$ = vehicle counts exiting the on-ramp during a data collection time interval like 20 seconds, which can be from passage loop detectors (veh).

Conservation Model with Volume Balancing Ratio

 * $$\textbf{Q}_{n} = \textbf{Q}_{n-1} + \textbf{C}\textbf{N}_{in} - \textbf{N}_{out} $$

where $$C$$ = adjustment factor to account for the miscounting of the detectors.