Method for assessing shock wave patterns at a traffic intersection
A method and apparatus for level of service assessment at signalized intersections is disclosed. In an exemplary embodiment, a method for estimating an average delay per vehicle at a signalized intersection with a traffic signal, including sampling vehicle arrival rates at the signalized intersection, sampling vehicle departure rates at the signalized intersection, analyzing generated shock waves at the traffic signal, wherein the traffic signal shock wave is a change in vehicle density due to changes in the traffic signal, and estimating the average delay per vehicle based on the vehicle arrival rates, the vehicle departure rates, and the traffic shock waves at the signalized intersection.
1 . A method for assessing a signalized intersection for shock wave patterns, comprising:
sampling, by a controller, vehicle arrival rates at the signalized intersection, wherein the signalized intersection comprises at least one traffic signal positioned at the signalized intersection, and the signalized intersection includes at least two roadways and at least 3 directions of traffic;
sampling, by the controller, vehicle departure rates at the signalized intersection;
analyzing, by the controller, traffic shock waves that occur at the signalized intersection, wherein the traffic shock waves are a change in vehicle density due to changes in the traffic signal selected from the group consisting of a backward queue forming shock wave and a backward recovery shock wave;
estimating, by the controller, an average delay per vehicle based on the vehicle arrival rates, the vehicle departure rates, and the traffic shock waves at the signalized intersection;
wherein the estimating comprises determining the average delay per vehicle in accordance with
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wherein,
C is traffic signal cycle length,
R is Red light time interval,
ω AB is shock wave speed between flow states, arrival state A and jam state B,
ω BC is the shock wave speed between flow states, jam state B and saturation state C,
Qa is arrival rate of vehicles,
k jam is traffic density at flow state B,
d is safe vehicle deceleration rate,
K a is traffic density of arriving vehicles;
determining, by the controller, a shock wave speed between an arrival flow state and a stopped flow state;
determining, by the controller, a shock wave speed between a stopped flow state and a departure flow state; and
determining, by the controller, a stop delay of the stopped flow state.
2 . The method of claim 1 , wherein
the stop delay of the stopped flow state is based on a red traffic signal time interval and a queue length.
3 . The method of claim 1 , wherein the sampling, analyzing and estimating steps are performed by the controller of a single level of service logging device.
4 . The method of claim 1 , further comprising:
performing, by the controller, a dynamic sampling method in which a sampling error is calculated after each reading, wherein the sampling error is dependent on a number of observations, variance of the observations, and a degree of confidence; and
after reaching a sampling stopping criterion based on the sampling error of the dynamic sampling method, performing, by the controller, the estimating the average delay per vehicle.
5 . The method of claim 4 , wherein the sampling error is less than an allowable error in arrival and departure headway observations, wherein the allowable error is a function of a human-machine error for a level of service logging device.
6 . A signalized intersection level of service data logging device, comprising:
wherein the signalized intersection level of service data logging device is positioned at a signalized intersection comprising at least one traffic signal, and at least two roadways and at least three directions of traffic;
a microcontroller;
a memory;
a display device;
a start button; and
at least one data entry button,
the microcontroller configured to
receive an input from the start button to start a level of service measurement and open a data storage file in the memory,
receive an input from the at least one data entry button when a first vehicle stops after the traffic signal turns red,
receive an input from the at least one data entry button when a second vehicle arrives and record an arrival headway as a difference between an arrival time of the second vehicle and an arrival time of the first vehicle,
continuously update a mean and a standard deviation of the arrival headway,
calculate a standard error of the arrival headway mean,
continue to receive the input for additional vehicles' arrival headways and update the mean and standard deviation of the arrival headway until a number of vehicles stopped at the signalized intersection reaches a predetermined queue number or the traffic signal turns green,
when the traffic signal turns green the stopped vehicles in the queue start moving, receive an input when the first vehicle discharging from the queue passes the traffic signal,
receive an input when a following vehicle passes the traffic signal and record the discharge headway during the departure as a difference between a passing time of the discharging vehicle and a passing time of a previous discharging vehicle during the departure,
update a mean and a standard deviation of the discharge headway during the departure,
calculate a standard error of the discharge headway mean during the departure,
continue to receive the input for additional vehicles and update the mean and standard deviation of the discharge headway during the departure until a data collection stopping criteria is reached,
when the data collection stopping criteria is reached, determine an average delay per vehicle, and
display the determined average delay per vehicle on the display device;
wherein the microcontroller is further configured to determine the average delay per vehicle in accordance with
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.
5
*
R
2
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AB
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BC
C
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wherein:
C is traffic signal cycle length,
R is Red light time interval,
ω AB is a shock wave speed between flow states, arrival state A and jam state B,
ω BC is the shock wave speed between flow states, jam state B and saturation state C,
Qa is arrival rate of vehicles,
k jam is traffic density at flow state B,
d is safe vehicle deceleration rate,
K a is traffic density of arriving vehicles; and
determine a shock wave speed between an arrival flow state and a stopped flow state;
determine a shock wave speed between a stopped flow state and a departure flow state; and
determine a stop delay of the stopped flow state;
wherein the shock wave speeds are based on a backward queue forming shock wave or a backward recovery shock wave.
7 . The signalized intersection level of service logging device of claim 6 , further comprising:
an output port to output the determined average delay per vehicle.
8 . The signalized intersection level of service logging device of claim 6 , wherein the data collection stopping criteria is when a number of vehicles arriving at the traffic light reaches a predetermined queue number or the error during arrival and the error during departure are below the error limit.
9 . The signalized intersection level of service logging device of claim 8 , wherein the predetermined queue number is based on a vehicle arrival rate, a saturation flow rate, and a jam density.
10 . The signalized intersection level of service logging device of claim 6 , wherein the data collection stopping criteria is when the mean of the arrival headway for arrival and departure reach a predetermined degree of confidence.
11 . The signalized intersection level of service logging device of claim 6 , wherein the display device is a liquid crystal display device configured to display text.
12 . The signalized intersection level of service logging device of claim 6 , wherein the logging device is a portable handheld device.