Laboratory 5 – Traffic Systems Queuing

1. Learning Objectives/Outcomes Be able to describe the components of the D/D/1 queuing model. Be able to relate the D/D/1 queuing model to the arrival and departure patterns

observed on one approach of a signalized intersection. Be able to collect arrival and departure data at a signalized intersection and estimate

vehicle delay using these data.

2. Textbook References Section 5.5 – Queuing Theory and Traffic Flow Analysis

3. BackgroundA queuing system is described by an arrival pattern, a service facility (and pattern), and a queue discipline. We can approximate or model the traffic flow pattern at a signalized intersection as a queuing system. Figure 1 and Figure 2 show the physical realizations of a queuing system representing one lane of the westbound approach of the intersection of Sixth and Deakin.

Figure 1 shows an aerial view of the intersection of Sixth and Deakin. Four vehicles are shown in this figure. The first vehicle is being served; it is “in the server position.” The three remaining vehicles are “in the queue.” Figure 2 shows another view of the approach at the intersection showing the server and queue.

Figure 1

Figure 2

There are four elements to this queuing system: The arrival pattern describes how the vehicles on the approach arrive at the

intersection. There are two common types of arrival patterns used to model traffic at a signalized intersection. One is uniform, in which there is a constant headway between the arrivals of each pair of vehicles. The other is random, in which vehicles arrive in a

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random manner that can be described by a Poisson process (in which the headways have a negative exponential distribution). A uniform flow pattern is illustrated in Error: Reference source not found.

Figure 3

The service pattern describes the manner in which the vehicles depart from the intersection, or “are served.” The service pattern depends on whether the signal indication or display is red or green. During the red indication, the service flow rate is zero. During the beginning of the green indication, the service flow rate is equal to the saturation flow rate (the maximum possible flow rate). After the queue has cleared, the service flow rate equals the arrival rate. This flow pattern is also illustrated in Error: Reference source not found.

Vehicles are served in the order in which they arrive, a queue discipline that is called FIFO, or first-in, first-out.

The vehicles arrive and are served in one lane, so this is called a single channel server system.

In this laboratory, you will learn how to apply a D/D/1 queuing model to a signalized intersection. A D/D/1 system consists of a deterministic arrival pattern, a deterministic service pattern, and one service channel. The queuing model is applied to each lane or each approach of a signalized intersection.

We will also use a queuing model to help us measure the performance of a signalized intersection, particularly with respect to how long drivers are delayed as a result of the traffic signal timing.

The following figures are also useful representations of traffic flow arriving and leaving a signalized intersection, particularly with respect to performance. Both assume uniform arrivals

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and uniform departures, with three specific departure rates. Figure 4 shows the cumulative number of vehicles arriving at and departing from the intersection. Again, the arrival rate is constant, so the number of vehicles that have arrived increases at a linear rate. The number of vehicles departing from the intersection remains at zero until the start of green, increases linearly at the saturation flow rate until the queue clears, and then increases linearly at the arrival rate as the queue is clearing. The number of arrivals equals the number of departures after the queue has cleared. Figure 5 is called the queue accumulation diagram and it shows the number of vehicles in the queue at any point of time.

Figure 4 Figure 5

You will answer the following questions as part of this lab:1. How are queuing diagrams used to represent the performance of a signalized

intersection?2. How do your observations in the field compare with the assumptions of a D/D/1

queuing model?3. What is the performance of the intersection approach to which you are assigned?

4. AssignmentQuestion 1: How are queuing diagrams used to represent the performance of a signalized intersection?

Step :. Study Figure 4 and Figure 5. What does the vertical distance between the two curves in Figure 4 represent, for a

given point in time? What does the horizontal distance between the two curves in Figure 4 represent, for a

given vehicle?

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What does the vertical distance between the x axis and the curve in Figure 5 represent, for a given point in time?

Using your answers from the three bullets above, what do the areas of the triangles represent in the two figures?

Step: Consider the model assumptions. One of the assumptions of the queuing model is that a vertical queue forms at the stop

line of an intersection. How does the real physical queue affect the construction of Figure 4 and the time that a vehicle is in the queuing system?

What modification do you need to make in this representation if you were to collect field data to construct Figure 4?

Question 2: How do your observations in the field compare with the assumptions of a D/D/1 queuing model?

Step 1: Go to the field data collection sited to make field observations. Go to the signalized intersection to which you have been assigned.

Step 2: Comparing the model with field observations. Prepare a sketch of the queuing system including the queuing area and the service area

for one lane or approach of the signalized intersection. Observe and document the arrival process for five cycles. How would you describe this

process? Does it fit any of the arrival patterns discussed earlier in this lab? Observe and document the service process, including the three different parts (service

pattern during red, the first part of the green when the queue is clearing, and the second part of the green after the queue has cleared). Note any differences between the theoretical figures and what you observe in the field.

Prepare a brief summary of your observations, noting particularly the similarities and differences between the model and your field observations.

Question 3: What is the performance of the intersection approach to which you are assigned?

Step 1: Determine how far (in number of vehicles) the queue extends from the stop bar. Observe the variation of the standing queue during three cycles. Note how far back the

queue extends from the stop bar for the lane that you are studying. This point is the “system entry point”. The stop bar will be the “system exit point”.

Step 2: Record times that vehicles enter and leave your queuing system for five cycles. One observer will stand at the entry point and the other observer will stand at the stop

line (exit point). Using a watch that shows “seconds”, each observer will record the times that vehicles

pass the “entry point” and the “exit point”. Start collecting data when there are no vehicles in queue. The times that vehicles pass the “entry point” should be recorded in the “arrival time” column on the form on the next page. The times that vehicles pass the “stop line” should be recorded in the “departure time” column on the form. The times should be noted in mm:ss format. For example, if a vehicle arrives at the “entry

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point” at 5 minutes and 35 seconds after 5:00 pm, the following data would be record: 5:35.

Step 3: Record free flow travel time. Record the travel time from the entry point to the exit point for five vehicles that do not

stop or slow down. Compute the mean value of this free flow travel time.

Step 4: Prepare a cumulative vehicles plot. Plot of the number of vehicles that have arrived at and departed from the intersection

vs. time using an Excel spreadsheet. Your chart should look somewhat like the cumulative arrival and departure plot shown in Figure 4.

Construct a second line representing the cumulative vehicle departures that is based on the original departure time data minus the free flow travel time.

Step 5: Compute vehicle delay. Compute the delay (or the time spent in the system) for each vehicle for which you have

collected data. Compute the average delay for all vehicles traveling through your system. Why is it important to consider the free flow travel time when computing delay? Based on the table presented on page 269 of your text, what is the level of service for

this lane?

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Figure 6. Intersection Characteristics Form

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Table 1 Field Data Collection Form

Cycle 1 Cycle 2Arrival Time Departure Time Arrival Time Departure Time

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5. ReportPrepare a two page report in which you summarize your answers to the questions that you considered during this laboratory. The report should include the following sections:

1. Laboratory title.2. Names of the authors of the report.3. Date that the report was completed.4. Answers to the three questions that were posed during the lab.5. One paragraph describing the main points that you learned from this laboratory.

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