## Using space-time diagrams for calibration

March 2023 — Technical note #78

Dimitris Triantafyllos

Senior Product Specialist

##### In this month’s pro tip, Dimitris Triantafyllos explains how to create speed contour plots in Aimsun Next to show the time, location, and subsequent propagation and dispersal of congestion on the highway.

Space-time diagrams have received extensive attention from researchers and traffic practitioners because they provide a heatmap that presents the traffic conditions on a spatiotemporal plane. Space-time diagrams are commonly used to plot the average speed on a highway corridor (speed contour plot) as it shows the time, location and subsequent propagation and dispersal of the congestion caused by a bottleneck.

Figure 1 shows examples of space-time diagrams showing average speed for 2 freeways during the afternoon peak.

###### Figure 1: Space-time diagrams representing average speed during PM peak on 2 different freeways (Yuan et al., 2015)

In these plots, the x-axis is the time, and the y-axis is the location along the corridor of subsequent detector stations. The color in each cell represents the average speed at that time and location. Green shades denote uncongested conditions, while yellow and red shades represent increasingly congested conditions.

In this technical note we are going to explain how to create a speed contour plot in Aimsun Next.

#### Historical dataset and typical day traffic pattern

We received detector speed measurements for several weekdays on a motorway. We noticed that almost every weekday during the morning peak two congestion events were occurring at the same locations. Figure 2 depicts the entire network where several detectors are installed on the motorway (Southeast direction) and the locations of the two events as well as the maximum queue length of each.

###### Figure 2: Motorway detectors and the locations of the two events as well as the maximum queue length.

The speed measurements were obtained from several detectors evenly spaced along the motorway (1 detector every 300m) and with a duration from 04:00 am until 11:00 am with a 5-min frequency. A speed contour plot (Figure 3 below) allowed us to better visualize and understand the data, immediately identifying the two bottlenecks and corresponding maximum queue length

###### Figure 3: Space-time diagram representing average speed during AM peak on a motorway for weekday pattern.

For both events the bottom-right cell (queue of the arrow) indicates the start of the segment at the beginning of the congestion, while the top left-cell (head of the arrow) indicates the end of the congestion. The two bottlenecks (the large, dark-red region) are clearly visible as well as the propagation of the queue which is indicated by the blue arrows. The first event started at 06:00 am at detector D+3.9 and the queue reached detector D+1.5 (2.4 km of queue length) at 08:15 am. The second event started at 07:10 am at detector D+1.2 and traffic recovered at D+0.6 at 08:15 am.

#### Traffic incident on a weekday

One of the days of the dataset we received did not show the same congestion pattern (Figure 4). An incident happened that contributed to abnormal (non-recurring) congestion on the south-east direction of travel during the morning started at 06:00AM at detector D+5.7 with a 30-minutes duration where it caused the closure of 2 lanes out of the 4 lanes at this location and thus, a significantly large queue spillback. Figure 4 depicts the speed drop using a space-time heatmap (speed). Traffic recovered at around 08:40 am on the motorway.

#### Simulating both typical day and incident in Aimsun Next

When building a traffic model, calibrating and validating a speed contour plot is a valuable practice, because it ensures not only that the time and location of the congestion is right, but also the extent of the queue, the speed at which it propagates upstream and the speed at which it recovers. In this case study, we reproduced two minor bottlenecks on the motorway for the typical day scenario and a major bottleneck for the incident scenario.

In Aimsun Next you can create a space-time diagram showing any outputs that are gathered by detectors (Count, Density, Headway, Occupancy, Speed), just follow the steps outlined below:

1. Activate the Space-time diagram by selecting Data Analysis from the Menu Bar and then click on Space Time Diagram.

2. Create a Detector Set. A Detector Set is an ordered collection of detectors. To create a Detector Set, click on the Detector Sets Tab and then click on Add Set. Then Add Detectors in that Detector Set by selecting the desired detectors (or detector stations, if you have one detector per lane) starting from the most upstream one and going downstream.

###### Figure 6: Aimsun Next Space Time Diagram – Detector Sets Tab
3. Go back to the Main Tab and select the Detector Set you have just created, the Column corresponding to the output you want to plot (in this case speed for the typical day scenario) and the representation as Space/Time.

Figure 7 depicts the speed contour plot of the typical day simulation; you can notice that it matches the real average speed data for the weekday pattern.

###### Figure 7: Aimsun Next Space Time Diagram – Main for the weekday pattern

Figure 8 shows the traffic density at 08:00 am on the motorway for the weekday pattern.

###### Figure 8: Traffic density at 08:00 am on the motorway for the weekday pattern.

Now select as Column the speed related to the simulation run with the incident. Figure 9 depicts the speed contour plot of the scenario with incident; you can notice that it also matches pretty well the corresponding real data.

###### Figure 9: Aimsun Next Space Time Diagram – Main for a weekday with an incident.

Figure 10 shows the traffic density at 06:35 am on the motorway for a weekday with an incident.

###### Figure 10: Traffic density at 06:35 am on the motorway for a weekday with an incident.

Note: The Settings tab can be used optionally to set the ranges to which the color scale of the space/time diagram is applied. The ranges can be customized and fixed (useful when you want to create plots that can be compared), or the Dynamic Values option will automatically adjust the range to the min and max values in each plot.

For more detailed info, check the Aimsun Next Users Manual – Space Time Diagram.

##### References:
1. Yuan, V.L. Knoop, S.P. Hoogendoorn: Capacity drop relationship between speed in congestion and the queue discharge rate, Transp. Res. Rec. (2015), pp. 72-80

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### Aimsun vehicle paths

September 2014: Josep Perarnau erläutert die verschiedenen Ansätze zur Analyse von Fahrzeugpfaden.

TEILEN

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Aimsun Next 23

Aimsun (2023). Aimsun Next 23 User’s Manual, Aimsun Next Version 23.0.0, Barcelona, Spanien. Zugriff am: July. 19, 2023. [Online].
Verfügbar: https://docs.aimsun.com/next/23.0.0/

Aimsun Next 20.0.5

Aimsun (2021). Aimsun Next 20.0.5 User’s Manual, Aimsun Next Version 20.0.3, Barcelona, Spanien. Accessed on: May. 1, 2021. [In software].
Available: qthelp://aimsun.com.aimsun.20.0/doc/UsersManual/Intro.html

Aimsun Next 23

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Aimsun Next 20.0.5

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