VS-pCoq Examples

Quality assurance - some examples

Signal Head Evaluations

By evaluating the signal head switching signals, the traffic engineer can visualize the traffic actuated modification behavior of every node. There are some basic evaluation types that will be shown in the next section.

Finally some examples will be given of the application named "Green" used in Zurich.

Cycles

 
Figure 1: Cycle time

The figure shows the cycle time of three signal heads. The left diagram shows the average cycle time development over time using a 3 minutes interval. The right diagram shows the distribution function of cycle time of the same three signal heads.

One can clearly see a strong mean value and a distribution function around the mean value that is due to public transport priority preemptions. The almost 0 cycle times helped the technicians discover a measurement problem of the system!

Green times and red times

The same evaluations can be done for green times and for red times of the signal heads, as shown in the next two figures.

 
Figure 2: Green time

 
Figure 3: Red time

"Green"

The city of Zurich uses an online signal head green time observation tool that is available through the Internet. It uses Java applets on the browser side and a Java servlet on the server side.

It is able to evaluate

  • mean green time of selected signal heads
  • statistical values per period as
    • minimum green time
    • maximum green time
    • maximum red time
    • variance of mean green time
    • average waiting time for pedestrians

The evaluation intervals are defined as

  • last hour or a selected hour
  • last 24h or a selected day
  • last week of a selected week

The next screenshots show some examples.


Figure 4: Measuring green time during one hour

8 Signal heads have been selected for evaluations, each represented with another color. The upper part of the panel contains a graphical diagram, the lower parts contains the numeric values. At the moment signal head 576.S.17 is selected (red). That's also why the red line in the diagram is thicker.

The statistical table values can be copied and pasted e.g. into Excel for further analysis.


Figure 5: Measuring green time during one day

The rose areas show invalid data. The traffic lights have been switched off between 01:00 and 05:30. Yellow shaded areas represent values with a lower level of confidence, e.g. due to some missing measured values. There are no such intervals in the figure.


Figure 6: Measuring green time during one week

Detector Evaluations

By evaluating the raw detector signals, the traffic engineer gains a deeper insight into the traffic behavior. Some basic evaluation types will be shown in the next section.

Finally some examples will be given of the application named "Count" used in Zurich.

Number of Detected Vehicles


Figure 7: Number of detected vehicles

The number of detected vehicles on a list of detectors is a basic measure for determining traffic demand.

Inter-Vehicle Distance

 
Figure 8: Inter-vehicle distance

The vehicle count impulsions can also be used for measuring the distance between vehicles. The distribution function on the right diagram shows clearly that most vehicles drive with a short distance to the next vehicle. This means that there is mostly platoon traffic detected by the shown detectors.

Occupancy Time

 
Figure 9: Occupancy time

Occupancy time is used to estimate the speed of the cars driving over the detectors. Higher speed means in general shorter travel times that might be a political goal of the city officials.

"Count"

The city of Zurich uses an online traffic count observation tool that is available through the Internet. It uses Java applets on the browser side and a Java servlet on the server side.

It is able to evaluate

  • count and occupation of one driving direction
  • counts of both driving directions

The evaluation intervals are defined as

  • last 24h or a selected day
  • last week of a selected week
  • last month or a selected month

The next screenshots show some examples.

 
Figure 10: Measuring count and occupancy during one day

The left figure shows count in red and occupancy time in blue. The numeric values are shown on the lower part of the diagram. They can be copied and pasted e.g. into Excel for further analysis.

The right figure shows the count of both directions (red and blue) of a street. The street has an unbalanced load distribution: the flows do not compensate each other over the duration of one day.

 
Figure 11: Measuring count in both directions during one week and one month

The light blue shaded areas mark missing measurement data.

More Evaluations

There are a great number of different evaluations that can be used for quality control. The chapter shows some more examples.

  • The first example is a program used by the city of Zurich for checking public transport priority behavior of the intersections.
  • The second example shows how the same evaluations could be done without the technology installed in Zurich.

"Tram"

The city of Zurich uses an online public transport regularity observation tool that is available through the Internet. It uses Java applets on the browser side and a Java servlet on the server side.

It is able to evaluate

  • time intervals between vehicles
  • travel time between stops
  • delays at stops and delays of vehicles in a synoptic diagram

The next screenshots show some examples. At the moment the application can be called under http://www.verkehrsmanagement.ch/tram/TramJSP.jsp. The application has not yet been published, so it will change its address and access rights in the future.

 
Figure 12: Measuring the time between two public transport vehicles

The left figure shows the time between two vehicles following each other. The right figure shows the distribution functions of these times, discretized to 1 minute. We see mean 10 minutes distance between vehicles.

 
Figure 13: Measuring travel time between two stops

The left figure shows how long a vehicle usually drives from one stop to the next. The right figure shows the distribution function of the travel time.


Figure 14: Observing delays

This figure shows all trains of a streetcar line, driving from bottom to top (the stop names are given at the right, the departure time at the first stop is given at the bottom). The diagram shows the delay of the anticipation of each vehicle at each stop, using different colors (see the legend at the right edge of the diagram).

  • In the case of horizontal contiguous areas there is a problem at the stop.
  • In the case of vertical contiguous areas there is a problem with a train.