A3.19 - Calculating bottleneck delay
- A3.1 - Travel time estimation procedures
- A3.2 - The stages for estimating travel time
- A3.3 - Determining traffic volumes
- A3.4 - Calculating free speed travel time
- A3.5 - Determining the free speed of multilane roads
- A3.6 - Determining the free speed of two-lane rural roads
- A3.7 - Determining the free speed of other urban roads
- A3.8 - Determining the capacity of road sections
- A3.9 - Determining the capacity of motorways
- A3.10 - Determining the capacity of multilane roads
- A3.11- Determining the capacity of two-lane rural roads
- A3.12 - Determining whether vehicle interactions are significant
- A3.13 - Types of delay
- A3.14 - Average peak interval traffic intensity
- A3.15 - Determining the peak interval
- A3.16 - Calculating the average peak interval traffic intensity
- A3.17 - Calculating the volume to capacity ratio
- A3.18 - Calculating the additional travel time
- A3.19 - Calculating bottleneck delay
- A3.20 - Determining whether to consider peak spreading
- A3.21 - Determining the additional travel time resulting from speed change cycles
- A3.22 - Calculating the time period total average travel time
- A3.23 - Traffic signals
- A3.24 - Priority intersections
- A3.25 - Roundabouts
- A3.26 - References
A3.19 - Calculating bottleneck delay
When to use
Use this procedure for all time periods during which demand exceeds capacity (volume to capacity ratio greater than one) at some time.
Blocking back onto upstream sections
Where traffic volumes exceed capacity, the resulting queues may block back onto upstream links. In such circumstances care must be taken to ensure that the delays that arise on the under-capacity section are not double counted on any upstream section.
Procedure
Follow the steps below to calculate bottleneck delay.
| Step | Action | |
|---|---|---|
| 1 | Select a time period to be analysed (usually the weekday morning or evening commuter peak). | |
| 2 | Determine the capacity of the road section. See appendix A3.8. | |
| 3 | Identify the time interval step that traffic data for the time period has been collected (usually 5, 10 or 15 minute periods). | |
| 4 | Set out the traffic data for the time period. Example: | |
| Time interval | Observed traffic volume | |
| 7:00 - 7:15 | 264 | |
| 7:15 - 7:30 | 475 | |
| 7:30 - 7:45 | 591 | |
| 7:45 - 8:00 | 600 | |
| 8:00 - 8:15 | 591 | |
| 8:15 - 8:30 | 475 | |
| 8:30 - 8:45 | 264 | |
| 8:45 - 9:00 | 250 | |
| 9:00 - 9:15 | 234 | |
| 5 | At each time interval, calculate the cumulative demand with a running total of observed traffic volume since the time period start. Cumulative demand at time interval = sum of observed traffic volume since time period start Example from step 4: Cumulative demand for time interval 8:00 to 8:15 = 264 + 475 + 591 + 600 + 591 = 2521 |
|
| 6 | At each time interval, calculate the vehicles discharged. If the traffic volume for the time interval is below the road section capacity then all the traffic is discharged. Only the number of vehicles equivalent to the road section capacity is discharged if the traffic volume exceeds capacity. Example from step 4: Time interval = 8:00 to 8:15 Capacity = 500 vehicles Traffic volume = 591 vehicles Vehicles discharged = minimum of traffic volume or capacity = minimum (591, 500) = 500 |
|
| 7 | At each time interval, calculate the cumulative discharge with a running total of vehicles discharged since the time period start. Cumulative discharge at time interval = sum of vehicles discharged since time period start |
|
| 8 | At each time interval, calculate the queue at the end of the interval when traffic volume exceeds capacity.< Example from step 4: Time interval = 7:30 - 7:45 Traffic volume = 591 vehicles Capacity = 500 vehicles Queue at end of interval = traffic volume − capacity, if traffic volume > capacity = 0, if traffic volume ≤ capacity = 591 - 500 = 91 vehicles |
|
| 9 | At each time interval, calculate the queue at the start of the interval. This is the queue at the end of the previous interval. Time interval = 7:30 - 7:45 Queue at start of interval = queue at end of previous interval = 91 vehicles |
|
| 10 | At each time interval, calculate the average delay in vehicle minutes. Average delay = interval time step x (queue at end of interval + queue at start of interval)/2 |
|
| 11 | Sum the average delays over the entire time period to obtain the time period total delay. | |
| 12 | Calculate the time period average delay per vehicle from the time period total delay divided by the cumulative discharge of vehicles at the time period end. Average delay per vehicle = total delay / cumulative discharge of vehicles at the time period end |
|
Example
An example of the bottleneck delay calculation using the data from step 4 and a road capacity of 500 vehicles.
| Start time |
Demand (veh) | Cumulative demand (veh) | Vehicles discharged (veh) | Cumulative discharge (veh) | Queue at end of interval | Queue at start of interval | Average delay (veh-min) |
|---|---|---|---|---|---|---|---|
| Step | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 7:00 | 264 | 264 | 264 | 264 | 0 | 0 | 0.0 |
| 7:15 | 475 | 739 | 475 | 739 | 0 | 0 | 0.0 |
| 7:30 | 591 | 1330 | 500 | 1239 | 91 | 0 | 682.5 |
| 7:45 | 600 | 1930 | 500 | 1739 | 191 | 91 | 2115.0 |
| 8:00 | 591 | 2521 | 500 | 2239 | 282 | 191 | 3547.5 |
| 8:15 | 475 | 2996 | 500 | 2739 | 257 | 282 | 4042.5 |
| 8:30 | 264 | 3260 | 500 | 3239 | 21 | 257 | 2085.0 |
| 8:45 | 250 | 3510 | 271 | 3510 | 0 | 21 | 157.5 |
| 9:00 | 234 | 3744 | 234 | 3744 | 0 | 0 | 0.0 |
Step 11.
Time period total delay
= 682.5 + 2115 + 3547.5 + 4042.5 + 2085 + 157.5
= 12630 veh-mins
Step 12.
Time period average delay per vehicle
= 12630 / 3744
= 3.37 min/veh
