To demonstrate the effects of what happens on a motorway in terms of how flows affect speeds, we’ve taken a point of the motorway at the Green lane interchange and analysed what happens here.
Figure 1 below is a typical speed versus traffic flow diagram for one lane on the motorway. This plot comes from real data collected from this location.
The vehicles per hour figure (vph) is the number of vehicles that pass a point on the road in one lane in one hour. So for Green Lane northbound there are three lanes. The total number of vehicles that can pass this point on the motorway is around 2050 vehicles per hour per lane. This maximum flow occurs when vehicles are travelling at approximately 70-80 kph. However, this flow rate is difficult to sustain as we will show.
When speeds are higher then there are typically fewer cars passing the fixed point. This is usually due to fewer people wanting to use the motorway and larger gaps between vehicles. Conversely, when traffic is denser and speeds are lower, then fewer vehicles pass the same point at the same flow rate as occurs at higher speeds. This is an important point to note.
Demonstrated on the graph and indicated by the red lines in figure 2 below.
For example, where 1600 vehicles per hour per lane flow past the interchange, there are two upper and lower speeds where this flow rate of 1600 vph occurs at. The range of speeds is between 90 kph and 32 kph where this flow rate occurs and depends on the traffic density at the time.
The best flow rates and speeds occur in the indicated green zone. This is when the most vehicles can get through the motorway and at the most efficient speeds. So at Green Lane northbound, the best flow rates of between 1700 and 2000 vph per lane occur when speeds are between 65 to 85 kph.
The maximum flow rate is indicated by the yellow line on the plot. This is typically not a sustainable flow rate as any minor hiccup in the flow such as a vehicle changing lanes can upset this balance and then we get congestion.
The ramp metering system is designed and operates so that it can try and minimise the impact of merging traffic so that speeds do not drop. When the speeds drop due to excessive merging traffic volumes or increasing traffic density at a location then the overall flow rate along the motorway drops and we see more congestion develop.
The ramp signal system also works by limiting the numbers of vehicles entering the motorway which in turn contributes to congestion further down the motorway. If fewer vehicles reach the congestion point then speeds can increase, flow then increases (as seen in the graph below (Figure 2) in the green zone). Once speeds and flow increase, then more vehicles can be allowed into the motorway system. There is often a fine balance between maintaining the flow in the optimal zone green zone and the point where the onset of congestion happens.
Also an interesting point to observe in the graph is that there is a physical limit to how many vehicles can pass a given point on the motorway over a 1 hour period. So even though there are no traffic lights, give ways, compulsory stops etc on the motorway, when there are more vehicles wanting to use the motorway than the physical constraints allow for, we see congestion. In this instance, Green Lane northbound has enough capacity to provide for about 6100 vehicles per hour (maximum) if the optimum flow is maintained. However we know that this limit is not practically sustainable. What we do see is flow rates around 5150 vph (Figure 3) during a typical peak period. This slightly lower value is due to congestion!
We know that the demand or the number of vehicles wanting to use the motorway exceeds this overall maximum flow capacity. This is why ramp signals are needed to help control how many vehicles are using the limited resource we call lane capacity.
The maximum flow does not happen at 100 kph as some people think. Another important point to note. The number of vehicles passing a given point cannot just keep increasing in total. It does reach a maximum flow and when that point is exceeded then congestion occurs as speeds drop and flow rates decline. Until the number of vehicles leaving the congestion zone exceeds the number of vehicles entering it then congestion will remain. Ramp signalling helps in flow recovery, by trying to reduce the flow of traffic entering so that the number of vehicles exiting the congestion point is greater, thus speeding up overall journey times.
But remember, at some stage congestion will happen! Ramp signals alone can’t fix everything.
Below is a plot of speed versus flows for one lane on the Southern motorway at Green Lane northbound.
Traffic volume plot for all three northbound lanes at Green Lane northbound.