Why fixed-time traffic light control is superior at preventing traffic congestion

Due to an increased demand for mobility, our urban road network has become increasingly oversaturated. As a result, the time we waste in congested traffic is growing at an exponential rate; this has huge consequences for our economy, our environment, our health and our quality of life. The majority of these negative consequences are caused during peak hours. Therefore, especially heavy traffic situations deserve our attention.

Since signalized intersections are natural bottlenecks in urban traffic networks, increasing their efficiency is crucial for improving urban mobility. Traditionally, signalized intersections are controlled using a fixed-time controller, which schedules the green intervals at predetermined time intervals. In the last decades, however, vehicle-actuated control, which uses live sensor data, has gained much popularity. In particular, controllers having complete freedom to choose the signal phasing have been gaining traction in recent years.

In this comparison it is clear that the performance of fixed-time control is superior in heavy traffic situations. This may seem counter-intuitive in a day and age where an abundance of fine-grained traffic data is available. So how come fixed-time control, a strategy that does not require such fine-grained data, is superior during peak hours? In this blog post we give an intuitive explanation. A hint: it is because controllers that have complete control freedom are continuously putting out fires as they come up, while fixed-time control keeps the necessary overview of long-term effects for all traffic flows.

Summary of this blog:

This post contains some claims that might go against the intuition of some traffic engineers. But please bear with us, as we have some very interesting insights on traffic flow performance in heavy traffic situations with some examples to back it up.

Many exciting initiatives focus on light to moderate traffic conditions.

We are living during exciting times, where innovations in the mobility sector are welcomed and stimulated. Recent developments in the area of Smart Traffic, e.g., talking traffic, have inspired exciting new initiatives. For example, in Rotterdam, The Netherlands, where bad weather is detected using rain sensors to give priority to cyclists and pedestrians on rainy days. Another initiative detects heavily-loaded polluting trucks and gives them priority at signalized intersections to reduce environmental impact. We are very enthusiastic about such initiatives. However, we also realize that they have a certain operating regime; these strategies are expected to be effective when traffic is light to moderate; in heavy traffic they may not make sense anymore.

For example, giving priority to (only the) polluting trucks may not be possible during peak hours; the polluting trucks are likely to be queued up behind many other vehicles that must first cross the intersection and, therefore, prioritizing individual vehicles is no longer possible. Moreover, giving priority to specific traffic streams, such as cyclists on a rainy day, has to be done with care in heavy traffic. As it otherwise may have a significant negative effect on other traffic flows. In heavy traffic these disruptive effects can accumulate and cause gradual buildup of traffic; this has huge negative consequences in the long run. Therefore, it becomes crucial to account for long-term effects of control decisions to prevent such traffic accumulation; keeping all traffic queues limited is essential and benefits all traffic streams in the long run. To this end, heavy traffic requires a different control strategy; apparently we are in a regime where fixed-time control thrives.

Any traffic light controller using a fixed and optimized phase sequence is expected to excel in heavy traffic.

Before we start our comparison, first let us give some nuances as a diversity of vehicle-actuated controllers exist. Many vehicle-actuated controllers used in practice today are, in essence, slight modifications of a fixed-time controller; they use an optimized fixed-time schedule as a basis and make slight modifications to this schedule based on live sensor data, e.g., they may decide to extend or shorten a green interval but may not change the sequence. As a consequence, just like fixed-time controllers, when well-designed, these controllers are expected to excel in heavy traffic.

In this blog we claim that traffic light controllers that use an optimized fixed phase sequences (that actually matches with the current traffic situation) perform superiorly to the ones that do not. Due to their increased flexibility, controller having complete freedom to choose the signal phasing have been gaining traction in recent years. This freedom can however also have a downside; the controller can drown in the overwhelming number of options. Therefore, to keep the options manageable they only focus on the near future: What to do next? Which signal groups should be switched to green next? Which of the current green intervals should be terminated? Their natural focus on short-term effects makes them very flexible and effective when traffic is light to moderate. They are however often not effective at handling large traffic intensities as they lack the required overview of long-term effects; we will explain this using an example.

Although the effects become more apparent for larger intersections, which have an enormous number of possibilities for scheduling the green intervals, to make our explanations more intuitive we will use a very simple example consisting of only three signal groups; this is the same example as we have used in a previous blog post. Even though we use a constructed example, be ensured that these effects can be much worse for larger real-life intersections.

Layout of a simple T-junction
Figure 1: An intersection with three signal groups. Safety restrictions are as follows. Each green time must be at least 10 and at most 45 seconds and is followed by a yellow time of exactly 3 seconds. Each red interval must take at least 3 seconds and at most 60 seconds. All three signal groups conflict with each other. The minimum clearance times required between the green intervals of two conflicting signal groups are visualized in Figure 2.

The importance of sequence in heavy traffic

In a previous blog post, we have shown the importance of sequence; in heavy traffic, selecting the right order for scheduling the green intervals could truly mean the difference between smooth traffic flow and traffic congestion. The underlying reason: minimum clearance times. Minimum clearance times are times needed to switch from serving one signal group to start serving a conflicting signal group; they ensure that all traffic can safely cross the intersection without encountering any conflicting traffic flows. The sequence of the green intervals directly influences the time 'lost' to such switches and, as a result, directly affects the time that is left for actual green times, which in heavy traffic can have a large impact.

The minimum clearance times for our small example are given in Figure 2.
Example clearance times of the simple T-juction.
Figure 2: The clearance times for the intersection in Figure 1. For example, signal group 2 has to be red for at least 4 seconds before signal group 8 may switch to green.

The two most obvious (periodic) sequences are visualized in Figure 3. Let us call these two periodic sequences: counterclockwise sequence (left) and clockwise sequence (right). The main difference between these two sequences is the time that is lost to clearance times. For the counterclockwise sequence, a total of 14 seconds is lost to clearance times each period, whereas only 10 seconds is lost each period for the clockwise sequence. This may seem like a minor difference; however, as can be seen in this video, the influence on traffic flow is enormous.
Clearance times associated with the two sequences.
Figure 3: Two different periodic sequences for planning the green intervals. For the counterclockwise sequence (left) a total of 14 seconds is wasted on clearance times every period. For the clockwise sequence (right) a total of 10 seconds is wasted on clearance times every period.

Traffic light controllers reacting based on short-term effects lack the necessary overview required in heavy traffic

We have seen that the sequence of the green intervals is crucial when traffic is heavy; but, what has this insight to do with our comparison of vehicle-actuated control and fixed-time control? When using fixed-time control, advanced optimization strategies allow computing the best fixed-time schedule by rigorously considering all possible sequences, their efficiency losses (time spend on switching), and their long-term effects on traffic flow; this allows selecting the best sequence possible.

On the other hand, traffic light controllers with complete control freedom react solely based on estimated short-term effects, for example, by continuously switching to the most critical signal groups (e.g., the ones with the largest estimated queues). These controllers do not oversee the possible sequences in which the green intervals can be planned, which often comes at the cost of a drastically worsened traffic flow in heavy traffic. In essence, by reacting based on estimated short-term effects, the vehicle-actuated controller is continuously putting out fires as they come up, while fixed-time control keeps the necessary overview of long-term effects for all traffic flows. Keep in mind that the number of possible sequences can be overseen for our small example. For more complex intersections the number of possibilities is often unimaginably large, and the differences between these sequences are usually substantial.

Self-control; a state-of-the-art controller without structural phase sequence.

We compare the fixed-time controller visualized in Figure 4, which is the optimal fixed-time controller using the clockwise sequence of Figure 3, to state-of-the-art vehicle-actuated controller, called self-control. Self-control is very similar to many other traffic light controllers that have complete design freedom to choose the signal phasing. Therefore, the statements that we make in the video and text below are also valid for other such traffic light controllers.

Clearance times associated with the two sequences.
Figure 4: The optimal fixed-time schedules for the clockwise sequence of Figure 3. The arrival rates are 480 vehicles per hour for each signal group. The maximum departure rates (during green) are 1920 vehicles per hour for the lane controlled by signal group 2, 1780 vehicles per hour for the lane controlled by signal group 5, and 1800 vehicles per hour for the lane controlled by signal group 8.

Let us first explain the basics of self-control. Self-control, originally proposed in this paper, is a state-of-the-art controller having complete control freedom. Although self-control can be used in more generic situations, we focus on the situation where, just like in our example, all signal groups need to be served sequentially. The control decisions are then limited to deciding when to terminate the current green interval and which signal group to serve next. To make these decisions, self-control attempts to maximize the total departure rate at the intersection. To this end, this controller continuously evaluates the short-term effects of two possible decisions:

A biased traffic light controller

A first challenge for vehicle-actuated controllers is serving the signal groups in a fair manner. Although, the above switching rule may seem reasonable, it creates a bias and, as a result, the controller prefers to serve some signal groups over others. For example, let us look at the small intersection in Figure 1; more details on the traffic situation at this intersection are given in the caption of Figure 4. To make our point, let us look at the extreme case where signal group 2 controls four lanes instead of one, and that its total arrival rate is four times as large (equaling 4 x 480 = 1920 vehicles per hour). The controller would then always prefer to extend any green interval of signal group 2 (SG 2); even when no traffic is waiting anymore and large queues have formed at the other signal groups! Reason for this is that continuing the current green interval of SG 2 is expected to result in a larger departure rate (at least 1920 vehicles per hour) than switching (at most 1800 vehicles per hour, which is the saturation flow rate of SG 8). Therefore, this controller has a bias to serve some signal groups much longer than actually needed, resulting in others receiving too little attention. It is clear that this bias is not desired! Obviously, this is an extreme case, where we in all circumstances would prefer to serve signal group 2. However, this undesired bias is also present in less extreme cases.

The inventors of self-control already anticipated their controller leading to instabilities (see also their paper). Therefore, they introduced a stabilization rule. This stabilization rule aborts the normal operation in order to give priority to the queues that have not received enough attention. Whenever one of the queues becomes 'too large', the controller starts serving this signal group as soon as possible and continuous serving it until its queue is emptied. Subsequently, the controller continuous with its normal operation unless some other queue has exceeded the threshold. This stabilization rule increases 'fairness' and makes the controller behave in a very similar manner to pressure-based approaches. Although this stabilization rule improves traffic flow in some cases, it does not improve the performance in heavy traffic to the level of a fixed-time controller; we will see this in the video later in this blog.

Difficulty with satisfying safety restrictions such as maximum red times.

Another difficulty for vehicle-actuated controllers such as self-control is satisfying all safety restrictions. Especially the maximum red times are difficult to account for. These red times usually span a larger time period during which many green intervals of other signal groups may be scheduled in complex patterns. Therefore, ensuring that the maximum red times are satisfied requires careful planning over a longer time horizon, which these controllers lack.

To prevent unsafe situations due to red negation, we introduce a third switching rule: the safety rule. This rule gives priority to the signal groups exceeding their maximum red times. Note that this allows the controller to (slightly) exceed the maximum red times, having a positive effect on traffic flow (and a negative effect on traffic safety) as this would reduce the switching frequency and, as a consequence, would reduce the switching losses. Therefore, this would give self-control a slight (unfair) advantage with respect to our fixed-time controller.

A video comparing fixed-time control to self-control

below we summarize the three switching rules of self-control in order of priority from high to low:
Icon for safety rule. Safety rule: Serve a signal group as soon as possible whenever its maximum red time is exceeded.
Icon for stability rule. Stabilization rule: If the threshold on queue length is exceeded, serve the signal group with the largest queue length; serve this queue until it is emptied. (alternative is to serve the signal groups exceeding this threshold in first-come-first-serve order, but this is not expected to improve performance).
Icon for stability rule.      Optimization rule: Switch to another green interval if this is expected to improve the total departure rate in some short term horizon.
Below we compare a fixed-time controller to self-control.

Vehicle-actuated controllers have a blind spot that is extremely difficult to overcome

It is clear that the fixed-time controller results in much smoother traffic flow. So what causes this difference? In short it is because self-control (or controllers alike) are reacting to short-term effects and are lacking a clear long-term strategy. They are continuously trying to put out fires by switching to the signal group that seems most critical, either because it has exceeded its maximum red time, its queue length has exceeded the threshold, or it is expected to result in a larger departure rate in the short term; the controller does however not adequately take into account efficiency losses due to clearance times. Let us look at the shortcomings of such vehicle-actuated controllers in a bit more dept to see that controllers like self-control have a blind spots that cannot be easily overcome.

Let us first look at the 'normal' operation of self-control. The current green interval is continued as long as it is expected to result in the largest traffic flow. If this is no longer the case, the controller switches to the green interval that is expected to maximize traffic flow. The controller tries to incorporate the effect of switching losses when making this decision. However, it cannot oversee all switching losses; the controller has a blind spot and cannot oversee the complete influence of sequence.

Sequence of switches forcing a large switch from SG 5 to SG 2
Figure 5: The preferred switches of self-control; the controller prefers a switch with the smallest (direct) minimum clearance time. For example after terminating a green interval of SG 5 the controller prefers to switch to SG 8 (over switching to SG 2).

Controllers that have complete freedom to choose the signal phasing include at most two types of switching losses: primary switching losses and secondary switching losses. Primary switching losses are losses for switching to a new green interval. For example, after terminating a green interval of signal group (SG) 2, switching to signal group 8 requires a minimum clearance time of only 4 seconds compared to a minimum clearance time of 5 seconds for switching to signal group 5. Therefore, the controller prefers to subsequently start a green interval of SG 8. In Figure 5 we visualize the switches that the controller prefers to make.

On the other hand, the secondary switching loss is an estimate for eventually having to switch back to a green interval that you currently can terminate. If this 'switch back' is expected to need a large minimum clearance time, then the controller is less inclined to terminate the current green interval. The secondary switching loss only affects the duration of the current green interval; it does not affect the order in which to serve the different signal groups.

Aren't these all the switching losses that are important? Well, no. Following the 'preferred' switches, which are based on estimated short-term effects, is often not best for the long-term. In our example, the controller is often not able to prevent a large switch from SG 5 to SG 2. In Figure 6a we have visualized the process that usually forces the controller to perform this large minimum clearance times. It starts with a green time of SG 2. Subsequently, two preferred switches are performed to start a green interval for SG 8 and SG 5. While serving SG 5, the maximum red time of SG 2 is reached, forcing the controller to perform the large switch to SG 2, closing the circle; the controller was completely blind to this large minimum clearance time coming up until now!

Vehicle-actuated controllers may be fragile in heavy traffic; small disturbances can cause the controller to get stuck in a bad operation mode.

Note that because the controller only looks at the first upcoming switch, it is essentially blind to the long-term effects of different sequences, which are oh-so important in heavy traffic. We can also observe this in the comparison video. We can see that the controller is alternating between different sequences, including (but not exclusively) the counterclockwise and clockwise sequence; it does so not by intent, but purely as a consequence of the short-term anticipations made by this controller; it cannot see the difference between the two sequences. As a consequence, the amount of traffic is steadily growing and eventually the queues have grown enough to activate the stabilization rule. From this point on the controller behaves similar to a pressure-based approach. Such approaches do not take into account any switching losses and have an even larger blind spot; the consequence on traffic flow is clear. You can image what the consequences would be for a complex real-life intersection, which may have tens of signal groups.

Essentially, in heavy traffic the signalized intersection becomes a fragile system when controlled by a vehicle-actuated controller like self-control. Even small disturbances can nudge the controller into undesired operation mode, such as the ones visualized in Figure 6. Even worse, it can get stuck in such an undesirable mode for a considerable duration. For example, when all queues have become unstable while using the counterclockwise sequence; the controller is then only able to escape this mode when one of the queues becomes stable again. This could take a while as all queues could be steadily increasing in this mode!

Sequence of switches forcing a large switch from SG 5 to SG 2
(a) Operation mode where two preferred switches (optimization rule) lead to a undesirable large switch from SG 5 to SG 2 (safety rule); the preferred switches might also be triggered by the safety rule instead of the optimization rule.
Operation mode where SG 8 receives twice as many green intervals
(b) Operation mode where SG 8 receives twice as many green intervals as the other signal groups; the switch from SG 8 to SG 5 might also be triggered by the safety rule instead of the optimization rule.
Operation mode where SG 8 receives twice as many green intervals
(c) Operation mode where the (desirable) clockwise sequence is used, but the green intervals fluctuate undesirably.
Figure 6: Several (sub-optimal) operation modes of self-control that can be identified in the comparison video.

Conclusion: fixed-time control is superior in heavy traffic

In contrast to the vehicle-actuated controllers like self-control, controllers using an optimized periodic phase sequence provide a robust and predictable system that can result in top-notch performance in heavy traffic as shown in the comparison video. To capitalize on these results, rigorous optimization is crucial. For more complex intersections the number of options for scheduling the green intervals is unimaginably large; only a select few of these options may result in top-notch performance. Therefore, selecting the best periodic schedule can be a very challenging task. To make this challenging task simple, Swift Mobility B.V. provides tools to find the best periodic schedules; completely automated and fast, even for the most complex intersections. To see the enormous impact yourself, please visit https://www.swiftmobility.eu/downloads to start using our tools.

We also provide an API that allows for real-time optimization of fixed-time schedules and their periodic phase sequences. This allows for breakthroughs in truly smart traffic control. Why? Using periodic phase sequences works extremely well in heavy traffic situations; that is, if the estimated traffic situation that is used to compute the optimal sequence indeed matches reality. In the past, computing these periodic sequences required much (human) effort. Therefore, they where designed 'offline' and the same sequence was used for several years (and not only in heavy traffic situations). As traffic situations change, it is likely that such a controller does not perform as well as one might hope. Hence, being able to compute optimal periodic phase sequences in real-time is a major breakthrough. This makes it possible to frequently adapt the periodic phase sequence to the current heavy traffic situation. This guarantees smooth traffic flow in the long run. Simultaneously, green times can be adapted quickly based on sensor data, which allows the controller to react or prioritize quickly when needed.