# How much time is spent at traffic signals?

While working on another piece, I came upon the question of how much time is spent at traffic lights, for which there is not a well-sourced answer. I posted to Twitter and got some useful replies.

With that and some additional digging, I attempt to answer the question.

As the saying goes: Your Mileage May Vary. This depends on your origin and destination and path and mode and time of day and local traffic signal policies and street design. Tom VanVuren notes: “Much of the impact is in slow moving queues, rather than waiting for the signal cycle to complete. I expect you can make this number smaller than 10% (time at the stop line) or larger than 50% (time affected by traffic lights).” For simplicity, I am considering vehicles that would be stopped if they could either move at the desired speed or must stop (i.e. they are subject to “vertical” or “stacking” queues), but clearly measurement will depend on assumption. Still, there must be a system average. I had heard the number 20% bandied about, which feels right, but let’s first begin with some thought experiment, then look for some empirical results. We take different modes in turn.

# Motor Vehicles

## Thought Experiments

### Thought Experiment 1 A

Imagine an urban grid.

• Assume 10 signalized intersections per km.
• Assume a travel speed of 60 km/h when in motion. (This is probably too high with so many intersections and no platooning, but we are imagining here that you would not be stopping.)
• Time to traverse 1 km=1 minute + signal delay.  (Some of the distance traversal time overlaps some of the signal delay time, but we will imagine a stacking queue, rather than one that has physical distance for simplicity, we can correct this later if it matters.)
• Assume each intersection has only 2 phases.
• Assume fixed time signals at each intersection evenly distributing green time between N/S and E/W directions.  So red time = 1/2 cycle length.
• Assume 1 minute cycle length
• If a vehicle stops, it waits 1/2 red time.
• Vehicles obey traffic signals.
• Assume no platooning.

This means that the average vehicle will stop at 5 intersections for 15 seconds each = 75 seconds (or 1.25  minutes) (vs. 1  minute in motion time). In this case, 1.25/2.25 minutes (55.5%) is spent waiting at signals.

### Thought Experiment 1 B

In contrast.

• Assume near perfect platooning.

In this case, the vehicle will stop at 1 intersection per km, for 15 seconds = 15 seconds. In this case 0.25/1.25 = 20% of the time is spent waiting at signals.

### Discussion

Now, not all travel takes place on an urban grid.

• Assume 25% of travel is on limited access roads (this is approximately true in the US),  75% on non-limited access roads.

With perfect platooning on the grid, and 25% off-grid, then 15% of travel time is intersection delay with near perfect platooning.

Clearly in practice platooning is far from perfect. My guess is the green wave breaks down after one or two intersections during peak times, but can survive well in the off-peak. As a rule of thumb, about ~10% of travel is in the peak hour, ~30% peak period. ~60% AM + PM Peak.

## Data

### GPS Studies

Eric Fischer of MapBox was kind enough to offer to run this question on their open traffic data. The results are not yet in. I will update when they are.

### Arterial Travel Time Studies

There are a variety of Arterial Travel Time studies for specific corridors, but nothing that is universally generalizable.  (And logically where people do arterial travel time studies, there is a congestion problem, otherwise why study it.)

I recall that in my childhood, I did a study in Montgomery County, Maryland using such data (from 1987 traffic counts and a floating car study published by Douglas and Douglas), I did not actually compute the percentage, but fortunately I reported enough data that allows me to compute the percentage now. (The sample is of course biased to what is measured). For the average arterial link, the speed was

 Variable Inside the Beltway Outside the Beltway Speed (km/h) 34.88 41.60 Length (km) 0.46 0.72 Time (min) 0.792 1.04 Downstream Delay (min) 0.27 0.24 Percentage of Signal Delay 25% 18.75%

Which is consistent with expectations that signals are more significant in more urbanized areas (inside the beltway is basically Bethesda and Silver Spring, MD), and with our general estimates. Now of course the speed here is impacted by downstream signals, and so is lower than the speed limit and certainly lower than the free-flow speed sans-signals. More details are in the paper.

### Engine Idling Studies

Moaz Ahmed pointed me to a Vehicle Idling Study by Natural Resources Canada.

The percent of time of vehicle idling ranged from 20-25%. (Not all vehicle idling is at signalized intersections).

(Engine idling of course burns fuel without doing work, so if the engine is going to be idling for an extended period, it would save fuel (and reduce air pollution) to turn it off. Turning the engine on and off also has costs, so the estimate was if idling was going to be longer than 10 seconds, it uses more fuel, but considering other wear and tear costs, the recommended threshold is if idling is longer than 60 seconds, then turn off the engine.  But at a signalized intersection, how will vehicles know how long they will wait? Smart traffic signals with connected vehicles could provide this, but now they don’t. Eventually this will be moot with a full electric vehicle fleet. Until that time, it matters. I suspect given the longevity and sluggishness of the traffic control sector, smart signals informing trucks will not be widely or systematically deployed before trucks are electrified.)

# Pedestrians

Now as noted above, Your Mileage May Vary. If you are a pedestrian, you are unlikely to hit a greenwave designed for cars, though of course your travel speed is slower is well. So redoing the Thought Experiment

## Thought Experiment 2

Imagine an urban grid.

• Assume 10 signalized intersections per km.
• Assume a travel speed of 6 km/h when in motion. (this is a bit on the high side, average pedestrian speed is closer to 5 km/h)
• Time to traverse 1 km=10 minutes + signal delay.  (Some of the distance traversal time overlaps some of the signal delay time, but we will imagine a vertical stacking queue, rather than one that has physical distance for simplicity, this is a much better assumption for pedestrians than vehicles.)
• Assume each intersection has only 2 phases.
• Assume fixed time signals at each intersection evenly distributing green time between N/S and E/W directions.  So red time = 1/2 cycle length.
• Assume 1 minute cycle length
• If a pedestrian stops, she waits 1/2 red time. (That is the “walk” phase for pedestrians is as long as the green phase for cars. Strictly speaking this is not true, it is more true in cities with narrow streets than it is in suburban environments with wide streets, as narrow streets can be crossed more quickly, so the amount of “walk” time allocated can be most of the phase. This is certainly not true in Sydney, where the “walk” phase is cut short so turning cars have fewer conflicts with late pedestrians.)
• Pedestrians obey traffic lights.  (This is not as good an assumption as vehicles obey signals, pedestrian signal violation is probably higher. This is not a moral judgment one way or the other, people tend to obey authority, even when authority abuses power.)
• Assume no platooning. (This is probably too severe, a quick pedestrian with some signal coordination can probably make a couple of lights in a row).

Here the average pedestrian will stop at 5 intersections for 15 seconds each = 2.5 minutes (vs. 10  minute in-motion time). In this case, 2.5/(2.5+10) minutes (or 20%) is spent waiting at signals. Now, this number is probably true for more pedestrians than the vehicle delay estimate is for vehicles, since pedestrians are more likely to be found on an urban grid and less in a suburban or limited access environment. (Self-selection at work).

# Bicyclists

If you are a bicyclist, you are unlikely to hit a greenwave designed for cars unless you travel at exactly an integer fraction (1/1, 1/2, 1/3) of the green wave, as your travel speed is slower is well. So redoing the Thought Experiment

## Thought Experiment 3

Imagine an urban grid.

• Assume 10 signalized intersections per km.
• Assume a travel speed of  20 km/h when in motion. (This is a typical for experienced riders). Time to traverse 1 km=3 minutes + signal delay. (Assume a stacking queue)
• Assume each intersection has only 2 phases.
• Assume fixed time signals at each intersection evenly distributing green time between N/S and E/W directions.  So red time = 1/2 cycle length.
• Assume 1 minute cycle length
• If a bicyclist stops, she waits 1/2 red time. (That is the ‘bike’ phase for bicyclists is as long as the green phase for cars.)
• Bicyclists obey traffic lights.  (This is not as good an assumption as ‘motor vehicles obey signals’, bicyclists signal violation is probably higher.)
• Assume no platooning. (This is probably too severe, a quick bicyclists with some signal coordination can probably make a couple of lights in a row).

In this case the average bicyclists will stop at 5 intersections for 15 seconds each = 2.5 minutes (vs. 3  minute in-motion time). In this case, 2.5/(3+2.5) minutes (or 45%) is spent waiting at signals in an urban environment.

## Strava Data

Strava, an app for tracking bicyclists and runners can produce some useful data. Andrew Hsu, e.g., reports “28 mile bike commute. 1:30-ish moving time. 10-15 minutes waiting at lights.” From this, for him, we estimate 15 / (15+90) = 14%. To be clear, 1:30 is an extreme commute. I don’t have access to the full database, and obviously this is biased by the nature of the trip.

# Buses

Alejandro Tirachini produced an estimate of travel time for buses finds delay at traffic signals (in suburban Blacktown, Sydney, NSW) is 10-13% of total time.