Monday, March 21, 2016

Capacity Case Study

Huch wood would a woodchuck chuck?  -or-  What is the real potential of a driverless system?

Lets start the devil we know. The present "system" is fairly well studied and, for all its diversity, exhibits fairly consistant behaviors across all its forms.  Different roads, weather conditions, and vehicles notwithstanding there is a common factor-- the driver. Drivers can be counted on to take a roadway of almost any design and reduce its capacity.   Give the driver a potholed, too narrow, and winding roadway and there will be more horns than progress. Create a broad, well lit multi-lane freeway and every commuter in the region will converge on it and create a parking lot. 

The driver, not the road, creates a fairly firm bottom line. The average capacity for a lane of traffic at highway speeds is about 1,200 vehicles per hour. Above this number and slowdowns and stoppages become inevitable.  At lower speeds the number increases marginally to a max of 1500 vehicles at 45 mph, but who wants to drive 45?  The bottom line is that it is not a large number (about one car every three seconds) and that it is inescapable, largely because it is rooted in the average driving abilities of a large and heterogenous population.

A driverless system, on the other hand, is all about the design of the road and the quality of the vehicles.   Its true capacity is intimately involved in the limits of technologies we haven't even fully explored yet. Theoretically this limit might be cars moving nose-to-tail down a single narrow lane at 150 mph (35,000 vehicles per hour, give or take). The practical limit is certainly lower, but by how much is above all an engineering question.

Case Study

Trying to determine the capacity of a driverless system therefore depends on creating a plausible picture of what technical capacities might be developed in the not too far distant future (our theoretical woodchuck). The case study that follows describes a mature technology, but not the theoretical limit of what can be achieved under controlled conditions. It imagines that two of Seattle’s most heavily utilized east-west arterials are converted to allow limited utilization be driverless vehicles.  It reserves the center lane for intermittent  (one minute out of five) use by automated traffic.

       The Pulse
Every five minutes or so a "pulse" of automated vehicles would pass down this center lane (westbound on 45th, eastbound on 50th).  Special signaling will alert traffic to vacate the center lane (and complete left turns) well in advance of automated traffic. Traffic at intersections along the route would be stopped in all directions and in a sequence allowing uninterrupted passage of vehicles at a steady speed of @ 35 mph along a route stretching from the UW to Ballard neighborhood in the west. The lane would be reserved for automated traffic for 45 seconds (including a 10 second warning period) every five minutes. Vehicles would travel in groups of three tightly spaced vehicles with three vehicle lengths between groups. Aggregation and disaggregation of vehicle groups would take place opportunistically as there would be no physical barrier between traditional and automated lanes. The lanes themselves, especially at intersections, would be heavily invested with sensors and the capacity to communicate directly with vehicles.


● 45 second passing times with 10 second warning period
● Automated traffic on 5 minute intervals
● 3 vehicle in each platoon, minimal spacing between vehicles (@16”)
● Average Speed 35 mph
● following distance between vehicle groups-- 3 vehicle lengths (@55')
● total platoon length = 3 vehicles (each 18') with following distance = 110ft

● Distance covered at 35 mph (@51 feet per second) = ½ platoon/sec = 1.5 vehicles/sec
● Total Number of vehicles in transit during available transit period at 80% efficiency = 45sec x
1.5 vehicles/sec x .8 = @54 vehicle capacity per transit period
● Total hourly capacity of Lane = 12 transit periods x 54 vehicles= 648 per hour 
● 35 mph Automated Lane 24 hr capacity = 15,500 (one way)
● Actual 45th street traffic (one way)=11,000 (max @ 900/hour)

It’s a startling result. A single lane of automated one-way traffic on an arterial such as
45th street, operating for less than one minute intervals every five minutes, could nearly double the one-way capacity of that arterial. A full time automated system would have about five times the capacity.

Extending the model to an interstate with its much higher speeds yields even more impressive results, especially if we keep following distances similar to the original model.

● 55 mph Automated lane hourly load capacity = 6,400
● Typical Freeway lane, hourly load capacity= @1,200
● 55 mph Automated lane 24 hr capacity (uninterrupted)= 153,000
● Typical freeway one-way 24 hr traffic (I-5 in downtown Seattle) = 150,000

Wit uninterrupted service a single automated lane (at 80% capacity) can carry the
equivalent of five lanes of traffic, essentially the entire freeway. 


The potential capacity of a driverless system is what usually fires the excitement of
someone who wrestles with the glaring inefficiencies of the modern car based transportation
system. Much of the time this excitement leads people to look at designing fully engineered
infrastructure, things like PRT’s. While it's fun to imagine the creation of a world tailored to
our transportation needs, history suggests a different path of change. The widespread use
of driverless cars would suggest a fundamental shift in our society and culture, and changes
that big must be driven by more than an engineered ideal. That is not to say that such an ideal
will not someday be reached. The reliability and efficiency of many systems, such as high
speed rail or the aviation industry in general, could hardly have been contemplated by even
the most enthusiastic visionaries of the 19th century. But the process of change is inevitably

From my office I overlook the ship canal bridge, an important component of I-5 as it passes through Seattle. Over 50 years old, the bridge carries vehicles whose basic design is older still. A driver from 1930 could more quickly learn to operate a modern car than he or she could learn to use a cellphone. The sheer scale of this structure, and the massive transportation system of which it is a small part, seems utterly resistant to significant modification of any kind. This is the story of the last half century. Will the next 50 years to be that much different?

Possibly. Changes on this scale do happen. History give us some idea of the dynamics that drive dramatic and rapid changes. It gives us examples of the forces that impede progress for long periods of time, and then drive it forward at speed when change finally does take place. That sounds like a big enough subject for another blog post eh?

45th Street at Latona, looking west.


  1. I love this concept! Is there more to it? Is this your own thoughts, or are you referencing another article?

    How are you accounting for the impact on the non automated traffic?

    I am a logistics major at University of North Texas and am fascinated with the progress of drivelers vehicles. Have you found any peer reviewed sources showing how much traffic flow will be impacted by the addition of driver less vehicles?

    1. No, this is more a "back of the envelope" calc, no hard data to go one. I'm fascinated by the subject as well (see all the entries on the apeless carriage blog), but even more about the possible implications for logistics. I'm working with a newly formed logistics consulting firm on sustainability issues in general, and we're trying to look ahead at what role autonomous vehicles might play logistics "best practices" in the future. Thanks for the comment!