The Capacity of a Personal Rapid Transit System

by J. Edward Anderson, Ph.D., P. E.

May 13, 1997


The purpose of this document is to explain the capacity needs and capabilities of the lines and stations of a PRT system, and to compare them with the needs and capabilities of conventional bus and rail transit systems. The capacity of a transit system depends on the size of the vehicles and on the minimum headway at which vehicles can operate safely and reliably day in and day out. The minimum safe headway of a PRT system has been a point of contention and is key to the discussion of the capacity of a PRT system. A major advantage of PRT is that, by using switchable vehicles sized for a single person or small party traveling together by choice and by placing all stations off the main lines, the trip time is competetive with automobiles and the guideway size and cost is low enough so that it is practical to deploy the system widely in networks even in less dense regions of a city. For the rider, the additonal advantages are travel, in seated comfort with one's own companions or alone, nonstop to the destination at any time of day or night. Optimized PRT provides a combination of accessibility, high service level, and low cost far beyond that possible with existing transit modes.

Transit Capacity Needs

Needs Determined by Experiment

To obtain a feeling for capacity needs in transit systems, consider people walking through a revolving door. The average spacing between individuals is rarely closer than about four feet, and average walk speed going through revolving door is somewhat less than the average speed walking down a sidewalk, which is about three feet per second. So assume two feet per second through a revolving door. With four-foot spacing between people, the average time headway would be two seconds, or an average of 1800 people per hour. If you actually time people going through a door, you find that the average time headway is usually no less than about three seconds, or 1200 people per hour. I measured the average time headway between people deboarding a loaded 747 aircraft and found it to be close to three seconds.

If you time cars coming out of a parking ramp, you find again an average of about one car every three or four seconds if they don't have to pay a fee upon exit. I once timed cars coming out of a full parking lot onto an arterial street after a hockey game in a 20,000-seat stadium and found again a headway in the range of three to four seconds.

When exposed to the concept of PRT, the first question most people ask is how it would handle the people coming out of a major sports event. Being interested in the question, I have observed what usually happens now as people leave an event. They walk to their cars in a parking lot or ramp and they wait, sometimes for 30 to 40 minutes, while the cars leave at a rate of about one every three to five seconds. So, typically over an hour is required for 1000 cars to leave. I watched people coming out of Fenway Park in Boston after a baseball game. Many go to the Kenmore Square subway station where they must walk slowly about four or five abreast through a tunnel to two ticket booths and two turnstyles, through which about one person every two to four seconds can pass.

I taught a class in transportation engineering to Boston University freshmen and at the beginning described PRT. One question was how PRT could handle the people coming out of the John Hancock Tower where 5000 people work. I had the students do various kinds of traffic surveys and one group of three decided to count the people coming out of the John Hancock Tower at the busiest time in the evening, around 5 pm. They talked to the guards to be sure that they covered all of the exits. They found, to their surprise, that only 1200 people came out in the busiest hour, or an average of one every three seconds. People don't all rush into or out of a building at once!

So, it seems that a transportation system that can move in the range of 1200 people per hour is quite significant. Today in most cities in the U.S. transit handles only a small fraction of the trips. Even into and out of central business districts, a mode split to transit of 20% is high. Suppose that a PRT system does so well that it moves 50% of the trips. Then a PRT system that handles 600 people per hour from a given point will cover a wide range of demands.

Needs Determined by Theory

As another way of examining the travel demand into and out of a station, consider a city of uniform population density. In typical American cities there is a total of about three vehicle trips per person per day of which about 10% occur in the peak hour. Thus, the number of peak-hour trips/sq-mi is about 0.3 times the population per square mile. Consider a square PRT network having east-west and north-south lines, each in alternating directions, spaced half a mile apart, which is a typical distance between major streets and a spacing that will place everyone within a quarter mile of a station, if the stations, as we will assume, are at the midpoints of each pair of intersections.

Let the population density be 12,000 persons/sq-mi, which is high for most U.S. auto-oriented cities. Then, within one of the quarter-square-mile squares between lines there would be 3000 people and, in the busiest hour, 900 trips. But each of four stations on the lines bounding a square serves two squares, so there are two stations per square, giving an average station-flow requirement of 450 persons per hour. But this is the total number of trips. If a PRT system were to be so successful as to attract half of these trips, the station-flow requirement would be only 225 persons per hour. As a formula, the station-flow requirement for all modes of vehicle travel is:

Peak-Hour Average Station Flow = 0.15(Pop. Density)L2

in which L is the line spacing.

It turns out that the formula for the peak-hour average line flow is obtained by substituting the average trip length, Ltrip, for one of the L's.


Peak-Hour Average Line Flow = 0.15(Pop. Density)LLtrip.

An average trip length by bus in a typical U.S. city is in the range of three to four miles, and the average auto trip is typically seven to ten miles. Suppose the average PRT trip length is in the middle, say five miles. Then with 50% of the trips on PRT, the peak-hour average line flow would be 225(5/.5) = 2250 people per hour. If there were say an average of 1.2 people per vehicle in a PRT system (increased over rush-hour auto occupancy by charging a fare per vehicle), the vehicle flow would be 2250/1.2 = 1875 vehicles per hour, corresponding to an average headway of 3600/1875 = 1.92 seconds.

Considering that in the U.S. the average mode split to transit is less than 3%, the described PRT system would be wildly successful, but it could quite likely not be able to attract 50% of the trips, nor would that be necessary to make a huge difference in congestion. It is interesting to observe that the line flow thus calculated is only a little more than the maximum exit flow from a parking structure. By comparison, the flow on a freeway lane under the best conditions does not exceed the range of 1800 to 2000 vehicles per hour. Thus, an extremely successful PRT system in a city of 12,000 persons/sq-mi need handle on each line no more than about one freeway lane of traffic. There of course will always be points where the flow will be higher, two to three times higher.

Rapid Rail Capacity vs. Needs

It is often advertised that a rapid rail system can handle up to about 40,000 trips per hour, which corresponds to 20 freeway lanes of traffic under the best conditions. Where does one need such capacity? During the 1970s, it was stated by Denver transit promoters that there was a transit requirement for 14,400 people per hour per direction, or more than seven freeway lanes of traffic in one direction under ideal flow conditions. Denver has a population density of about 5000 persons/sq-mi, so why would there be a need for such a high flow on a transit system in a city with a transit mode split at the time of about 2%?

Such total traffic flows occur only in dense cities in which the flow from about a quarter of the city is concentrated onto a single corridor. And even then there are few cities in which the freeways have seven lanes in each direction. In the Twin Cities, in the early 1970s, it was stated by rail advocates that there was a transit requirement for 15,000 persons per hour per direction, which happened to be the capacity of a system then being promoted.

Actually, these extraordinary demands occur only in very dense cities such as New York, in which transit ridership is very high. With a PRT system, by networking, the demand on each line is substantially reduced.

Capacity Capability of a PRT System

In railroad practice, the minimum headway between trains is determined by the condition that, if one train stopped instantaneously the train behind can stop before a collision occurs. This is called a "brick-wall stop." To provide a margin of safety, the minimum headway is usually taken to be at least two of such stopping distances. Since trains stop on-line so that each would block the train behind, the headway is determined by the flow into and out of stations, and the trains are long. Combining these factors results in minimum headways of around two to three minutes. Thus, train engineers have been baffled by statements that PRT systems could run safely at fractional second headways.

In a PRT system, all of the stations are off-line, on by-pass guideways. Thus station stopping is not involved in determining the safe main-line headway. As mentioned, in railroad practice the safety philosophy must be that if a brick-wall stop occurs, the train behind must stop before colliding. But, if a train stops instantly, people have already been killed.

A PRT system runs on an exclusive guideway, usually elevated. Its safety philosophy must and can be that even if there is only one vehicle on the guideway there is no reasonable way for it to stop suddenly. One would like to say that it would be impossible for a vehicle to stop suddenly. Going back to the train, one can design the system so that there will be no collision if there is one major failure. However, suppose the brakes fail just as the train ahead derails. This is what in technical jargon is called "simultaneous major failures", i. e., at least two major failures occuring so close in space and in time that the conditions for a collision are set up. This can happen, but in a well-designed system its probability is so low that we live with it, notwithstanding occasional collisions.

Careful analysis of failure modes in a PRT system shows that it is possible to design the system in such a way that a sudden stop can occur only if there are at least two simultaneous major failures plus what is often called an "Act of God" event. In this case the Act of God would be an "out-of-the-blue" voltage pulse of an exact shape and duration needed to throw a solenoid. In a properly designed PRT system, the mean time between such events is measured in millions of years. Using failure-modes-and-effects analysis (FMEA), it is practical to design a PRT system in which the minimum safe headway is well under one second. Such systems will use checked redundant computers and monitoring of every reasonable cause of a failure. For the past two decades, serious PRT designers have designed for headways at least as close as a half second.

This year the National Automated Highway System Consortium plans to test ten Buick LeSabres running on a special highway near San Diego at 50 mph at a bumper-to-bumper spacing of only six feet. This corresponds to a 0.3-sec headway. At 30 mph, a more reasonable urban PRT speed, half-second headway corresponds to a nose-to-nose spacing of 22 feet. With nine-foot-long PRT vehicles, a practical length, the bumper-to-bumper spacing is 13 feet. Thus a position tolerance in the range of a few feet would be satisfactory, yet with today's control systems it is practical to control the spacing to a few millimeters.

If the minimum headway is half a second, the average headway in the rush period will generally be no less than about one second. Thus an average PRT line flow of 3600 vehicles per hour is practical, which is roughly equivalent to two freeway lanes operating under ideal conditions in which a speed of at least 30 mph is maintained. When the speed falls off, as it does every day in congested areas, the throughput of a freeway lane drops rapidly. By comparison with bus systems, if the PRT system averaged only one person per vehicle, a system of 60-passenger buses each full of passengers would have to operate at one minute headways to achieve the same capacity.

Movement of Empty Vehicles

Many simulations of PRT systems have shown that about one third of the vehicles in the system will be empty. Such vehicles are automatically rerouted to stations where they are needed. A checked-redundant station computer observes and manages the flow through each station. When an empty vehicle parked in the first berth in a station is not needed, the station computer commands it to go to the next station. On the incoming side of each station, the station computer checks each approaching vehicle. If it is occupied and is destined for that station, the station computer commands the vehicle to switch into the station, otherwise it is ordered to go to another station where it is needed.

In a properly designed PRT system, the chance that there is no room is very small, but if such an event occurs, the vehicle is switched away. If the approaching vehicle is empty, the station computer, knowing if it needs an empty, determines, in cooperation with the central computer, if it is to be switched in. Knowing how many passengers are waiting at each station, the central computer may request that a particular empty vehicle bypass a particular station for another in which the demand is greater.

Near each line-to-line diverge point there is a diverge-point computer that determines which way each vehicle, empty or occupied, should switch. This computer is also in communication with the central computer, where knowledge of the number and wait time of waiting passengers at all stations is known, and the whereabouts of all vehicles in the network, empty and occupied, is known. Based on this knowledge, which improves as the computer "learns," empty vehicles are switched to meet demands in an optimum way. Near the end of the day, when fewer vehicles are needed, excess empty vehicles are switched into storage stations. Since it is not necessary to get a specific vehicle out of storage at a certain time, as is the case with automobiles in parking structures, the volume required for storage is surprisingly modest. In an n-berth station, generally at least n-1 vehicles will be stored overnight, ready to serve demands at any time.

Station Capacity

The simplest PRT station has a single by-pass guideway and a number of loading berths, generally varying from two to about 12, used for both boarding and deboarding. A disadvantage of such a station is that someone slow to board or deboard slows down everyone behind. But the important variable is the statistical average, which is generally reasonably short, particularly in the rush periods where people move quickly to work or home.

Parallel by-pass guideways could be built if necessary, but usually have an unfavorable ratio of added benefit to cost. Numerous analyses and simulations have verified that the capacity of stations with a single bypass guideway varies from about 300 vehicles per hour through a 2-berth station to 1300 vehicles per hour through a 12-berth station. As shown above, such stations, sized to demand will serve a very wide range of needs in all cities except those of very high density. In dense cities, system capacity would be at least doubled by placing lines every two blocks instead of every four blocks apart. An advantage of PRT is that each station can be sized to its own demand, whereas, in a rapid rail system all stations must be sized to the longest train.

Final Comment

A PRT system, properly designed, can serve a very wide range of transport needs in a typical urban area. It can be sized to meet reasonably high peak demands with average waiting times (not discussed above) of less than three minutes any time of day or night. But, to meet the highest possible peak demands quickly will require additional costs not necessarily commensurate with the benefits. As is the case today, when very large concentrations of people want to leave at the same time, they will not be able to do so, and observation shows that they don't try to do so. Many will have to wait just as they do now when leaving concert halls or sports events.

J. Edward Anderson is President and CEO of the TAXI 2000 Corporation. He can be contacted via e-mail at


Last modified: August 27, 1998