Automated Microbus Systems and Operations

Automated Microbus systems with 2, 5, 9, and 10 stations are analyzed, but first the advantages of high frequency service are reviewed.

High frequency vs. high speed for short trips

For short trips, frequency of service is more important than speed. The table below compares a 25 mph (40 kph) system with two 60 mph (97 kph) systems. Trip length is 2 miles (3.2 km), and trips are non-stop. The slower vehicles depart every minute, while the corresponding number is 4 minutes and 7 minutes for the 60 mph systems. The vehicles are assumed to run at full speed from the moment they leave the station, an approximation that favors the 60 mph system, which will actually take longer to reach top speed. The average wait time will be half the service frequency.

  Average Time Average weighted time (wait time weighting factor = 2.5) Maximum time
25 MPH (40 KPH)
1 min frequency
0.5 avg wait
4.8 travel  
5.3 total
1.25 avg wait
4.80 travel  
6.05 total
1.0 max wait
4.8 travel  
5.8 total
60 MPH (97 KPH)
4 min frequency
2.0 avg wait
2.0 travel  
4.0 total
5.0 avg wait
2.0 travel  
7.0 total
4.0 max wait
2.0 travel  
6.0 total
60 MPH (97 KPH)
7 min frequency
3.5 avg wait
2.0 travel  
5.5 total
8.75 avg wait
2.0 travel  
10.75 total
7.0 max wait
2.0 travel  
9.0 total

The cell with the shortest time in each column is shown with a green background, while the longest time is in red. It can be seen that a 60 mph system with a 7 minute frequency is slower than the 25 mph system by all measures, while the 25 mph system is quicker than even the 4 minute, 60 mph system in Average Weighted Time and Maximum time. The weighted time is important because most mode choice models assume riders dislike waiting roughly 2.5 times as much as traveling, so the 25 mph system should have the highest patronage.

Operation of Automated Microbus systems

Microbus system with two stationsThe Automated Microbus is a six-passenger automated vehicle operating on an exclusive two-way roadway. Top speed is 25 mph (40 kph). Vehicles are shared, not private, and most trips are non-stop origin to destination. The simplest possible Microbus system would consist of two stations connected by a two-way exclusive roadway. Vehicles would leave every minute from each end, and more often if demand warranted. However, a trip would be skipped if 1) no one boarded and 2) the vehicle wasn't needed at the other end. The one-minute value for headway is arbitrary, but was chosen because a lower value would not improve service significantly (although shorter headways might be needed for greater capacity).

In periods of low demand, many vehicles would carry one person, but because the Microbuses are small and with limited power, this shouldn't lead to excessive costs. Studies by the U. S. Department of Energy show that 4-passenger Neighborhood Electric vehicles use about 2 cents worth of electricity per mile. A reasonable expectation is that the 6-passenger Microbus would use 6/4th this amount, or about 3 cents per mile. Other costs, such as tire and brake wear should be minimal because of limited acceleration/deceleration rates (although battery replacement cost could be significant).

The fleet size will depend on demand and on the length of the exclusive roadway connecting the stations. To keep the calculations simple, it will be assumed that vehicles spend one minute at each end, and half of this time will be allocated to the trip in which the vehicle arrives, and half to the departure trip. The minute includes an allowance for dwell time and time lost in acceleration/deceleration when leaving/approaching a station. Otherwise, the vehicles travel at a constant 25 mph (40 km/hr).

If the distance between stations is one mile, the one-way trip time is 0.5 min + (1 mile)/(25 mph) + 0.5 min = 1.0 + 2.4 = 3.4 minutes. Each vehicle can make 60/(2*3.4) = 8.8 round trips per hour, or a round trip every 6.8 minutes. Rounding up to 7.0 minutes, this means a fleet of 7 vehicles would be sufficient to provide a vehicle leaving each end every minute. The table below gives fleet size for various distances and two headways.

miles (km)
One-way trip time = 1.0 + 60*distance/(25 mph) Fleet size (without spares), 1 min headway, 360 seats/hr Fleet size (without spares), 10 sec headway, 2160 seats/hr
1.0 (1.6) 3.4 min  7  42
2.0 (3.2) 5.8 min 12 78
3.0 (4.8) 8.2 min 17 102
4.0 (6.4) 10.6 min 22 132

The fleet size values in the one-minute-headway column were derived by doubling the one-way time and rounding up to the next integer. The rightmost column has values for 10-second headways to show that Microbuses can handle fairly high volumes, while still operating at headways well below their ultimate limit of 5 seconds. The figures in the 10-second-headway column are not from precise calculations, but are simply six times the values in the one-minute-headway column. If the vehicle cost is estimated at $100,000 in quantities of 100+, then the vehicle cost per two-way mile for a four-mile system capable of carrying over 2000 pphpd is 132*100,000/4 = $3.3 million. This is an approximate value, since the actual number of vehicles needed would be somewhat higher to allow for those out of service, and to store a few empties at each end in case of an upward fluctuation in demand.

A step up in system complexity is a single Microbus line. The example considered has five stations and provides access to a rail station:

Microbus system with five stations

Close-up of Microbus system with five stationsA close-up of part of the system is shown at right. While the Microbus stations are all near an arterial, the main Microbus line is set back 400 feet (120 m) in this particular example, and is assumed to run next to a freeway or along an abandoned rail line or some other suitable right of way. Each station is connected to the main line by a short spur which joins the main line in a "T" intersection. The entire system is at grade, except for short tunnels or bridges (not shown) to cross roads or other obstacles. The main line is about two miles (3.2 km) long, with stations every half mile (0.8 km).

Alternative sets of Microbus routesTwo alternative sets of service routes are shown in the diagrams to the right. While the two-station system discussed above had only one possible route, the five-station system has ten possible non-stop station-to-station routes, as shown in the upper diagram. It can be seen that four routes share the main line Microbus roadway between Stations 1 and 2, and also between 4 and 5. The roadway is used by six routes between Stations 2 and 3, as well as 3 and 4. Since the minimum headway on the roadway is assumed to be 5 seconds, then all ten routes could be run with headways as short as 30 seconds (5*6 = 30). There are probably limitations at the T intersections that would reduce capacity, but they will not be considered here.

Running direct service between every station pair can be inefficient if demand is not uniform. For the system shown, it's reasonable to assume heavy demand to and from Station 1, near the rail station, and lighter demand for trips among Stations 2, 3, 4, and 5. With every station pair having its own route, many vehicles traveling from, say, Station 3 to Station 4 would have only one passenger, even during peak periods. In order to use Microbus roadway capacity and vehicle seats more efficiently during peak periods, the routes shown in the bottom diagram may be desirable. One route consists of local, all-stop service from Station 2 to Station 5, and back again. The route doesn't include Station 1, since non-stop service to and from that station is available everywhere. Some riders would have to make intermediate stops, but the percentage should be small, since most are going to or from Station 1. With local service, a trip couldn't simply be canceled if no-one boarded, because the vehicle might be needed farther down the line. In periods of low demand, with most vehicles on all routes having 1 or 2 passengers, it would probably be better to revert to non-stop service between all station pairs, knowing that most trips will be skipped because no one boards.

Close-up of part of two Microbus linesA second Microbus system with five stations would give access to the rail station from another direction. As shown in the drawing to the right, the second system could be a mirror image of the first. The two systems would be essentially independent, and anyone who wanted to travel from one system to the other would first travel to the Microbus station nearest the rail station, deboard, walk through the rail station, and then board at the other Microbus station. If there were very little demand for travel between the two Microbus systems, the two independent systems could be the most efficient layout.

Close-up of part of Microbus system with 9 stationsIf there was substantial travel between the two sides of the rail station, then it might be worth while to connect the two systems as shown on the right. With a tunnel under the rail line, Microbus passengers could travel between any two of the nine stations. However, during peak periods, it would still be the policy to require riders to transfer at Station 1 to travel from one side of the system to the other. By not attempting to provide direct service between every station pair, it will be possible to achieve higher average vehicle occupancies.

In the off-peak, riders would be able to travel non-stop between any pair of stations. Since the number of possible non-stop routes connecting station pairs would be 9*8/2 = 36, it would probably not be practical to have scheduled service, even if trips were skipped when no one boarded. Instead, vehicles would wait in stations and users could walk up to one and select its destination before boarding. The vehicle would then wait half a minute or so with the destination name displayed before leaving, in case anyone else was going to the same station. If demand were low enough, each person or group traveling together could be guaranteed their own vehicle. When a user selected a destination, it wouldn't be displayed to others, and the vehicle would leave almost immediately. In this mode, the Microbus would operate like a Personal Rapid Transit system.