Assessing the Capacity of a PRT Network
November, 1998, updated 02/20/2010
Capacity Concepts and Definitions in
Relation to PRT Network Design
The ideal way to define the capacity of a Personal Rapid
Transit (PRT) network is to ask: Is it capable of moving X
people from their origins to their destinations, during a
specified period of time, with a specified areawide or
station-specific average (or median) waiting time? Such a
definition deals with the PRT network as a system instead of
a set of individual links with particular physical
properties. Describing the physical capacity of an individual
PRT link is somewhat helpful but it is the overall system's
carrying capacity that is of greatest importance to the
evaluation of any proposed PRT project. It is also needed to
compare PRT with other competing transit modes, such as Group
Rapid Transit (GRT) and Light Rail Transit (LRT).
There are three main dimensions to the problem of
estimating the capacity of a PRT network. One is the physical
attributes of the network itself - the route layout and its
geometric properties, the number, size and locations of the
stations and the number, size and locations of the storage
and maintenance facilities. A second is the control software
used to control the movements of individual PRT vehicles.
There are several variables in the software that can be
controlled by the system operator which will affect the
capacity of the system. Some examples are: 1) setting the
minimum headway (distance) between adjacent vehicles, 2)
selection of the parameters that will determine how empty
vehicles are stored for recall, and 3) setting the maximum
speed of vehicles on the mainline guideway and 4) determining
how many vehicles are available in the system. The third
dimension, critical but often ignored, is the spatial pattern
of the demand for service, which is usually presented in the
form of a future year Origin/Destination (O/D) matrix
(table).
In all PRT planning studies, one must generate a
forecast (e.g. 10-15 years in the future) of demand which
describes the number of people likely to arrive at each
station in the network during the specified time period,
their propensity to travel together in groups and their
destinations. Such a forecast is difficult to derive, fraught
with uncertainty and should be treated only as a rough
estimate. Still, the PRT network design should be able to
accommodate this "best estimate" of the demand for
service, as well as a variety of other likely levels and
spatial patterns of demand. As in all design studies that
deal with uncertain demands (loading patterns), one or more
safety factors are needed to insure that it can handle loads
that are substantially different from those generated by the
"most likely" forecast.
Various factors influence the pattern of flows in such a
matrix. Time of day, day of the week, season, special events,
expected land use changes, fare policies, employer or
retailer programs to promote PRT ridership, recreational
riders (locals and their visitors plus tourists) are
examples. As these factors come into play, singly or in
combination, the spatial pattern as well as the total
quantity of people to be served will change.
The numbers in the cells of this matrix indicate the
number of persons who are expected to wish to travel from
each station to all other stations during a specified period
of time. These values are forecasts and represent the demand
for PRT service at some future time. The degree to which the
flows in this matrix are uniformly distributed will strongly
influence the capacity of the PRT system. All else being
equal, greater uniformity will yield greater capacity. But,
if some flows in the matrix are large, relative to the
average, the capacity of the system will be diminished due to
the difficulties of managing convergent traffic at a few
stations and larger numbers of empty vehicles. Clearly, as
the number of empty vehicles moving about in the system
rises, the capacity of the system falls and its economic
viability is diminished.
One must deal, simultaneously, with all three of these
components when assessing the capacity of a PRT system. To
simplify this task, the physical characteristics and
operating regime typically are held constant and the network
is "loaded" with the values in the O/D matrix. This
description of system demand is chosen to represent a maximum
load on the system, - i.e. the design year requirement. If
this requirement cannot be satisfied by the initial design,
then physical design modifications and/or changes in
operating policy can be made to see if a satisfactory result
can be obtained.
Until such time as a powerful optimization technique
becomes available for dealing with this problem, solutions
will have to be derived from a trial-and-error process. This
is similar to many types of engineering design problems which
have not yielded to mathematical optimization techniques. The
problem is made more complicated by the fact that some
physical design changes (e.g. adding a station, moving a
station) will produce changes in the O/D matrix that can, in
turn, modify the performance and capacity of the system.
With these concepts in mind, it should be clear that the
estimation of the capacity of a PRT system is not a simple
task. There is no one answer to this question that will stand
up under the wide variety of questions that may be asked
about it. It reminds one of the old (pre-digital) analog
computers that presented the user with a set of dials, each
of which could be rotated through a range of values. For each
setting pattern of all of the dials, the computer would
generate a "solution" to the problem at hand.
Changing the setting of any one of these dials would generate
another "solution" to the problem. Each solution is
correct for the situation represented by the pattern of dial
settings but no one solution is more correct than any other.
The capacity of a PRT system is similarly determined by the
numerous values specified for the three main dimensions
described above.
Load Testing the Proposed PRT Network and Associated
Operating Policies
The arguments above suggest that a given physical
network and PRT operating policy will have several
"capacities" that are a function of the load
imposed upon it (i.e. the values in the O/D matrix and travel
group size propensities assumed for the future year
assessment). This fact indicates that one needs to explore a
variety of likely loading patterns to see if the given
physical network can satisfy everyone's trip desires with an
acceptable areawide waiting time at the points of origin (PRT
stations). This task is far beyond the capabilities of any
type of intuitive or manual approach. It can be done only
with the aid of a computer-based
simulation model and a set of carefully designed
tests.
The simulation model has to be a true representation of
the control system and empty vehicle management strategy that
would actually be used to operate the PRT system. The
projected demand at each station has to be modeled by an
"arrival" distribution that approximates the rate
and arrival pattern at each station during the time period to
be simulated. Not all stations will be the same in this
regard. Finally, the assumed willingness of people to travel
in groups has to be based on realistic assumptions until such
time as empirical data are available to deal with this
problem (i.e. after a PRT system has been built and operated
for some substantial period of time). Again, the propensity
to form groups should not be assumed to be identical at all
stations as the people using certain stations are more likely
to know each other and be more likely to travel in groups
than alone or in pairs.
This testing process should be somewhat similar to the
process that a structural engineer uses to understand how a
particular design for a building (or bridge) will stand up
under different (static and dynamic) loading conditions,
including shocks from the movement of soil, rock and
foundation elements associated with earthquakes of different
magnitudes occurring in different locations at different
times. The results are not a single number but consist of a
range of numbers, each of which is associated with a
particular set of loading assumptions. PRT networks need to
be subjected to the same kind of load testing which will lead
to a comprehensive assessment of the capacity characteristics
of the network design and operating policies. It is likely
that such results will lead to the redesign of some of the
physical elements of the network or to changes in operating
policies - or both. This is, of course, true of the building
or bridge design process as well.
Since there are so many uncertainties involved, it may
be useful to try to determine the demand level at which the
system's capacity could be said to have reached a maximum
value. Loads beyond this value can be expected to result in a
"failure" - defined as a situation when the waiting
time standards would be violated. There are at least two
types of waiting time standards that could be considered: (1)
an areawide standard and (2) a station-specific standard.
These two measures are not likely to be in agreement all of
the time. One can have a satisfactory areawide waiting time
with waiting times at one or more stations being unacceptably
high.
Probably, the station-specific standard (i.e. wait times
should be no larger than X minutes at any one station) would
be harder to satisfy that an areawide standard. However, use
of a station level standard would eliminate situations where
some people at some stations might have to wait 10-20 minutes
for a ride while the areawide standard was satisfactory. One
could decide what an unacceptable wait time standard to use
and then increase the maximum expected load (e.g. ratio it up
proportionally) on the system in successive increments until
that value is reached. This load could be called the
"maximum capacity" that is produced by a given
network design and the assumed set of operating policies.
If the areawide standard wait time is used, it is likely
that one or more stations would have unacceptable average
wait time even though the areawide average value was judged
to be satisfactory. Alternatively, one could apply the
maximum waiting time criterion to each station in the network
and when any one of them reached this level, the system could
be said to have reached a maximum capacity. Such an approach
is similar to the "load it until any structural member
fails" testing routines used in a variety of engineering
fields.
The results of such a testing program would result in an
O/D matrix that could be said to represent the
"capacity" of the PRT network and associated
operating policies. Simply stated, it might indicate that
this PRT network and operating policy is capable of moving
X-thousand people with a maximum wait time at any station of
Y- minutes during a Z- hour period.
Explaining PRT Capacity Concepts to Prospective PRT
Clients
Given the above discussion, what does one say to the
elected official, developer, interested citizen or investor
that asks: How much capacity does PRT offer - compared to
some conventional transit mode that is "proven"?
Clearly, this is a complex question that does not have a
simple answer. Yet, it must be answered - as PRT is unlikely
to become a mainstream transportation technology unless and
until it can be answered in a manner that is comprehensible
to people who must be convinced that it is a worthwhile
investment. What are the possibilities?
Clearly, one must be able to "prove" in a
convincing and understandable way, that a PRT network can do
the job (i.e. satisfy the demand with a reasonable waiting
time) in a particular location during a particular time
period. This can be done only with reference to a given
physical design, a set of reasonable system operating
parameters and a computer-based simulation model that uses
the same control and empty vehicle management system that
would be used by the actual system. The simulation model
should provide the user with graphic displays that show how
the system (particularly its stations) is operating under
different loading conditions and should be capable of
responding to a wide variety of "what-if"
questions. It should highlight problems in system operation
so they are clearly visible and easily recognized with
graphic symbols and/or audio to provide clues as to how the
network's physical design might have to be altered to deal
with them.
For example, if the wait time at a particular station is
always well above the areawide average, it should be possible
to add some berths to that station quickly and rerun the
simulation to see if that change reduces or eliminates the
problem -- or merely shifts it to another station. Or,
perhaps adding 20 more vehicles to the system would
accomplish the same objective with far less effort and cost.
It is not likely that many lay persons would be willing
to sit through one or more such testing exercises. However,
it might be possible to get the more technically inclined
transportation planners to do so in a given situation. If
these people can be convinced that the PRT technology can
deal with their problem, they may be willing to assure others
of the wisdom of making such an investment. Certainly, it is
unlikely that elected officials or investment bankers will
approve a PRT plan without the supportive testimony of
credible transportation planning professionals. These
risk-takers need to bring the perceived risk of investing in
PRT down to pretty low levels -- as the media is likely to
spotlight the performance (or lack thereof) of the first few
PRT projects in a highly visible manner.
Conclusions
First and foremost, one should look for PRT applications
that exhibit a strong many-origins-to-many-destinations
travel demand pattern throughout much of the day. In such
cases, the capacity of the PRT network is likely to be as
large as possible ( i.e. load factors will be high) and
waiting times as small as possible. Such a network is also
more likely to be able to provide the capacity flexibility
needed to cope with the spatial-temporal fluctuations in
demand that are likely to occur over time and in response to
system extensions.
Second, it is likely that one will have to design a PRT
network, estimate a most likely travel demand matrix (O/D
table) and be able to simulate its likely performance with a
computer-based simulation model, capable of addressing
quickly but credibly a variety of "what-if"
questions in a "hands-on" mode of operation. This
is the only way that local or project planners can be assured
of the viability of the PRT technology for their particular
application. Without the support of these people, elected
officials and others whose support and approval is needed is
not likely to be obtained. Obviously, considerable effort
would be required to accomplish these two objectives but
without them, doubts about PRT's capacity sufficiency will
still be a major impediment to the acceptance of the PRT
technology in those crucial initial application
opportunities.
Last modified:
February 20, 2010