Assessing the Capacity of a PRT Network
by J. B. Schneider
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.
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