William G. Turnbull

We have had considerable discussion in these proceedings on the advantages of specific hardware, the type of guideway, the need for a specific variant of dualmode, and similar issues. These have been mostly related to the vehicle itself. Judging by the papers posted on this site, there has been very little thought given to the operation and control of an extensive, fully implemented system. As some may recall , I believe this to be a serious omission. Accordingly, if for no other reason than to stimulate the needed debate, I submit these thoughts.


A. General

The principal reason for building a dualmode or PRT system is to move people about more quickly and conveniently, without requiring significant additional real estate. I know there are numerous other advantages, but this remains the primary one. Thus it is incumbent upon us to make optimum use of the guideway. This means high speed and close-packed operation. Of course, these must be moderated to be consistent with both safe and economic operation.

To realize the advantages of high speed, all station operations must be off-line. That is, any acceleration to or from the system speed is accomplished on an auxiliary guideway – all operations on the main line are at the maximum, and only operating velocity. This specifically includes switching to and from the main line. This is not a new idea, other have expressed similar views; but I believe it sufficiently important and basic to bear repeating.

The question of how close-packed requires additional examination. Maximum efficiency would indicate only a few feet at most. At 125 miles per hour, as some have advocated, the vehicle is traveling at over 183 feet per second (55.9 meters/second); or one foot (0.305 meters) in less than 5.5 milliseconds. In electronics a millisecond is a long time; with accelerating mechanical devices it is a very short time, particularly when it involves large masses. I am uncomfortable with accelerating a variable mass from a standing start to system speed and inserting it into a traveling slot with a tolerance of a few milliseconds. It should be noted that this acceleration zone can be from several hundred to several thousand feet long; it is a function of the square of the target velocity. Thus consideration of this may limit the system speed. I am not arguing that it could not possibly be done; I do suggest it offers an opportunity for collision that need not exist.

Instead, organize the vehicles in packets of a maximum, of say, 20 to 25 vehicles in intimate contact. Between the packets, provide a minimum separation, or headway, of something like 100 to 150 feet, possibly more for very high speed operation. Incoming vehicles would enter in the inter-packet headway, accelerate slightly and attach themselves to a passing packet.

Departing vehicles would have to depart from within the packet. But the problem is very much simpler in separation. By definition there is no initial relative motion. Thus If the angle that the departure track makes with the main line is small (3 to 5 degrees), a minimally compliant connection would allow the departing vehicle to simply slide sideways until it is clear. We must at all costs avoid the possibility of the departing vehicle pulling other vehicles off the guideway, thus it is essential that there be no transverse forces applied between exiting and remaining vehicles. As a redundant safeguard, before departing, a short separation of the departing vehicle from the rest should be created. After the departure, the remaining vehicles then move up to reform the packet.

A significant advantage obtains from intimate contact within the packet. In the event that unscheduled braking is required, there will be no opportunity for relative motion to build up between the vehicles and the packet will slow as a single entity. Moreover, by concentrating all excess space between the packets; aside from facilitating entry, we also provide room for following packets to execute emergency braking.

The coupling between individual vehicles can be either electronic or mechanical. By electronic, we mean simply that each vehicle maintains a small positive force on the preceding vehicle to assure an intimate contact.

A mechanical coupling would simplify the dynamics of intra-packet motion. Railroads and subways have been dealing with multiple engines for years. On the other hand, they don’t have to deal with in-motion de-coupling. While the mechanical details are not essential to this discussion, it is imperative that the design be such as that it can impose only longitudinal forces, and essentially none transversely. Before any departure action could be undertaken, all coupling to the departing vehicle must be severed; and if for any reason it was not, it should still be possible for the mechanism to simply slide apart, with little or no application of transverse force.

B. System Speed and Packet Operation

Although the issue of system speed has been referred to previously, it is an essential part of the operational philosophy and is thus worth further discussion. The idea is to mandate that all movement along the main track be at a constant velocity. Once a vehicle enters the system, it is essential that we be able to accurately anticipate the associated packet’s arrival at each transfer station; accordingly, each packet must pass specified locations at precise times. We allow for minor separation in exiting, but this involves only inches. Moreover, the velocity of the packet leader remains constant. After an exit, the remaining vehicles increase velocity slightly and re-establish the packet. Thus the packet velocity remains constant.

A minimum headway, consistent with safe and efficient operations, must be maintained, always. Headway discipline, along with system speed and precise packet positioning, are enforced by the packet leader (i.e., the lead vehicle in the packet) which must continuously monitor and maintain these. The sundry monitors, discussed below, also provides a redundant oversight of these quantities and may institute corrective action or close down portions of the system if necessary.

While the maintenance of headway is essential for safety; for maximum efficiency we must also accommodate an optimum packet size. The set periodic intervals, referred to earlier, provide main line space for the specified maximum-sized packet and the requisite headway between packets.



A. General

The general approach to controlling operations is reflected by a distributed, somewhat benevolent, computer system - rather than specific commands, superiors provide general guidance to subordinate computers. It is specifically not intended that the system maintain real-time control of upwards of a hundred thousand vehicles spread out over thousands of square miles. That would constitute a daunting, if not impossible, task. Moreover, a failure in any part of the system could jeopardize the entire system.

Thus, the intention is to distribute decision-making to the lowest practical element. The vehicle makes many of its own decisions, including initiating the switch to other lines, and/or to exit the system. While it lacks authority to launch on the system; once launched it proceeds inexorably to is destination; deferring to the packet leader during main line packet operation, and to the transfer station during transfer operations.

Although this may sound like a recipe for anarchy, order is imposed by relying on statistical access to minimize destination bunching, a willingness and means to regulate access, and a strict adherence to system speed and packet discipline

In furtherance of this, each vehicle will:

a. Have the means to propel itself along the system, know where it is in the system, and have the sensors to know its position relative to other vehicles.

b. Know how to get from any entrance station to any exit station on the system, including alternate routes; and have the means to effect transfer and exit switching.

c. Posses a means to communicate with vehicles within the packet. The vehicle will also be able to communicate directly with each of the several sector monitors tracking all activity along the system.

B. Program-model and Quota Allocations

a. General   As detailed in the following, the basic control block is the packet. Although the packet really is only an abstraction; it is an essential operational property of each line. It exists whether there are vehicles in it, or not. As vehicles transfer from one line to another, they leave one packet and become a member of the next. Vehicles transfer, packets do not. Under normal operation, cognizance of individual vehicles, and their destination, applies only in the launching sequence and only occasionally in the transfer sequence.

The central theme of this approach is an ordered denial of access. While at first thought this might seem inimical to our purpose; in assessing this, it is useful to remember that, depending on the specifics of the system, packets are passing at the rate of one every 3 to 5 seconds. Thus denial of access to one or two packets would not seem excessively burdensome.

In operation, it is assumed that a detailed knowledge of traffic requirements is at hand and that a detailed computer model has been derived therefrom. It should be noted that we are provided these data, from a 100% sample, daily. This operations-model is used to assign launching quotas to each entrance station and which, in turn, regulates access to individual packets. As long as the demand for access does not exceed assigned limits, the entrance station effects the launching.

The operations-model must be sufficiently flexible to accommodate differing traffic patterns, seasonal variations, and (predictable) emergencies. In fact there is no single model. A specific scenario is designed for each specific traffic pattern, or a specific event or series of events. As each will have been previously downloaded to the entrance stations, it is only necessary for the central authority (computer or otherwise) to designate the specific scenario and time of execution to alter the system. These scenarios are continually being developed and discarded as varying traffic patterns demand.

Accordingly, at each entrance station along the line, knowing the actual makeup of the packet and the quota for each subsequent intersection, the stations must calculate and apply two maxima; the maximum that can be allowed to depart at the intersection, and the maximum that can be permitted beyond. Failure of either requires denial of access to that specific packet and deferral to a following packet.

b. Control of a Simple System The primary reason to employ quotas is to minimize conflict at main line intersections. Note the use of the word minimize. It is believed to attempt to eliminate them altogether would require extensive coordination throughout the system, and thus is too restrictive. The idea is minimize conflicts, and deal with them as they occur. Please note what is meant by conflict. It is not simply two vehicles approaching an intersection; that is accommodated in the usual way, i.e., an under/overpass. It is about insuring adequate space is provided for a vehicle wishing to leave one line and join another.

How might this work? Let’s assume that, in a particular scenario at the intersection of lines A and B, it is determined that line A can receive 3 vehicles from B, and B can receive 6 from A. Thus at the intersection, line A must provide 3 vacancies and limit the number of departures to 6; the corresponding numbers for line B are 6 and 3. In most instances, departures will occur before arrivals, so the number of departures can be used in determining the number of vacant spaces. It might seem that as 6 are departing from line A, one need have no concern for the 3 coming from B. The 6 are a maximum, not necessarily the actual. Assume, for the moment, that the maximum packet is 20 vehicles. If there were none departing, the most that could theoretically be in the packet as it approached the intersection would be 17 - as discussed in the following, a practical value would more likely be 14.

It is instructive to consider how often this might occur. It is clear that as long as the quota capacity exceeds the average input, that over time, the input would be accommodated. The question is what is the nature of the delay incurred by an individual vehicle as it awaits "the law of averages" to work its magic. In considering this, it is well to remember that the numbers are small, and are limited to integers (i.e., no fractional vehicles). We must, therefore, use Poisson statistics, rather than the more familiar Gaussian.

Consider first the quota of 6 departures. A Monte Carlo calculation (with a 100 thousand samples) indicates a delay averaging less than one cycle (i.e., the time between successive packets), can accommodate, on average, 5.5 vehicles per packet. Moreover, greater than 99% are accommodated within 4 cycles. Assuming a 4 second cycle - less than 16 seconds - an occurrence of a completely empty quota happens less than 0.15 per cent of the time. It would seem of limited advantage to attempt to convert that capacity.

A similar calculation for the remaining 14 shows similar delays for an average of 13.5 vehicles per packet. Accordingly, as packets approach the intersection, the combined average usage provides a 95% utilization of the 20 positions. It is well to remember that this applies at this location only. As traffic is building up, the utilization will obviously be less. The same would apply if space was reserved for downstream entry.

c. A More Complicated System If our system consisted only of lines A and B we could insure that there would never be a conflict, but of course, that is not terribly realistic. For instance, if we use the Los Angeles area freeways as a model, there might be dozens of lines (presently, there are 36 named freeways in the Los Angeles area, however some of these only represent a name change, rather than a new freeway). Accordingly, in a fully implemented system it would be impracticable to allocate destination quotas for the entire system at each station. Thus, except as noted below, quotas apply only to the initial transfer.

However, by enforcing quotas at entrance stations along the line we can significantly reduce conflicts at intersections. In allocating quotas, consideration is given to both down-stream entering traffic and traffic transferring-in from other lines. Thus, in the above example, at the beginning of line A the quota for line B might be only 2, gradually increasing to 6 before the intersection with line B. While quotas apply only to the initial transfer, it should be noted that journeys in their entirety are considered when allocating these.

Once a vehicle has entered the system, it will be permitted to proceed as far as it can get. It will be permitted to transfer as long as it does not exceed the physical limitation of the new packet i.e., does not exceed the specified maximum number for any packet. It will not be denied access simply because that will result in exceeding the new line’s quota for a subsequent transfer. As noted above, the quota for departure on a specific intersection may be graduated. Thus, while the transfer may result in exceeding the quota at one location, the quota is presumed to expand to accommodate it downstream. This would, of course, be at the expense of a downstream vehicle that would otherwise be eligible to enter. Once admitted to the system, a vehicle gains a defacto priority over other vehicles awaiting entry, and is allowed to proceed until it departs the system or encounters the maximum allowed for any packet.

Under this approach each line can control entering vehicles completely, but to some degree it is at the mercy of transfer traffic. Occasionally, the benefit of an expanding quota may not be forthcoming. The consequence of this is discussed below.

In a few locations this "benefit" may not be expected to occur. For those circumstances, a compound quota may be applied (i.e., a quota for the first two transfers). For instance, assume that a vehicle travels along line A, transfers to line B, and then almost immediately transfers to line C. Further assume that along line B, in the intervening region, there is little or no opportunity to adjust the traffic. Then, a specific quota along line A for B-C must be established, along with a separate one for destinations other than C. Clearly, quotas along B for transfer to C must reflect this. If capacity along this section becomes critical, a short section of dual guideway can always be considered.

It is worthwhile to consider what the number of transfers might there be in a typical journey. If our system were a perfect rectangular grid, then it would be possible to go from any place to any other place on the system with a maximum of two transfers. None, if the destination is on the same line as the origin; one, if the destination is on a perpendicular line; and two, if the destination is on a parallel line. Now clearly, a real system is not represented by a perfect rectangular grid; however, it does surprisingly well. For instance, with the Los Angeles freeway system, I believe it is possible to go from any point on the freeway to any other with no more than three transfers, while the overwhelming majority of journeys can be completed with two or less.

Given this, it may be useful to revisit the question of transfer-in vehicles causing a conflict. In the first instance, a significant fraction of those entering the system complete the journey with only one transfer, and thus, by themselves, can not cause a conflict. Our primary defense against conflict occasioned by previous transfers remains the ability of the second line to absorb the vehicle by limiting additional access. Moreover, a second transfer usually results from a journey to a "parallel" line. Thus, in most instances, there are several lines that can be used to cross over to the new line. It is within the scope of assigning quotas that the least problematic of these is selected. For instance in our initial example, line A after the intersection with B, is virtually guaranteed to have 3 vacancies.

But for that matter, essentially all lines will (or should) have vacancies after passing an intersection. One of purposes of quotas is to insure equality of access, thus space is reserved for those wishing to enter the system downstream of the intersection. As long as it happens infrequently, we are justified in usurping that allocation. As this would be the offending vehicles’ second, and likely last transfer; in all likelihood, if it makes it through here it completes its journey and causes no more mischief. Even if that were not the case, it makes little sense to actually interrupt the journey in favor of a possible interruption downstream.

Recall that our objective is not to completely eliminate conflict ; as was stated initially, the idea is minimize conflicts, and deal with them as they occur

d. Alternate Means There are additional ways to avoid conflict. One such is the creation of virtual lines. These would be intended for regions having a strong community of interest. In some instances, we may wish to route traffic around congested areas, thus requiring several transfers.

With any packet, the time of arrival at any intersection can be calculated precisely. Thus a specific packet on line A is designated a packet on virtual line X until it reaches the intersection with line C (i.e., line A cannot assign vehicles to it in the region they share) ; then all the vehicles transfer to actual line C which has, correspondingly, not assigned other vehicles to that specific packet until it reaches the intersection with line G; we have in effect created the virtual line X traversing physical lines A, C, G and so on . All affected entrance stations also become entrance stations on line X. They may assign vehicles to line X or to their physical line; the choice would depend on the desired destination in the same way that bus lines may share the same street


A. Overall System Monitor

To the extent that traffic is primarily between suburbs and some central location, each line system can operate essentially independently. We anticipate that, increasingly, this will no longer be the case. Accordingly, there is a need for an overall system monitor to coordinate the activity on the several lines, and in particular to administer the program-model. The term monitor, for this and the various subordinate monitors, is illustrative. Aside from facilitating communication, under normal operation, these play no direct role - they only monitor.

This oversight of the operation-model is needed primarily to determine the appropriate scenario, and thus how best to alter interline quotas and other inter-system concerns. Any alterations would be transmitted to individual system monitors which, in turn, will alter individual station quotas. As indicated earlier, these would already have been downloaded to the stations; it would only be necessary to indicate the specific scenario and the time of execution. In this, at this level, it would not be unreasonable for human involvement.

These monitor functions and data interchanges are essential to an ordered system. It is anticipated that each function will have redundant support and the data flow will be over secure land lines. Secure protocols, and possibly encryption, will be required to insure integrity. In this connection, it is noteworthy that the communication is basically only from one station to next in line; thus making an easy case for scalability. As lines increase, the length increases, but the density of the data traffic does not.

B. Line and Sector Monitors

Each line functions under the aegis of a redundant, fail-safe line monitor. In this sense, a line is defined as one direction on a given line, and the sector is one direction in a specific geographic area. Periodic track-side sensors provide real-time position and velocity data throughout the system. Each sensor reports to the system monitor through the appropriate sector monitor.

Each station will provide data to their respective section monitors on the updated status of each packet as it passes. These data are passed to downstream stations for processing of their launch, transfer, and separation functions.

In addition, these data are used by the line monitor in two separate, and important roles. The first, and most important, is safety. The system continuously compares actual traffic with the predicted traffic derived from upstream sources. Any discrepancy is an occasion for corrective action, and in extreme circumstances, for shutting down parts of the system.

This information is also compared with the system program-model for general compliance. Any anomalies in this comparison may provide the basis for changing the operating scenario or instituting other modifications or restrictions along the system.

C. The Launching System

The launching process is critical to assure equitable access and to prevent overloading the system. As stated previously, it is the intention to limit only the initial access.

The sequence begins with the assumption that the vehicle is stationary on a launching track, and has signaled the requisite information, including destination, and its readiness to be launched. (It may in fact be moving slowly, but at this point that is a detail.) This track runs generally parallel to the main track.

The launch system will have received data about the next available packet(s) from upstream stations via the sector monitor. These data will include the identification of the packet, the number of vehicles, along with the destination of each. Upstream sensors, adjacent to the main track, will have confirmed this. These data are compared with the appropriate quotas for the approaching packets - if the launch vehicle is in compliance, the launch sequence is initiated.

Thus, having determined that a valid launch window does exist, the launch system notifies the launch vehicle of the specific route (if multiple routes are available) and the precise time to commence. The vehicle then begins a specific acceleration protocol designed to bring the launch vehicle parallel (actually slightly behind) and matching the speed of the packet. The packet should be traveling at the system speed, but the on-board sensors will confirm that this, and all other conditions for a launch, are extant - no launch will take place if all are not within prescribed limits. It should be noted that this sequence must have begun well before the packet reaches the station so as to insure that both reach the merge point with appropriate simultaneity.

In some instances it may be desirable to launch multiple vehicles on to a single packet; if each meets the criterion, this is permissible. Conversely it may be required to deny launching onto a particular packet. It can not always be that vehicles will arrive in precisely the order appropriate for launch. To accommodate either of these conditions, there will be several parallel entrances to the launch track. Thus, if a launch is denied to one vehicle, this will not necessarily deny an opportunity to another.

D. The Separation System

The function of the separation system is to provide a smooth transition from the main line to the exit station. As we are dealing with close-packed vehicles, a single separation line can accommodate only a fraction of the main line traffic. This fraction is essentially the ratio of the speed in the exit station to that of the main line; something on the order of ten percent.

On average, this may be entirely adequate for a particular station. If not, of course, multiple parallel lines may have to be considered. The operative phrase, however, is on average. An orderly system must accommodate instantaneous rates two or three time this, possibly higher.

As we have repeatedly emphasized, if it is to operate properly the system can not allow any slow down on the main line; a vehicle may not begin braking until well clear of it. To accommodate this, a buffer track is provided. If there are no previous vehicles in the separation system, an exiting vehicle will travel to the end of the buffer before executing a braking protocol. Subsequent vehicles would then be instructed to commence their own braking at an appropriate distance upstream from the end of the buffer. It should be noted, however, that these instructions are intended for a routine, uneventful halt. The on-board sensors on each vehicle continually monitor the situation ahead, and should the occasion warrant, call an emergency stop.

E. Transfer Between Lines

A transfer from one line to another is essentially a combination of exiting and re-launching. That is, upon approaching a selected transfer point, the vehicle signals its intention to exit. It exits and under the direction of the transfer system it slows to a transfer speed or, on rare occasions ,comes to a complete stop. By timing the beginning and duration of the transfer speed, the transfer system effectively synchronizes the two lines. Actually, there are three since the receiving line, in general, receives from two (e.g., line A west receives from line B north and south). This is required because the transfer vehicle can depart from any position in the previous packet, but it must append to the rear. Further, the new packet may be of any length up to the maximum.

Obviously, the receiving line must provide an empty position for the transfer vehicle, and it is a primary responsibility of the transfer station to validate this. As stipulated earlier, it is not intended to interrupt simply because of quota limitations. Thus, the transfer station need only assure that physical room is available on the new packet. The only interest the transfer station has in the destination is to pass this information to the next station downstream.

If, however, in spite of our best intentions a vehicle(s) enters a transfer station and it cannot be physically accommodated on the next packet, it will be instructed to enter the buffer and halt. It then becomes a new applicant to the system and must conform to the new line’s quotas in the same way an applicant would at a regular entrance station. It is intended that a judicious use of quotas will limit these. Thus, while this action may result in some minor inconvenience to the commuter, it does not result in collision. This is an essential part of the coordinated scheme of allocated quotas.

As with the separation system, it is essential that transfer stations have sufficient buffer space to receive any exiting vehicles and/or packets; and when necessary, to bring them to a complete halt.



A brief outline of a control philosophy has been presented. It is my hope and belief that this may prove useful for both PRT and dualmode systems. To the degree possible, it was intended to be independent of specific hardware. The overriding objective was to describe a fail-safe, easily scalable system, in which faults could be easily isolated. In furtherance of this, a specific objective has been to minimize both data traffic and real-time control of individual vehicles. To this end, the idea of a platoon has been extended to become a basis for control. To distinguish this role, I have chosen to use the term packet. If nothing else, this reduces the control task from specific individual slots to a non-specific reservation on a multi-vehicle packet.

The use of a packet also provides an opportunity for greater capacity. For example, assume a system speed of 120 feet/second (81.8 MPH, 131.7 km/hr), and a packet of twenty vehicles, each 16 feet (4.9 meters) in length. With a minimum headway of 150 feet (45.7 meters); the maximum capacity of the guideway is over 18,000 vehicles/hour.

The full utilization of the guideway will depend critically on the way demand builds up. Traditionally, demand has built up along a single line, growing larger towards a central location, usually referred to as the central business district (CBD). Under this model, control is relatively straightforward. The traffic simply is allowed to grow toward saturation, in our example 18,000 vehicle per hour. Under these conditions, the probability of reaching something very close to the theoretical capacity would be high.

It is anticipated that this traditional model may grow increasingly less predictive – that is, there will likely be considerably more suburb-to-suburb travel. Thus, it will become increasingly more important to develop a thorough understanding of system requirements, both present and future. This is true independent of whatever means of control we adopt. As demand grows, we must insure that the system remains balanced and provides equality of access. We must not allow parts of the system to become clogged to the extent it starves the rest. Thus quotas, to some degree, are probably inevitable.

These quotas would reflect actual traffic distribution, however they would be scaled to near maximum capacity. Thus if the system were operating at something like 50 per cent capacity, the quotas would be, in general, twice the average traffic. Under these conditions, quotas would have little effect except to suppress anomalies at the extreme of the statistical tails.

One would hope that it would take several years before the capacity of a new system is seriously in question. If not, we have done a poor job of planning. Nonetheless, even if the full advantage of this approach would not be tested early; it is not too early to examine, thoroughly, these vitally important issues. We can not afford to wait until the problem is manifest.

And finally, this proposal depends at least in part on stochastic processes, thus the need for an effective computer model would seem particularly evident. Indeed, some might inquire what is the point of discussing this, absent such a model. Even models need a premise, and in particular, the model must reflect a particular operational and control philosophy. Thus, it is useful to subject the premise to extensive scrutiny. Constructive criticism is welcome. In any event this a work in progress, a computer simulation that reflects this philosophy is currently under development.


Last modified: March 27, 2001