PART TWO

 

 

 

          In part two, we describe in somewhat more detail the functions of the several parts of the system.  As before, the emphasis is on the management and operation of a complex system, rather than innovation or invention.

 

          What follows, in this and subsequent sections, is not intended as an engineering specification, and is clearly not a specific design.  It is intended, only, to provide an outline guide to a general system approach, and to suggest confidence that an optimum design can be developed.  Where specific design approaches are described they are primarily for illustrative purposes, and should be viewed as advisory only.  While we believe them to be valid and workable, we  do not  necessarily warrant them as optimum.

 

We proceed in the belief that most will accept that some type of a carrier, guideway and related apparatus can be designed and built.  What many may be less sanguine about it is how to keep the carriers from banging into one another, and how to assure that they arrive at their destination in a safe and timely manner.  Thus, we begin with a discussion of operation and control.

 

 

IV  OPERATION AND CONTROL

 

The principal reason for building an individual rapid transit (IRT) system is to move people about more quickly and conveniently, without requiring significant additional real estate.  Numerous other advantages obtain, 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. Obviously, the extremes of 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 – with the exception of appending to or reforming the packet, all operations on the main line are at the operating velocity. This specifically includes switching to and from the main line. This is not a new idea, others have expressed similar views; but we believe it sufficiently important and basic to bear repeating.        

 

 

 

 

 

A.     General Considerations

 

          In considering control of these systems there are two general schools, or philosophies. These are synchronous, and point or block synchronous.  In the former, sometimes referred to as clear path, a vehicle is held at the entrance station until a clear path to its destination can be established and reserved.  In the latter, vehicles are allowed to enter any vacancy in the first block, with adjustments to velocity made en route to accommodate entrance to subsequent blocks.  We propose a system of pre-allocated quotas that borrows from both and is neither.  To provide some insight, it is useful to consider some aspects of these two.  

 

          a.  Clear Path  This approach  poses no serious problem with those vehicles whose destination is on the originating guideway; however, we anticipate that most journeys will involve at least one transfer, and many will involve two, or more.  Accordingly, we need to consider the consequences.

 

Assuming a well-regulated system, each vehicle applies to enter and occupy a designated slot on the initial guideway.  If the journey requires transfer(s), corresponding slot(s) in the new guideway(s) must also be identified.  Further, let’s also assume that the system is operating at 80 percent capacity and that vehicles are randomly positioned.  Thus, for a given initial slot, the probability of a vacant slot at the first transfer point is 20 per cent.  The same can be said for the next transfer; that is, for any given slot on the second line, the probability of a vacant slot on the third line is also 20 percent.  But the probability that from the initial line, the two empty slots will be aligned to allow an uninterrupted journey is the product to the two, or 4 percent.  If a transfer to a fourth line is contemplated, the probability drops to 0.8 percent.  Accordingly, a significant majority of otherwise vacant slots on the initial lines must be rejected as not providing a clear path to the destination.  It is worse than it might appear; 25 tries on a two transfer journey does not guarantee entrance any more than 2 flips of a coin guarantees a head (or tail).

 

Real considerations will modify these numbers.  For instance, multiple paths will increase the probabilities, and previously reserved slots downstream from the transfer point will decrease them.  Moreover, because the system provides for advanced reservations, it is not truly a random system, in the strict definition of the term.  Nonetheless, the limitation is clear.  It is unlikely that anything like an 80 percent capacity can be sustained.  That is, unless the overwhelmingly majority of traffic is confined to the initial line.  But increasingly, this would seem the least likely option.     

 

 

 

b.  Block Synchronous   In this approach, individual vehicles are allowed to enter the system at the first available vacancy without regard to downstream considerations.  As the vehicle approaches a need to transfer, the velocity is adjusted to coincide with a vacancy in the next line.  However, to first order, capacity is proportional to velocity; thus any appreciable reduction in velocity is reflected in a reduced capacity.

 

  Some have suggested that a vehicle wishing to transfer depart the line completely, come to a complete stop, and is re-launched onto the new line.  This will “work” in the sense that it will provide more utilization of the system.  However, unless one is prepared to consider multiple tracks in the transfer region, this also seriously restricts capacity.

 

Accordingly, while the advantages of block synchronous control provide for better utilization of the system; we are of the opinion that it is deficient in two respects.  We believe that adjusting velocity on the main line to accommodate the next transfer creates control problems of significant proportion.  This requires that a central control authority must know the exact location and velocity of each vehicle under its control, and issue instructions accordingly. Moreover, this approach does not really provide for uninterrupted journeys.

 

For the reasons discussed in the following, we believe that all operations on the main line must be at a constant system speed, and that by a system of pre-determined quotas applied at entrance, we can reduce the number of interrupted journeys to a wholly acceptable number.     

 

c.  An Improved Approach  The odds get considerably better, when if one is willing to consider multiple slots on the second, and subsequent lines.  Even as few as ten alternatives brings considerable advantage. 

 

How might this work.  Instead or requiring the transfer vehicle to occupy only the specific slot that would require no change in velocity, we allow consideration of, say, 10 contiguous slots.  The first of these would be the previously designated no-change-in-velocity slot.  Let’s examine the probability that all ten of these will be occupied.  Each will have an 80 percent probability of being full.  The probability that all  ten will be full is

 

p = (0.8)10

 

or slightly over 10 percent.  Since either all ten are full, or there is at least one vacancy; the probability of finding a vacant slot approaches 90 percent (89.2%).  In the same way as before, we can concatenate individual probabilities and arrive at approximately 90 percent for one transfer, 80 percent  (79.7%) for two, and 70 percent  (71.1%) for three.  All one needs is an auxiliary (i.e., off the main line) transfer line which allows individual vehicles to slow and slide back the appropriate number of slots.  Remembering that capacity is proportional to velocity, these transfer lines need to be of sufficient length so as the necessary velocity remains sufficiently high to handle the expected traffic.

 

As before, specific slots can be identified and reserved for subsequent occupancy.  While a definite improvement, it still requires significant data handling.  Although, we have improved the probability of finding a solution, the fact that we are still dealing with individual slots requires investigating each possible individual path until a solution is found.  Further, it also complicates the instructions transmitted to each vehicle, as it now must include specific instructions for navigating each transfer track.  Moreover, it does not insure equality of access nor provide for balancing the system for maximum efficiency. 

 

  c.  Further Improvement   With a first come, first served system there is no assurance that traffic will be routed for maximum efficiency.  If the first to arrive at upstream stations are allotted priority on the most direct route, this may well have the effect of depriving a downstream vehicle from entering.  On the other hand, if we route the upstream vehicle along a different path, perhaps slightly longer, and less heavily traveled, we may be able to accommodate both vehicles.  That is, if one is willing to relax real-time control, and accepts consideration of ordered assignment on the basis of a priori information.  Once you accept this concept of an ordered assignment of paths based on previously collected information, you are well along the path toward quotas.

 

As before, it we do not require a specific slot, considerable advantage obtains.  Let’s consider the next step and require only a non-specific vacancy in a specific packet.  Clearly, if the composition of each packet exactly matched the average, the entire system could be managed to its maximum efficiency.  While a full realization of this is no doubt unrealistic, the application of quotas will tend to smooth the distribution of traffic.  In effect, they tend to flip the high side of the distribution tail over to the low side.

 

For those who would argue that we must provide immediate access to all, with no delay or extended routing; we suggest that to all is the operative phrase.  We should not allow upstream entering vehicles to unfairly monopolize the system  - the opportunity for any given user to gain access should be equal, independent of location.  As detailed below, we believed that this advantage can be realized, almost completely, by applying quotas only to the initial transfer.   Moreover, it is only when the system is operating at near capacity will this impose any real restrictions.  The quotas will reflect actual traffic patterns, but will be scaled to full capacity.  As long as the quota remains unfilled, entrance to the system is granted.         

 

A corollary advantage realized by adopting this general approach is that it greatly reduces the requisite operational information, thus facilitating a distributed control system wherein an individual carriers can make many of its own decisions.  The only data required is the composition, including individual destinations, of the approaching packet and the destination of the applying carrier.  Thus providing a concomitant advantage of a greatly reduced data burden.  This latter is of particular advantage when considering scaling to increasing larger systems.  In the following we begin to discuss how one might develop such a system.   

 

 

          B.   Operational Philosophy

 

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 carrier makes many of its own decisions, including initiating the transfer to other lines, and 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

 

Even though the packet is the basic building block of control; it is really only an abstraction.  Nevertheless, 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.  The packet proceeds, always, at a constant system speed.  In this way, the packet leader (assuming the packet is occupied) can always calculate precisely where it should be and make whatever adjustments are necessary to comply.  The system monitors the compliance of the packet, not individual carriers - under normal operation, cognizance of individual vehicles, and their destination, applies only in the launching sequence and only occasionally in the transfer sequence.

 

A 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 (4.25 seconds in our previous example). Thus denial of access to one or two packets would not seem excessively burdensome.

 

b.  Program-model and Quota Allocation  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. 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 launching function 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.  Exceeding either requires denial of access to that specific packet and deferral to a following packet.  These quotas would be specific for close-in intersections, and may be more general for those further along.  That is a quota for all journeys beyond the intersection with Line X.   In general, these apply only to an initial transfer.

 

 

C.   Application to a Simple System

 

a..  Control of a Single Line  Control of a single line is not difficult.  In the simplest sense, it can be limited to insuring that the maximum packet size is not exceeded.  Carriers are allowed to enter the line till it saturates.  While this provides safe operation, it does not necessarily provide equality of access.  That is, if the line does saturate, those down stream are denied access.  Accordingly, there would be a tendency to enter the line up stream of their usual entrance, thus rendering the system less useful.  To combat this, a system of quotas can be incorporated limiting access at up stream entrances stations so as to provide vacancies further along.  That is, initially the quota might be 2 or 3, incrementally increasing to the maximum; with each increment reflecting the relative fraction of users seeking access.            

 

          b. Control of a Simple System While equality of access in no doubt a laudatory objective, 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 be entirely 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., the two lines do not cross at the same level.  It is about insuring adequate space is provided for a vehicle wishing to leave one line and join another.

 

How might this work.  Consider the intersection of lines A and B[1].  Let’s assume that, in a particular scenario, it is determined that line A can receive 3 vehicles from B, and B can receive 7 from A. Thus at the intersection, line A must provide 3 vacancies and limit the number of departures to 7. In most instances, departures will occur before arrivals, so the number of actual departures can be used in determining the number of vacant spaces.

 

c.  Statistical Considerations  It is instructive to consider why this is so. 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. A simple example suggests that this delay can be minimal.

 

In considering this, it is well to remember that we are dealing with small number, and are limited to integers (i.e., no fractional carriers, or entering vehicles). We must, therefore, use Poisson statistics, rather than the more familiar normal, or Gaussian.  In Poisson, the probability of the number, n, entering the system in a given cycle is[2]

 

p n = (r n / n!)exp(-r)

 

where r is the average value.  The value of n is limited to integers, while r can take any value.

 

Consider a quota of 7 departures. The results of a Monte Carlo[3] calculation (with a 100 thousand samples) are provided in Table I. We show three different utilization factors.  In this way we can indicate actual usage.  For example, with a quota of 7 and a utilization factor of 80 percent, the mean value is assumed to be 5.6 vehicles per cycle.

 

 

Table I – Calculated Wait Probabilities for Quota of 7

 

 

                                                          Nmbr of         Pct of      Cumulative    

                                                          Carriers       Carriers           Pct

 

            50 Percent Utilization (3.5 carriers/cycle)

 

Wait  0

345232

98.71

98.71

          1

4502

1.29

100.00

Total

349734

 

 

 

                                                                   Average Wait: 0.002 Cycles

 

            80 Percent Utilization (5.6  carriers/cycle)

 

Wait   0

462176

82.44

82.44

          1

92921

16.58

99.02

          2

5047

0.90

99.92

          3

352

0.06

99.98

          4

96

0.01

100.00

Total

560592

 

 

 

                                                                    Average Wait: 0.196 Cycles

 

            90 Percent Utilization (6.3 carriers/cycle)

 

Wait   0

378422

60.10

60.10

          1

194535

30.90

91.00

          2

45105

7.16

98.16

          3

8954

1.42

99.58

          4

2031

0.32

99.90

          5

535

0.08

99.99

          6

69  

0.01

100.00

Total

629651

 

 

 

                                                                   Average Wait: 0.513 Cycles

 

 

Even with 90 percent utilization, the average wait is slightly over one-half a cycle, and 99 percent of those applying for entrance are accommodated within three cycle – assuming a cycle of 4.25 seconds, less than 13 seconds.

 

 

D.  Application to a Real System

 

If our system consisted only of two lines, 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.[4] 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.

 

a.  Application of Quotas  However, by enforcing quotas at entrance stations along the line we can significantly reduce conflicts at intersections. Even though quotas are applied only to the initial transfer; in allocating these, consideration is given to both downstream entering traffic, traffic transferring-in from other lines, and the needs of similar journeys – the entire demand matrix.

 

In the same way as quotas are applied as described for a single line, quotas for transfer are incremented.  This, so as to accommodate transfers from another line.  Thus, in the example given above, at the beginning of line A the quota for line B might be only 2, incrementally increasing to 6 before the intersection with line B.  Thus, if a carrier transfers into Line A with a subsequent requirement to transfer to line B, it will usurp the quota from a carrier applying to enter downstream that would otherwise be an eligible entrant to line A.    

 

b.  Priorities  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 are graduated. Thus, while the transfer may result in exceeding the quota at one location, the quota is presumed to expand to accommodate it downstream. 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. Thus, occasionally, the benefit of an expanding quota may not be forthcoming. The consequences of this are discussed below.

 

In a few locations this "benefit" may not be realistically be expected to occur.  For instance, assume that a vehicle travels along line A, transfers to line B, and then almost immediately must transfers to line C. Further assume that along line B, in the intervening region, there is little or no opportunity to adjust the traffic i.e., few or no intervening stations.

 

 For those circumstances, a compound quota may be applied (i.e., a quota for the first two transfers). 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.

 

c.  Transfers  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, a real system may not be well represented by a perfect rectangular grid; however, it is surprisingly effective.  For instance, with the Los Angeles freeway system, we 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 likely to have 4 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.   This would likely be the offending vehicles’ second, and last, transfer.  Thus, in all probability, if it makes it through; it will complete its journey and cause 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.

 

          d.  Statistical Considerations   In a manner similar to the deve­lopment of the statistics of delay in a simple system, it is useful to provide some appreciation for how often a conflict might occur.  Recall that quotas apply only to first transfers.  Thus an entering carrier, in an of itself, can not cause a conflict - the quota is not oversubscribed at this point, otherwise it would be denied entry.  That is not to say it can not be involved in a conflict, however.  If the receiving line is oversubscribed and has insufficient physical room (i.e., an additional carrier would cause the receiving packet to exceed the limit for any packet), the initial carrier would be denied transfer, even if it were within its own quota for transfer.  Thus conflicts will occur, the question is: how often.

 

          How might these occur.  Consider again Lines A and B.  Line B is the receiving line, Line A is the transfer line (i.e., the source of carriers transferring to Line B).  Well upstream of the intersection, it quite unlikely that either will be oversubscribed.  This is due both to the graduated system of quotas, and the ability of each to absorb excess transfer-in carriers in preference to downstream carriers applying to enter.  Thus, conflicts are occasioned by a second-transfer.   Moreover, by only those that transfer-in close to the intersection, where only a limited opportunity is available to absorb an over-subscription from a transfer line.

 

To gain some insight, we have constructed a computer model of south-bound traffic in the Los Angeles County portion of Interstate 405, the San Diego Freeway.  This is one of the main north-south commute arteries of the Los Angeles freeway system, sometimes referred to as the “dreaded 405”.

     

Complete details are provided in the appendix; however it may be worthwhile to review some of the highlights here.

 

A self-consistent model of the traffic was constructed from published data generously furnished by Caltrans (California Department of Transportation).  Ramp data was available only as average daily traffic.  Accordingly, we constructed the entire model on this basis.  To simulate peak demand, we multiplied average traffic by an appropriate constant.  Thus the system “breathed” together, with all locations gaining the same.  We are aware that traffic does not necessarily develop in this manner.  However, if assumed traffic at a particular point exceeds the maximum, then the fact that the actual traffic is less at some other point does not invalidate the results of the model.  The actual traffic is accommodated.

 

    We found that in the proposed system, a single guideway would conveniently accommodate approximately 2.2 time the average daily traffic (ADT).  The system would not become unsafe at higher values, the system will simply not admit an unsafe quantity.  However, the delay at entrance would start to become excessive.

 

  In this connection, we have somewhat arbitrarily assumed that 24 wait-cycles is a maximum.  Although very occasionally exceeded at the busiest on-ramps, for most it is not even approached.  A typical example of wait-cycle distribution is given below for the west-bound Wilshire Blvd. on-ramp.  

 

 

TABLE II – Calculated Wait Probabilities

 

   

            Number             Number              Fraction             Cumulative

                of                       of                        of                      Fraction

         Wait-cycles          Carriers                Total

 

57 4 SB ON FR WB WILSHIRE BLV

 

                             0           130719            6.2433e-001            6.2433e-001

                             1             54816            2.6181e-001            8.8614e-001

                             2             16387            7.8266e-002            9.6440e-001

                             3               5030            2.4024e-002            9.8843e-001

                             4               1577            7.5319e-003            9.9596e-001

                             5                 552            2.6364e-003            9.9860e-001

                             6                 190            9.0746e-004            9.9950e-001

                             7                   74            3.5343e-004            9.9986e-001

                             8                   28            1.3373e-004            9.9999e-001

                             9                     2            9.5522e-006            1.0000

 

                Total entering:   209375                       Average: 1774 vehicles/hr

 

 

          For this example, 62% of applying vehicles are launched immediately, while greater than 99% are launched within 4 cycles (17 sec).  A complete listing of all on-ramps is given in the appendix. 

 

Our model also shows, with a slight break in Carson, over 40 of the 48 miles extant in Los Angeles County contemplates an average peak traffic of over 10,000 vehicles per hour (VPH); approximately 13 miles maintain capacity over 12,000 VPH, and several instances are found with over 14,000.  The maximum is in excess of 14,750 VPH.  The latter represents slightly over 87% of the maximum theoretical capacity.  Please note that these are average values during peak demand, not instantaneous peak values. Moreover, these figures refer to the entire south-bound freeway, not simply a single lane.  Thus we suggest that a system of this description might accommodate in excess of the peak traffic of the entire south-bound 405.

 

As the reader will recall, our objective was not to eliminate altogether the possibility of conflict.  But rather, to minimize these so as to have a negligible impact on traffic flow, and to deal with them safely when they occur (i.e.; bring the vehicle to a stop and re-launch it after a minimum delay.)

 

At, perhaps the busiest intersection in the LA System, the 405-Ventura Interchange, we calculate a conflict rate of less than 6.0e-4 (less than 1 in every 1667 vehicles attempting to leave the 405 for the Ventura freeway.)  What are the real consequences of this.  For the average commuter - essentially none.  Consider that the typical commuter will make approximately 250 round trips a year, or 500 one-way trips.  Assuming the return trip encounters similar statistics, this represents a minor inconvenience less than once every three years.  Contrast this with a major inconvenience twice a day.

 

That is not to say that a conflict will occur every three years.  A conflict will happen at a rate of slightly over one an hour.  However, at this rate it causes no appreciable degradation in the traffic flow.  More importantly, the means are at hand to deal with it.               

 

While these calculations are encouraging (perhaps very encouraging), we make no claim that they are a valid substitute for a comprehensive calculation involving the entire system.  They are not.  We have made (what we believe to be realistic) assumptions regarding cross traffic. They are valid for the particular assumptions made.   Nonetheless, we believe them to be not totally unrealistic, and suggestive that a comprehensive calculation would provide similar results.

 

          Moreover, we believe the methods developed here lend themselves readily to a more comprehensive calculation.  It would only be necessary to make a similar calculation for each guideway (freeway) separately making an initial assumption of the contribution of other systems.  These would then be compared with calculated output from each.  The inputs are adjusted (relaxed) to reflect the new data, and the calculation is repeated.  A relative few such calculations should suffice as it is not necessary that they be exact; it is only necessary that the input assumptions of one system be equal or greater than the calculated output from another.  We are not particularly interested in an exact number, only in demonstrating that it is less than some reasonable standard.

 

          In this we have chosen to model the 405, not because we believe it necessarily represents the best model for an Individual Rapid Transit system.  Rather, it represents a real entity for which real traffic demand data exists, and the advantages of this approach can be demonstrated.

 

 

          E.  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 independently 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

 

 

F.  Packet Operation

 

          Just as the carrier is basic element in the system, the packet is the basic building block of control.  One must understand packet operation to understand the control philosophy.

 

We have suggested that for maximum efficiency that, operation must be close-packed.  Just 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.  We are 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.[5] We are not arguing that it could not possibly be done; we 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 200 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. Thus as a redundant safeguard, before departing, a short separation, or exit distance, of the departing vehicle from the rest is 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; 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.  

 

However, a mechanical coupling would simplify the dynamics of intra-packet motion. Railroads and subways have been dealing with multiple engines for years. For these reasons, we prefer mechanical coupling. On the other hand, railroads don’t have to deal with in-motion de-coupling. While mechanical details are discussed elsewhere, from an operational viewpoint, it is essential to understand that the coupling must 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.

 

 

G.   System Speed and Packet Discipline

 

System speed plays an essential part in the merging and transfer of individual carries and thus is an integral part of the operational philosophy.  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 periodic intervals. We allow for minor separation in exiting, but this involves only inches.

  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 both the specified maximum-sized packet, and the requisite headway between packets.

 

 

H.  System Monitors

 

          Oversight of the system is provided by a correlated combination of   sector and system monitors.  The term is illus­tra­tive.  Aside from facilitating communications, under normal operation these play no direct role - they monitor.  As we have discussed, the intention is to move decision-making to the lowest practical element.

 

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 landlines. 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 the next in line, via the sector monitor. This makes an easy case for scalability. As lines increase, the number of stations and monitors increases, but the density of the data traffic does not.

 

It should be noted that by routing data from individual station and trackside sensors through the various monitors, we facilitate reconstruction of the data should communication fail. 

 

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

 

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.

 

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 is reported to the overall system monitor and may provide the basis for changing the operating scenario or instituting other modifications or restrictions along the system.

 

 

I.  Summary and Comment

 

An outline of a control philosophy has been presented. 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; one in which faults can be easily isolated.

 

 In furtherance of this, a specific objective has been to minimize both data traffic and centralized 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, we have chosen to use the term packet.  Use of a packet as the primary control unit, greatly reduces the control load.  Specifically, it reduces the requirement to identify individual slots, to one in which it only required to determine if one of 20 or so non-specific locations is vacant. 

 

          We favor packets and distributed control for an additional reason.  Any sort of central control introduces a latency between the occurrence of some untoward event and the its recognition by the central computer. This is so because the central computer can not simultaneously receive data and communicate separate instructions to every carrier.  Nor can it instantly resolve every potential conflict.  Any attempt to reduce this latency places an additional burden on data handling, with its concomitant additional exposure to failure.

 

Alternatively, with individual packets and/or carriers continually scanning ahead for potential difficulty, this latency is essentially reduced to zero.  Both packet leaders, and in some instances individual carriers, possess both the means and authority to take corrective action instantly; while simultaneously notifying the appropriate sector monitor.  Undoubtedly, in many instances this could have a significant impact; or rather, (forgive us our puns) be the reason for the lack of one.

   

The use of a packet also provides an opportunity for greater capacity.  As noted previously, we suggest how a peak value of something approaching 15,000 vehicles per hour might be achieved.

 

Assuming this, one can expect that it would take several years before the capacity of the system is seriously in question. If not, we have all done a poor job of planning.  Thus, the early application of quotas would be, as previously stated, has little effect except to suppress the extremes of the statistical tail.  This provides ample opportunity to develop accurate control scenarios from data that is collected daily.

 

And finally, as this philosophy depends, at least in part, on stochastic processes, the need for an effective computer model of an entire system would seem particularly evident.  With this we wholeheartedly concur.  Our purpose, primarily, has been to suggest that such a model would likely prove successful.

 

In modeling an entire system, rather than simply replicating the existing freeway, it most likely would be useful to begin the process of making choices about what a real system might look like.


[1]At an intersection in a real system, there would be four.  Both A West and A East would each intersect with B North and B South.  However, each would function identically.

 

     [2]R. Evans, The Atomic Nucleus, (McGraw-Hill, 1955)

 

[3] We can not apply pure random chance here as the probability is not random.  It depends critically on what has occurred previously.  We get around this by what is referred to as a Monte Carlo calculation.  In this, a computer simulation of a large number of vehicles applying  for entry is maintained.  The distribution of the number applying at each cycle is made to reflect a Poisson distribution.  While the number applying at each cycle is random, the number accommodated is not.  If the number applying for a particular cycle exceeds the quota, the excess is shunted to a queue, and given priority for the next cycle.  If at the next cycle, the combination of waiting vehicles plus the number of entering vehicles again exceed the quota, the excess is again shunted off to the queue, and so on.  By compiling a large number of histories, we thus obtain the probability of delay.  See the appendix for a fuller explanation.,

   

[4] Presently, there are 36 named freeways in the Los Angeles area.  However, some of these only represent a name change, rather than a separate freeway.

 

[5] It should be noted that this acceleration zone can be from several hundred to several feet – it is a function of the square of the target velocity.  Consideration of this may limit the system speed.