William G. Turnbull

In a recent submission, Kim Goltermann (Guideway Network Philosophy, 6 August 2001) links my views with those of Francis Reynolds as thinking to narrowly and not providing sufficient accommodation for those wishing to transfer between lines. In this, I presume he classifies us as favoring the so called "managed chaos" method of guideway control. Whether he does not, and while I can not speak for Reynolds; with regard to my views, this is simply not the case. I most certainly do not favor the sort of unrestricted access such a system contemplates. I strongly believe that it is essential that some means of regulated access must be imposed to insure an orderly flow of traffic, as well as to insure equality of access. It is with precisely these goals in mind that that the system of "packets with quotas" was developed. Perhaps further clarification is called for.

However, it is also true that I do not subscribe to the "clear path" philosophy advocated by Goltermann and described by Dr. Guadagno for his InTransSys. In support of this approach, Goltermann discounts Reynolds’ description of this as inefficient. Let me suggest a reason it might be.

In the clear path approach, entering vehicles are held at the entrance station until a clear path to its destination can be established and reserved. This poses no serious problem with those vehicles whose destination is on the originating guideway; but as Goltermann correctly points out, most journeys will involve at least one transfer, and many will involve two, three or more. Accordingly, we need to consider the consequence of these.

Assuming a well regulated system , each vehicles 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 only 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 this is precisely the condition that Goltermann charges us to avoid.

The odds get considerably better, however, if one is willing to consider multiple slots on the second, and subsequent lines. Even as few as ten alternatives brings considerable advantage. This option may not be agreeable to Goltermann as he rejects the "The need to slow down, reprogram, or shunt-off large number of cars when traffic gets heavy is, in [his] view, not a viable option." In principle, reprogram and shunt-off can be eliminated, but slow down, as a practical option, cannot be.

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. These transfer lines need to be of sufficient length so as the required 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.

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, and 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.

Where might we get this information? We collect it every time a vehicle applies to the system. We already know where it enters, and to enter it must supply a destination. Thus we can build up a series of scenarios that predict traffic for each of numerous specific conditions. These conditions, and the consequent assignment of quotas, are continuously examined and updated, albeit not in real-time.

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 traffic to the norm, and thus more closely to the ideal.

For those who would argue that we must provide immediate access to all, I 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 in my previous discussion (Some Thoughts on Operation and Control, 27 March 2001), it is believed that we can realize this advantage, 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.

In a short note not all details can be explored, and I can not necessarily expect that Goltermann will adopt this as his preferred system. I would hope, however, that he now understands that, unlike his previous statement, not inconsiderable thought was given to the problem of transfer between lines. Whether sufficient, remains to be seen.


Last modified: August 23, 2001