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Slots Journey
Placement of the distal interlocking screw is the most difficult part in all intramedullary nail interlocking screw systems and the Surgical Implant Generation Network (SIGN) interlocking system is not an exception. SIGN nails are interlocking implants designed with a precision instrumentation set for use in treatment of long bone fractures without an image intensifier. Locating the distal slots of SIGN nails could be challenging for young SIGN surgeons when treating very complex comminuted fractures and in obese patients. This study was stimulated by a patient who presented one year after surgery with knee pain due to a migrating nail because of missed distal screws. A total of 48 patients divided into two groups of 24 were studied retrospectively and prospectively. The retrospective studies revealed that failure to locate distal locking slots in ten antegrade nailing procedures was due to wrong entry point and comminution of the fracture. The challenges encountered led us to innovating methods to overcome the difficulties of placement of distal screws in a prospective study. Application of methods A and B made location of the distal slots easier in the prospective study even though there were more complex comminuted fractures. The methods also reduced the antegrade operation time by 1 hour 11 minutes. We concluded that SIGN nailing could be challenging and frustrating at the early learning stage. Application of the two innovative methods will make distal slot location easier. They will also make SIGN interlocking nailing less difficult for young SIGN surgeons as they journey through the learning curves.
It’s inherent in the Clear-Path concept that NO vehicle will EVER be allowed entry onto the guideways unless it has been positively established that a clear path all the way to the destination is available and the relevant slots have been reserved for said vehicle’s exclusive use. This means that ALL conflicts have to be solved ’a priori’ and the only method available to achieve this is ’entry delay’. Vehicles will simply have their entry delayed until such time that the necessary vacant slots are available.
The most common criticism leveled at the Clear-Path concept is pertinent to this method of ’entry delay’, since it is often claimed through the application of simple math that the probability of finding the necessary vacant slots will rapidly approach zero as the number of intersections passed en route goes up – especially if the guideways are intensively utilized. This in turn will result in very long and completely impractical delays for users trying to access the system.
A Clear-Path Operational Control system is inherently very simple. It solves ALL conflicts prior to launching a vehicle onto the guideway; creating a cleared path of reserved time-slots from the vehicle’s origin all the way to its destination. A ’conflict’ is an occurrence where two or more vehicles are destined to occupy the same location on the guideway at the same time. Such an occurrence requires some means to solve the conflict since it would otherwise result in vehicles colliding. A ’time-slot’ (hereafter called slot) is a precise location on the guideway coupled to an equally specific time.
Operating vehicles in singletons, outside of platoons/packets, will certainly warrant a lot of data, that will have to be verified, processed, transported and stored. Each trip will ’produce’ a lot of storable data about the route taken, the proceedings of the journey, the time, the price for the user, any irregularities during the journey and possibly many other pieces of information, but unless the proponents of platoons envision that users will be invoiced as a group rather than as individual users will more or less the same data have to be produced, processed and stored regardless.
However, this formula is very simplistic and doesn’t take into account the principle of a Clear-Path Operational Control system where all slots are booked immediately before a journey commences. This means that the actual utilization figure for each junction a vehicle will cross should only include those other vehicles which has already booked their slots PRIOR to when our vehicle makes the reservation. Vehicles booking slots AFTER we have booked ours will not ’monopolize’ the guideways seen from our point of view since we already have our slots secured, but these later vehicles will still be part of the final utilization percentage.
It should be obvious that the very first junction encountered on a trip will have been ’monopolized’ to a much higher degree than the very last junction encountered, simply because almost all other vehicles have already booked slots for our first junction while very few vehicles have booked slots at our last junction by the time we book. Other vehicles’ ’monopolization’ of the junctions will, considering my previously mentioned premises, drop off with a constant (equal to 10% of the utilization rate in this example). Therefore, instead of a probability of
which is 0,0128 or 1,28% (the corresponding figure for 50% utilization rate is 3,27%). In other words, taking into account the simple fact that junctions are only ’monopolized’ by vehicles booking slots at an earlier time than the vehicle in question has in this particular example improved the probability of finding a clear path roughly hundredfold compared to the simple formula often used by ’Clear-Path Control’ adversaries.
However, it’s even more complicated than that. We also have to take into consideration that an entering vehicle searching for vacant slots will not ’compete’ for slots with those vehicles taking the same course. If we therefore consider a vehicle that has already found a vacant slot on a guideway utilized at 60% and the vehicle is scheduled to continue ’straight ahead’ at the first junction encountered, it follows that the 80% of traffic (occupying 48% of all slots) going ’straight’ will not interfere with our search for a vacant slot after the junction. Our only ’competitors’ are the 20% of traffic (occupying 12% of all slots on the transfer line) transferring from the other line onto our line. We also know that these 12% of slots will merge with the 52% of slots that are vacant on our line. This means that our chance of continuing ’straight ahead’ (= finding a vacant slot after the junction, but on the same line) at the first junction encountered will be (52 – 12)/52 = 0,7692 or around 77%. Using the same method will our chance of a successful transfer to the other line be (88 – 48)/88 = 0,4545 or roughly 45%.
which is 0,1239 or a respectable 12,39% (the corresponding figure for 50% utilization rate is 20,34%). This figure is conditioned on all the premises previously listed and is valid for a trip encountering 10 junctions, so we still need to take into account the problem of finding a vacant slot when entering any random guideway line in the first place. This probability is a simple 40% so the final figure will be 0,1239 x 0,4 x 100 = 4,96%. Translating this into ’entry delay’ it means that vehicles will on average wait around 20 slots or 10 seconds at 2 slots per second before they can commence their trip. It also means that 95% of all users will have to wait less than 60 slots – or less than 30 seconds at 2 slots per second. 30 seconds is a shorter time than most traffic lights let us wait for the green light.
’Multiple’ means ’more than one’, so in principle it could indicate 2 or 200 alternative slots, except 200 would probably be impractical and 2 doesn’t really offer enough advantages to be worth the trouble. I did some primitive calculations based on a ’5 alternative slots’ Multiple-Slot system as a starting point and it turned out to be such a fortunate choice that I’m going to use only that in the following presentation. Five alternative slots means that a vehicle can either remain in the same slot, jump one or two slots ’forward’ – or drop one or two slots ’back’. This is done by increasing or decreasing speed slightly just long enough to effect the shift from one slot to another. In principle can slot shifts – or ’slot-jumping’ – be done everywhere on the guideway at any time, but for simplicity I envision that it will only be allowed at junctions. Nevertheless, even with this restriction will it be evident that 5 alternative slots to choose from will improve the chance of finding at least one slot that is vacant.
However, the slot we would need to jump to is unfortunately often occupied or blocked by a preceding/following vehicle thereby somewhat reducing our options. A vehicle just in front of our vehicle will prevent any jumps ’forward’ and a vehicle right behind us will prevent any ’falling back’. Our final number of alternative slots will depend on the utilization rate and the exact position of other vehicles relative to ours. The bottom line is that a 12% utilization rate (the transfer line from the examples above) will allow for 4,31 alternative slots on average and a 48% utilization rate (the continuing line from the examples above) will allow for 2,58 alternative slots on average. Each specific utilization rate yields a different number of slots (which I manually calculated the hard and painful way for all 10 junctions in the following example). A utilization rate of 100% will allow only one slot (the one we already occupy) while a utilization rate of 0% always allows 5 alternative slots.