Computer Simulation of the Network

The definition of insanity is when you repeat, over and over again, the same behavior, and expect a different result from before.

Simulation of a planned beam network is a necessary first step before one starts investing time and money into the actual planning and construction of the network. This is a fairly technical page, but it is not really a tutorial. It is intended primarily as a guide for persons who are unfamiliar with city traffic planning. We would here like to draw the reader´s attention to the simulation program that Joerg Schweizer has made and which is available on the "Modular Automated Individual Transport", (MAIT) website. In October of 2004, Joerg released version 2.0 of the The innovative Transport Simulator iTS MAIT. You can also check out the SimPyTransit website.	This page is divided into the following chapters: Why Computer Simulation? What has to be done? How the Simulation is Performed Information which is specific to FlyWay® can be accessed from this page.

1. Why Computer Simulation?

t will, of course, be necessary to perform simulations of various traffic scenarios during the planning stage, before the actual construction of a beam network. The computer is the best tool for this. All traffic planners are familiar with this kind of proceedures, so this webpage is mainly intended as information for the general reader, who might be interested. Traffic scenarios such as these are being done all the time, around the world, and many computer programs for this purpose have been written. The whole process is highly iterative, and consists of the following stages: An estimate of the area to be serviced initially is made. A rough estimate of required traffic capacity in this area is made. Various solutions to fill the required needs are put forward. Those solutions that are not judged feasible are weeded out.

The remaining solutions are subjected to computer simulations, where various parameters are trimmed to optimal performance. The results of the simulations for the proposed solutions are compared to each other, and a further weeding-out of not-feasible solutions can be made. The one or two remaining solutions are then subjected to detailed analysis, through performance simulations of each ingoing part. When those parts have been trimmed to optimal performance, simulation of the whole network will have to be done again (and again, and again and....) The end result will then have to be subjected to economical estimates. Cost parameters are of course included in the simulations, but there are always costs that cannot be applied until the whole "package" is ready. Hopefully, this will lead to the conclusion that the project as such is profitable.

The illustration at right shows the components whose capacity will have to be trimmed in points 5 and 7 above, to meet the required needs and remove bottlenecks. Car capacity (or train capacity) as regards throughput Car capacity as regards number of cars/seats for peak loads Car capacity for handling freight Stations (speed of loading/unloading and place to buffer waiting cars) Car depots, garages and maintenance facilities Traffic throughput of local lines Traffic throughput of trunk lines Traffic throughput of Nodes Number and capacity of alternative routes to use in case of mishaps

Figure 1:1

et's go through that list and see what parameters are relevant in each case!

1: Car capacity (or train capacity) as regards throughput Since a safety distance has to be maintained between cars, it is clear that the more people (or freight) a beam car can take, the more the overall capacity will be enhanced. Big passenger cars (or trains of cars) can be used during peak hours, at sporting events, tourist groups and the like. Otherwise, the ideal beam network should be dominated by small cars that are booked, leased or mayby privately owned. The basic commuter pattern would have to be established in each case.

2: Car capacity as regards number of cars/seats for passenger transport during peak traffic time This is to ensure that there is a sufficient number of cars of different categories for peak traffic load. 3: Car capacity for handling freight The FLYWAY system allows for 3 general types of freight cars: Flatcars Vehicles with Grappling Hooks Carriers of adapted road vehicles (example with carrier for electric car illustrated in figure 1:3 below).

Figure 1:3

4: Stations (speed of loading/unloading and place to buffer waiting cars) There are 3 ways to increase the commuter-handling capacity of a station: Increase the number of berths, for simultaneous loading/unloading Increase the buffer space to hold car in readiness Reduce the time that leaving cars have to wait for a free timeslot to get out on the trunk line Figure 1:4 5: Car depots, garages and maintenance facilities These have to be of sufficient size, to hold all cars. They also should be strategically placed, so that cars don't have to travel a long way to reach their starting-off point for their "shift".

6: Traffic throughput of Local lines Can be increased by: Increasing allowable speed, if possible Increasing number of parallel beams Reducing the number of nodes the cars have to pass 7: Traffic throughput of Trunk lines Can also be increased by: Increasing allowable speed, by making the guideway as straight as possible Increasing the number of parallel beams Reducing the number of shunts, requiring a slow-down of speed, that the cars have to pass. 8: Traffic throughput of Nodes These will probably be the primary bottlenecks in a well-designed network. The way to increase their capacity is to increase their complexity! Build more alternative routes, parallel routes, with many shunts! The network is computer controlled, and compters excell in quick calculations and evaluations of huge amounts of data. 9: Number and capacity of alternative routes in case of mishaps The solution here is basically the same as for nodes: Provide more alternative routes. If possible, every locality should be reachable from at least two different directions.

2. What has to be done?

In the initial stage, 3 computerized models have to be constructed: A matrix, showing the transportation needs A model of the intended beam network, with all stations, nodes, etc, to indicate capacity and bottlenecks A mathematical model of the guidance system Let's look closer at the first listing, at the top of this page. 1) Estimate of the area to be serviced. This would in most cases be a metropolitan area, including its' suburbs. In the case that the city has grown so much that it has merged with cities in its vicinity, it would obviously have to be a political decision, since it will be a question of who pays for what. Otherwise, the most consideration should be shown towards the commuting pattern of the inhabitants of the whole area and the need to freight goods. One should provide for the many people who live or work outside the area to be served, by making adequate, free, parking areas at the stations on the fringes of the area to be served by the beam network.

Figure 2:1

2) Estimate of required traffic capacity. Make one estimate for the need to handle freight; amount, time of day and departure/destination points. Make another estimate of commuting needs. One way to do this would be to divide the area into neighborhoods, small enough to be serviced by one station of the intended beam network. The present patterns with bus stops and tram stops could serve as a guide. Interview commuters on these buses/trams as to their travel patterns, existing and preferred. Do the same interviews with employees at big employment sites. Complement this with the traffic flow statistics from the throughfares. Do not forget the people who are traveling to and from areas outside the area to be served, as mentioned in the previous paragraph! Also, leisure time travel patterns are just as important here as commuting to and from work. As these are not scheduled occurences, statistical generation of data have to be used, but the amount of this travel has to be known fairly well. Leisure travel should be expected to increase, as people discover the ease and comfort that beam travel offers, as compared to the old alternatives! This investigation should supply a reasonably reliable guide as regards: Passenger flows to each intended station on the network, for all hours and for every day of the week. A statistical estimate of what percentage of passengers for each station are going to what destination, and when. Corresponding info for the freight to be handled.

As can be seen, this would result in a matrix proportional to the number of intended stations. For a network of 200 stations and upwards, this matrix would likely be so huge that it could only be handled by a computer program. It is probably a good idea to make separate matrixes for passengers and freight. The reasons for that is: Passenger transportation will likely have a higher priority than freight handling Passengers and most goods will probably be handled at different hours of the day. It would be advantageous if most of the goods could be transported during the night.

3) Various solutions to fill the required needs. The matrix from 2) would then be applied to the various alternative networks put forward. Include all alternative routes that are deemed feasible! The more alternative routes there are, that can be tested against the commuter needs in the matrix, the greater the chance of hitting upon the best solution. There is a marked difference between downtown, inner suburbs and more outlying areas. For downtown areas where traffic is very concentrated and distances between stations could be made short, special solutions can be tried, solutions that are not viable anywhere else.

On the basis of some calculations made by J. Edward Anderson, we have made some estimates of our own, with a city network where, from each point in the city, one has less than 400 meters to walk to either of 4 stations. Each of these 4 stations have one-way traffic going in each of the four cardinal points (See The Capacity of Personal Rapid Transit Systems).

4) Solutions that are not judged feasible are weeded out. The main criteria for this "weeding out"-process are that people and freight should travel the most direct path possible to their destinations, at the shortest possible time and to the lowest cost. Aestetical and practical considerations should also come into play. A trademark of the ideal beam traffic system should be "unobtrusiveness". It should not be more visibe than is necessary, nor should it get in the way of other activities nor obstruct a desirable view.

5) Remaining solutions are subjected to simulations, where parameters are trimmed to optimal performance. This step should not put too much emphasis on the matrix of commuter travel, considering that those figures are mainly estimates. Instead, the emphasis here should be put on attaining a certain percentage of redundance as regards traffic handling capacity, number of cars, availability of alternative routes, etc. The object here should be: Getting the most redundancy to the least additional cost.

6) The results are compared and a further weeding-out is made. It could happen here, that flaws in the simulations have been corrected, making it interresting to once again test solutions that were previously weeded out. 7) The remaining solutions are subjected to detailed analysis. This entails applying the model to real life. For instance, a station needs to handle a certain number of people during rush hour. Is the street where it is to be placed big enough to handle a station of that size? Do buildings need to be torn down, or does the station have to be moved? When this step is done, we will hopefully have a model that is optimal as regards traffic handling capacity, speed and economy.

8) Simulation of the whole network. This is where the mathematical model of the guidance system will enter the simulation. Also, safety aspects and aestethic considerations for the city landscape will have to be considered thoroughly.

3. How the Simulation is Performed

et us here confine ourselves to transportation of people. Transportation of goods will follow approximately along the same lines. The main differences would be: Transportation of goods is more predictable The capacity requirements would be more even for goods The emphasis on quick transporation is lower for goods Transportation of motorvehicles should, in most cases, be included with transportation of people. Dual-mode transportation and carrying motorcars on flatcars will be a necessary service in order to draw enough passegers to the network. The importance of this depends of course on: How many percent of the affected population that owns motorcars. What policy the authorities have, or intend to implement, regarding motorcar use. Make separate simulations for passengers and goods. Then, at a later stage, make a common simulation for all traffic on a 24-hour basis.

The Preparatory simulation: The simulation phase is perforformed by first constructing a routing table. For each departure - destination combination on the whole network, there has to be information about how long time it takes to complete the trip, using various routes. The table should confine itself to the 3 or 4 quickest routes. This table will be updated by the beam cars as the simulation proceeds, but at the outset a rough estimate will have to be made, based on the geographical distances between all stations on the network. Don't devote too much time to this, use very rough figures. Then, do a trial simulation, where the cars are manually directed along the various routes. This could be done by letting a program loop continually alter the "routes of best choice" in the routing table. The cars will then test all the routes and update these figures in their tables as they complete their trips. After going through this, the routing table will contain figures that are usable for the real simulation!

The "Real" simulation: As the "real" simulation starts, the time is advanced in small steps, with each step corresponding to one time slot, typically between 1 and 2 seconds. One can say that the scenario is run through in slow motion. One could start this phase from zero, i.e. pretend that this is the start of a new day. But it is more efficient to start it with beamcars already running, some with passengers, etc. according to a basic set of statistically generated figures. In other words, start the simulation from an arbitrary point in time during an average day. For each such step, the contents of various tables have to be updated, as outlined in the steps below. Although it will generate a tremendous amount of figures, the simulation would, sooner or later, have to encompass the full 24 hours of a day. When these figures are observed, it will be noted that it usually takes some time after the start of a simulation, before the figures are stable enough to be trusted. But these figures can then be used when the next simulations start, shortening the time it takes for the simulation to stabilize itself.

1) Each station is fed with the departure information from the matrix mentioned above. Arrivals during peak traffic times should adhere pretty close to the matrix figures, as these are based on interviews with people commuting to and from their works. For other hours of the day, a general pattern would have to be followed, based on available traffic statistics. People go to the malls to shop, go to football games, visit the movie theaters, etc. Continued

A station which "has it all" might look something like this illustration: A denotes the beam for traffic that passes thru without stopping. B is the beam reserved for "taxicab" cars. They just stop for entering or leaving travelers and then gets going again. If they are sent to pick up a certain customer at a certain time, they had better pull into one of the berths (numbered 1 to 8) reserved for the purpose. C: From this beam, the cars going on scheduled routes pull into their assigned berths. In this example, there are 4 berths in a row, which thus can take 4 cars for simultaneous loading. Let's say that beams 5 through 8 are used for scheduled transports. Beams 1 through 4 could thus be used for available cars for on-the-spot bookings, as when you enter a taxicab at a cab station. Beam D would be used as a car depot. These are activities that are pretty irregular, but nevertheless take place daily and generate a lot of traffic. Use a poisson-randomized distribution for generating arrivals of passengers at the stations, and make separate simulations for big events, such as football games.

2) For every passenger waiting for a booked beamcar, there has to be information about arrival time at the station of departure, i.e. the traveler waiting at a station should have information available on a monitor regarding when the beamcar he/she wants to travel with will be available. This time would then be compared to the arrival time at the destination, and both travel time and waiting time would be calculated. This kind of system already exists for bus- and train commuters in several cities.	The target for a simulation would be to bring this waiting time as near to zero as possible for as many travelers as possible. For each passenger there would also have to be information about stations of departure and of arrival. If some passengers stop along the way at certain points, the easieast would probably be to regard that journey as several small trips in succession.

3) Every beam car would make several trips a day. For each trip, stations of departure and arrival would have to be listed. When one (or more) passengers enters, the table item for that particular beamcar will have to be updated with their destinations. If the car stops along the way, the journey should be listed as several trips. For each trip, the car has to retrieve a listing of what nodes to pass to reach its destination the quickest way. If the car is on a scheduled run, its adherence to the time table should be noted. Also, for each car one has to keep track of what nodes are passed, and at what times. It is not guaranteed that those nodes agree with those in the listing for preferred route. Also, in this manner, queueing can be detected. A lot of passengers would have to be assumed to travel together with the scheduled cars. On the basis of travel patterns, it would have to be decided before simulation starts;

How close together those cars should travel Between what points they should travel At what stations they would stop along the way At what hours they should travel How many passengers they should take. These estimates could be based on present bus and tram traffic patterns. The passengers' incentive to use the bigger, regular vehicles is that it would be much cheaper than booking a car of their own. One could let empty cars disregard the need for safety distances and allow two (or more) cars to pass during the same time slot.

4) Every node is assumed to have a queue, although this queue most of the time is (hopefully) empty. A node, as we use the term here, can consist of: One or more convergence shunts, in which case it is called a weaving node One or more divergence shunts, in which case it is called a divergence node A succession of convergence and/or divergence shunts in any number or order; we call this a combined node. Several shunts will have to be regarded as one node if they are so close together that the traffic between them will have to be regulated in a synchronous fashion.

The table item for each node counts the number of cars that pass through, differs between those that are empty, that carry passengers and (if applicable) those that carry freight. For each car that passes, the time is noted, and the car is added to the queue of the next node. 5) Car depots can be randomly distributed around the network. As the simulations proceed, one soon notices where the depots should be placed to do the most good. From a traffical viewpoint, the depots should be placed close to station that have heavy traffic. The rule is that needed cars are fetched from the nearest depot, unneeded cars are likewise sent to the nearest depot. Then, as travel conditions on the network permits, empty cars are transferred from depots where they are not likely to be needed, to those depots that statistics show that they will be better available.

6) Choice of Route.Each car takes this information from a routing table that is constantly being updated with the reported travel times from the cars that have completed their trips. Thus, for each departure - destination combination, there is information about how long time it takes to complete the trip, using various routes. A car, starting on its journey, peeks into this table, and chooses the quickest route. It then steers in each shunt according to the succession of nodes that have to be passed in order to travel this route.

As queueing and other disturbances experienced by the cars are reported, this table is updated. It could be that the route chosen suddenly is not the best route anymore. The car that is out there, traveling, might suddenly discover that it's progress is not as fast as it ought to be, according to the routing table. It then checks the table again, for the best travel route from where the car is right now to where it's going. The answer might agree with the route the car has stored, or it might not agree. In case of disagreement, the car will alter the remaining part of its route from the one originally planned. Thus, when the car arrives at its destination, it can update the routing table with new information. The design of the routing table becomes a very complex issue as the network grows. A "flat" table will grow exponentially with the number of possible destinations. The background is dealt with on the web-page about addressing. For further reading, see "The Routing Table".

7) Weaving nodes.These are the nodes where 2 or more beams converge, and they are of course potential bottlenecks. In SwedeTrack´s terminology, a weaving shunt is where 2 beams converge. There are never more than 2 beams converging at each shunt, but there can be several shunts in succession for each node, if they are so close together that they are administered as one node. Each travelling beamcar is allocated one time slot (in FlyWay occassionally two), the car nearest to the shunt getting ahead of the other beamcar, coming on the other beam. This means that the cars have to adjust their speeds so that they arrive at the shunt at a predetermined time. Since there has to be safety distances between cars, this could mean that the cars might have to slow down, maybe even to a temporary stand-still. The exception would be 2 (or more) empty cars, that could travel in the same timeslot, disregarding the safety distance between them.

For further information: J. Edward Anderson is President and CEO of the TAXI 2000 Corporation. He has written a lot about PRT systems and made traffic calculations that are valuable for traffic simulation purposes. He can be contacted via e-mail.. Much of his writings can be found at Innovative Transportation Technologies.