It’s been a busy week. Managing a ski area through the peak of the season leaves little time for anything else. The office door cracks open and a head pokes in. “The new lift is all wrong! The lift line is pushing 25 minutes, and lift #4 is still running at only 60% utilization. The extra burden on trails 13 and 14 is causing skier densities we didn’t expect. What should we do?”
The response comes after several minutes of careful consideration. “Let’s move the new lift to the alternate location on the North slope, and cut a new trail to parallel #14. Then put 6,000 skiers on the mountain for four hours and see what the lift lines look like.”
Is this guy crazy? Not really. He’s testing the possible results of a new lift system by using a computer simulation, that is, a custom computer program which can simulate the movement of skiers through a real or proposed lift and trail system.
The basic concept of representing a physical system by a mathematical or numerical model is quite old, but only since the advent of the high speed digital computer has the numerical simulation of complex dynamic physical systems become a valuable planning and management tool. The authors, in cooperation with Don Tarinelli, president and general manager of Stratton Corporation, have developed and implemented simulation techniques which are being employed to provide realistic information regarding the effect of proposed new lifts and trails on uphill capacity, downhill densities, and lift line lengths.
Metaphorically speaking, a ski area simulation is a sort of “number machine,” the various parts of which, when set into motion, behave much like their real life counterparts, the lifts, trails, and skiers which make up the actual ski area being simulated. From a design and management point of view, the simulation offers several advantages over the actual facility to be studied. These advantages include speed, accessibility of information, cost of implementing changes, reversibility of decisions, and low environmental impact of mistakes.
The speed of a simulation, once it is designed and residing in the memory of a digital computer, is almost scary. An entire day’s operation of your favorite ski area, with capacity crowds, takes only a few minutes. A few minutes more and detailed information regarding lengths of lift lines, skier density on trails, and per cent utilization of lifts is made available via the computer’s printer. Besides actual speed of operation, the simulation offers speed in another area…construction time. A new lift may be “added” in a couple of days, thoroughly tested for impact, moved around, or eliminated. Trails may be added just as easily.
Because the simulation is in fact a collection of numerical information residing in and being manipulated by a computer, the desired information about its operation is easily extracted. Skier densities and lift line variations which would take days to collect and compile by census techniques on the actual mountain are almost instantly available from the computer simulation, at little cost (the purchase of a computer is not necessary).
Naturally the cost of a simulation is much less than the cost of developing a mountain (although, admittedly, it’s difficult to enjoy skiing on a computer). A more realistic comparison is that the cost of an entire simulation, complete with several alternate locations for proposed lift and trail additions is still a very small fraction of the cost of adding one lift. It goes without saying that the cost, both in dollars and environmental impact, of building one lift or cutting one trail which turns out to be even a marginal mistake, is huge. The cost of simulating one additional lift, by comparison, is negligible. And, if it should turn out to be a mistake, the only environmental impact is a few sheets of scrap paper.
Just how well a numerical simulation can mimic a physical process is a function of how well the actual process is understood, and how well this understanding is translated into a piece of computer software, the program which actually controls the flow of information within the computer. To successfully simulate a particular ski area, someone with an intimate understanding of the lift and trail system to be modeled, and a knowledge of the skills and preferences of the skier population using the facility, must work closely with the software designer in creating the simulation software. Specific inputs needed to design a simulation fall into three broad categories: Lift operating parameters and locations, trail classifications, and skier skills and preferences.
Lifts may be quite easily described. Each lift has a particular load point and partcular discharge point (or points). The load points are accessible from specific trails and parking areas. The discharge points give access to specific trails. In addition, each lift has a design capacity and a specific transit time. This information for each lift is sufficient to describe the uphill transportation system, and link it to the trail system.
Trail description is somewhat more complex. While each trail also has specific entry and exit points, transit time may vary widely from skier to skier. All trails are not equally suitable to all skiers; some may be too difficult for the novice, while others will not be sufficiently challenging to the expert. Accordingly, trails are given mean transit times which are weighted according to skier skill level, and as the simulation runs, individual skiers’ times are distributed about the mean times.
The skier population which is to be placed on the lift and trail system must also be described. The total number of skiers, the percentage at each skill level (usually three levels are defined), and the time span over which they arrive must be specified.
Some additional information, mostly of a statistical nature, is needed to link the lifts, trails, and skiers together into a complete simulation. Primarily, the probability that a skier of known skill level will ski each of several trails or ride each of several lifts must be specified. The skier’s decision may be affected by the lengths of various liftlines at the time the decision must be made.
With this information in hand, the software designer creates a lift and trail system within the computer, imposes a particular skier population on it, and allows the model to run. The output of the model includes lengths of liftlines and skier density on each trail at the end of each hour, maxima of these quantities during the previous hour, and per cent utilization of each lift for the hour. If the first output doesn’t “look good” or “feel right” to everyone involved, specific decision points may be tuned up until things do look right. At this point, the planner is off and running, with a new tool to test ideas and help make decisions.
Just how good is the output of a computer simulation? The answer of course depends on how good the input is. At Stratton, the answer seems to be “very good.” In the fall of 1977, a simulation was done of the facility as it then existed. Over Washington’s birthday week, with record breaking crowds on the mountain, a very complete skier census was taken. The results compared remarkably well with the predictions of the simulation. Stratton is basing much of their planning on this census and the simulation. Don Tarinelli expects to continue to use the computer simulation technique as an aid to future planning and mountain design.
Len Bugel and Dave Tyburski are co-owners of Tycom Associates, a computer consulting firm dealing primarily in software development for customer applications. Tycom’s address is 68 Velma Avenue, Pittsfield, MA 01201.
