This is a review of the approximation formula and stochastic model research for analyzing the pace of play in golf, conducted by Qi Fu and Ward Whitt.
Golf courses are always looking to maximize profit without affecting the golfers’ enjoyment of the game. Stochastic models and computer simulations provide information regarding how to optimize the organization of a golf course from the best interval between tee times to how many groups should be scheduled to play each day.
An approximation model is developed using single-server queues, without precedence constraints, followed by an approximation formula for the expected value of the length of time it takes a group to play the entire course. The approximation is designed for use with a course that is in high demand and is well balanced with no bottlenecks.
On a course at any point in time, there will be golfers with widely varying skill levels. To handle this, stochastic models of group play are created for each of the four types of golf holes, par 3, par 3 with wave up, par 4 and par 5. Performance measures for each group for a hole are the waiting time, playing time, and total time. These models can be combined to correspond with a golf course’s series of holes. The capacity of each hole is determined as well as the critical playing time, which is the time it takes a group to play the hole.
Using this information approximation formulas for the mean and standard deviation of the total time it takes a group to play a round of golf, relationships of intervals between tee times and the maximum players playing each hole to traffic intensity are generated. The formula assumes that the golf course is balanced with no bottlenecks. Assuming a balanced golf course lends itself to using only par 4 holes in the analysis.
The approximate performance formula for total playing time can be used to help design golf courses by creating an optimization problem with the purpose of maximizing the number of groups of players allotted time to play each day.
Simulations can be run to estimate the expected performance descriptors for any number of groups on any golf course regarding stage playing times and tee times. Courses can be tested to determine if they are, in fact, balanced. This can be done by estimating the stage playing time and mean critical cycle for each hole. If they are approximately the same for each hole, the course is balanced. Another way to test if a course is balanced is to look at waiting times for each hole. Courses that are not balanced tend to have a few holes with longer waiting times, which then create longer waiting times at successive holes.
Tournament organizers can use this information to determine which golf course is the most suitable for their purposes. Course designers can use the model to help design a course that is balanced, allowing a maximum number of golfers to play the course on any given day.
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