Analyzing the Pace of Play in Golf

We develop performance approximations that can help manage the pace of play in golf. In previous work we developed a stochastic model of successive groups of golfers playing on an 18-hole golf course and derived expressions for the capacity (maximum possible throughput) of each hole and the golf course as a whole. That model captures the realistic feature that, on most holes, more than one group can be playing at the same time, with precedence constraints. We now facilitate further performance analysis with that model by developing two new approximations. First, we develop an approximation involving a series of conventional single-server queues, without precedence constraints. The key idea is to use the times between successive departures on a fully loaded hole as aggregate service times in the new model. Second, we apply established heavy-traffic limits for a series of conventional queues to develop explicit approximation formulas for the mean and variance of the time required for group n to play the entire course, as a function of n. We conduct simulation experiments showing that both approximations are effective. We show how these formulas can help design and manage a golf course.