| Abstract: | We develop stochastic models to help manage the pace of play on a conventional 18‐hole golf course. These models are for group play on each of the standard hole types: par‐3, par‐4, and par‐5. These models include the realistic feature that k−2 groups can be playing at the same time on a par‐k hole, but with precedence constraints. We also consider par‐3 holes with a “wave‐up” rule, which allows two groups to be playing simultaneously. We mathematically determine the maximum possible throughput on each hole under natural conditions. To do so, we analyze the associated fully loaded holes, in which new groups are always available to start when the opportunity arises. We characterize the stationary interval between the times successive groups clear the green on a fully loaded hole, showing how it depends on the stage playing times. The structure of that stationary interval evidently can be exploited to help manage the pace of play. The mean of that stationary interval is the reciprocal of the capacity. The bottleneck holes are the holes with the least capacity. The bottleneck capacity is then the capacity of the golf course as a whole. |
