Models to Study the Pace of Play in Golf

Successive groups of golfers playing on an 18-hole golf course can be represented as a network of 18 queues in series, but the model needs to account for the fact that, on most holes, more than one group can be playing at the same time, but with precedence constraints. We show how to approximate the model of group play on each hole by a conventional G/GI/1 single-server queue, without precedence constraints. To approximate the distribution of the sojourn time for each group on a full 18-hole golf course, we consider an idealized model consisting of 18 i.i.d. holes in series. We combine these approximations to obtain a series of 18 i.i.d. conventional single-server queues. We then apply heavy-traffic approximations to develop relatively simple analytical formulas to show how the mean and variance of the sojourn time depends on key parameters characterizing group play on each stage of a hole. Simulation experiments confirm that the approximations are effective. Thus, we provide useful tools for the analysis, design and management of golf courses. The techniques also should be useful more broadly, because many service systems combine the four complicating features of the system studied here: (i) network structure, (ii) heavy-traffic conditions, (iii) transient performance and (iv) precedence constraints.