Scheduling appointments via fluids control

In this research a fluid based appointment book is designed to be used for managing appointment systems. We propose a deterministic fluid control approach for modeling a stochastic single server appointment system with several types of customers. Optimal control functions for the minimum average waiting time objective are presented and used to suggest a scheduling heuristic. The heuristic is then used for constructing our appointment book for scheduling customers in the original stochastic system. We demonstrate the performance of the obtained schedule using simulations.