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A problem in health care is the lengthy waiting time for patients to receive an appointment. Long appointment delays cause patient dissatisfaction with the health care clinic and also has clinical ramifications. Long appointment delays are also found to increase patient no-shows, which further wastes medical resources and leads to a decrease in clinical care. A model of the health care clinic is built to understand the casual relationships in the system contributing to the problem. The model is used to investigate two possible policies. A policy of eliminating multiple appointment types can be effective in reducing appointment delay and as a consequent no-shows. Using data from several clinics, our study also suggests that an effective policy is to segregate habitual no-show patients and double-book them whenever they make appointments. This policy is equally effective as general overbooking without penalizing the entire patient population.