Queueing approach for social welfare under appointment delays

Many patients experience the congestion in the healthcare system. In this case, the primary care (e.g. outpatient, MRI) usually provides appointment for patient in order to make better schedule. Patients´ behavior, such as last-minute cancellations or “no-shows”, will lead to the capacity waste, and then overall social welfare. We use a single server M/D/1/K queueing approach to obtain a stationary distribution of the patients who have chance to behave no-shows and may rejoin the queue when no-show take place. A social welfare function which includes the trade-off between patients´ reward and cost is developed. We try to figure out the impact of some queueing variables such as no-show rate on the outcome of social welfare. The experimental result shows that we should take no-show into account when decision objective is a good social welfare outcome.