On the effects of patient unpunctuality in appointment scheduling

We consider a doctor's consultation session in which K patients have an appointment. Their effective arrival time however is determined by adding a stochastic unpunctuality time to the appointment time. Patients have general, distinct consultation distributions and their unpunctualities form a general, possibly non-homogeneous, Markov chain. The moments, up to any order, of the patient waiting times and the doctor idle time are calculated, as well as the mean waiting and idle time seen by a new patient that is added to the schedule at time t. All computations are done in finite time without requiring any truncation or approximation