Modeling Indirect Waiting Times with an M/D/1/K/N Queue

Indirect waiting times or access times of patients are an important indicator for the quality of care of a physician. Indirect waiting times are influenced by the panel size, i.e., the number of patients regularly visiting the physician. To study the nature of this influence we develop an M/D/1/K/N queueing model where we include no-shows and rescheduling. In contrast to previous work, we assume that panel patients do not make new appointments if they are already waiting. For a given panel size we calculate the steady state probabilities for the indirect queue length and further aspects such as the effective arrival rate of patients. We compare those results to the outcomes of a simulation and show that the simplifications we used in the analytical model are verified. The queueing model can help physicians to decide on a panel size threshold in order to maintain a predefined service level with respect to indirect waiting times.