On Scheduling the Delivery of Babies

With the advent of elective induction of labor, the management of an obstetrical practice has assumed the problem of scheduling the delivery of babies. The problem can be thought of as a delay queuing system with a modified finite-source arrival pattern. This paper analyzes the case of a single server to determine the probability of interference (viz. the obstetrician must serve two or more patients simultaneously), solves the special case of “Poisson” arrivals and gamma (Erlangian) service times, and presents numerical values for these cases. An extension is presented wherein the probability of interference occurring within a finite time is analyzed.