## How Often Does the Oldest Person Alive Die? a Demographic Application of Queueing Theory.

**Trifon I. Missov**, *Max Planck Institute for Demographic Research*

**Roland Rau**, *University of Rostock & Max Planck Institute for Demographic Research*

**Marcus Ebeling**, *University of Rostock & Max Planck Institute for Demographic Research*

**Joel E. Cohen**, *Rockefeller University & Columbia University*

We develop a formal model to answer the question: How often does it happen that the oldest person alive dies? We assume that the oldest person alive is at least 110 years old and that the number of people turning 110 is constant over time. Previous research has shown that mortality reaches a plateau at those advanced ages. According to standard queueing theory, the population above 110 years in our model follows a Poisson distribution with parameter λ/μ where λ depicts the rate at which people turn 110 and μ represents the force of mortality. These analytical results were consistent with the results from our simulation studies. Our simulation studies also suggested that the waiting time between the deaths of the (respective) oldest person alive follows an exponential distribution with parameter μ and, thus, with a mean duration of 1/μ if λ > μ. At the moment, we do not have an expression for the case of λ ≤ μ.

Presented in Session 1064: Data and Methods