Monitoring a Poisson process subject to gradual changes in the arrival rates

Abstract

We look at a Poisson process where the arrival rates change from a known λ₁ to a known λ₂. Whereas in most of the literature the change-point is abrupt, we model the more realistic assumption that states that the change happens gradually over a period of time η where η is known. We calculate the probability that the change has started and completed. We also look at optimal stopping rules assuming that there is a cost for a false alarm and a cost per time unit to stop early. We conclude with some numerical results.

Keywords:

• Bayesian stopping rules
• change-point detection
• dynamic programming
• gradual changes
• poisson processes

SUBJECT CLASSIFICATIONS:

• 62L15
• 60G40