Quickest Change Point Detection with Measurements over a Lossy Link

Motivated by Industry 4.0 applications, we consider quickest change point detection (QCD) when process measurements are transmitted by a sensor over a lossy wireless link to a decision maker (DM). The sensor node samples measurements using a Bernoulli sampling process, and places the measurement samples in a transmit queue of the transmitter. The transmitter uses a retransmit-until-success transmission strategy to deliver packets to the DM over the lossy link, which is modeled as an independent Bernoulli process and has different loss probabilities before and after the change. We pose the QCD problem in the non-Bayesian setting under Lorden's framework [1], and derive a CUSUM algorithm. By defining a suitable Markov process, involving the DM measurements and the queue length process, we show that the problem reduces to QCD of a Markov process. Characterizing the information measure I per measurement sample at the DM, our analysis proves the asymptotic optimality of our algorithm when the false alarm rate tends to zero. We discuss extensions of the analysis to periodic sampling and no-retransmission cases. Through numerical analysis, we demonstrate trade-offs that can be used to optimize system design parameters such as the sampling rate of the measurement process in the non-asymptotic regime.