Multi-Stream Quickest Detection with Unknown Post-Change Parameters Under Sampling Control

Qunzhi Xu, Yajun Mei

Abstract: The multi-stream quickest detection problem with unknown post-change parameters is studied under the sampling control constraint, where there are <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$M$</tex> local processes in a system but one is only able to take observations from one of these <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$M$</tex> local processes at each time instant. The objective is to raise a correct alarm as quickly as possible once the change occurs subject to both false alarm and sampling control constraints. We propose an efficient myopic-sampling-based quickest detection algorithm under sampling control constraint, and show it is asymptotically optimal in the sense of minimizing the detection delay under our context when the number <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$M$</tex> of processes is fixed. Simulation studies are conducted to validate our theoretical results.