Quickest detection in multiple on-off processes

We consider the problem of quickest detection of the idle/off periods in multiple on-off processes. Each time, only one process can be observed, and the observations are random realizations drawn from two different distributions depending on the current state (on or off) of the chosen process. The objective is to catch an idle/off period in any of the on-off processes as quickly as possible subject to a reliability constraint on the probability of mistaking a busy period for an idle one. We show that this problem presents a fresh twist to the classic problem of quickest change detection that considers only a single change in one stochastic process. Assuming geometrically distributed busy and idle intervals, a Bayesian formulation of the problem is established for both infinite and finite number of processes based on the theory of partially observable Markov decision process (POMDP).;For the case involves infinite number of processes, we show that the optimal joint design of channel switching and change detection has a simple threshold structure. We demonstrate that the key to quickest change detection in infinite processes is to abandon the current process when its state is unlikely to change in the near future as indicated by the measurements obtained so far and seek opportunities in a new process to avoid realizations of long busy periods. Extensions to arbitrarily distributed busy/idle times and in particular, heavy tail distributions, are discussed.;For the case involves finite number of processes, switching back to a previously visited process is allowed, and measurements obtained during previous visits are taken into account in decision making. Basic structures of the optimal decision rules are established, based on which a simple threshold policy for switching among processes and for declaring idle periods is proposed which converges to the optimal decision rule for the infinite case as the number of processes increases. Extension to heterogenous on-off processes is discussed.;The problem of quickest detection in multiple on-off processes finds applications in spectrum opportunity detection in cognitive radio networks where a secondary user searches for idle channels in the spectrum.