A Covert Queueing Problem With Busy Period Statistic

In this letter, we consider a covert queueing problem where server Bob is in agreement with Willie to serve his jobs exclusively and yet would like to admit non-Willie jobs covertly. Willie jobs arrive according to a Poisson process and have an exponential service requirement. Bob desires to admit a Poisson stream of non-Willie jobs at a rate λ b . Bob schedules jobs according to an arbitrary work-conserving policy and as part of usage statistics informs Willie of either the lengths of n successive busy periods or the number of jobs served in each of them. Willie performs optimal hypothesis testing to detect the presence of non-Willie jobs. In this work, we identify sufficient conditions on λ b such that Bob can allow non-Willie jobs without Willie knowing about it with high probability.