  Based on the covert communication framework, we consider a covert queueing
problem that has a Markovian statistic. Willie jobs arrive according to a
Poisson process and require service from server Bob. Bob does not have a queue
for jobs to wait and hence when the server is busy, arriving Willie jobs are
lost. Willie and Bob enter a contract under which Bob should only serve Willie
jobs. As part of the usage statistic, for a sequence of N consecutive jobs that
arrived, Bob informs Willie whether each job was served or lost (this is the
Markovian statistic). Bob is assumed to be violating the contract and admitting
non-Willie (Nillie) jobs according to a Poisson process. For such a setting, we
identify the hypothesis testing to be performed (given the Markovian data) by
Willie to detect the presence or absence of Nillie jobs. We also characterize
the upper bound on arrival rate of Nillie jobs such that the error in the
hypothesis testing of Willie is arbitrarily large, ensuring covertness in
admitting Nillie jobs.
