  Consider a channel where authorized transmitter Jack sends packets to
authorized receiver Steve according to a Poisson process with rate $\lambda$
packets per second for a time period $T$. Suppose that covert transmitter Alice
wishes to communicate information to covert receiver Bob on the same channel
without being detected by a watchful adversary Willie. We consider two
scenarios. In the first scenario, we assume that warden Willie cannot look at
packet contents but rather can only observe packet timings, and Alice must send
information by inserting her own packets into the channel. We show that the
number of packets that Alice can covertly transmit to Bob is on the order of
the square root of the number of packets that Jack transmits to Steve;
conversely, if Alice transmits more than that, she will be detected by Willie
with high probability. In the second scenario, we assume that Willie can look
at packet contents but that Alice can communicate across an $M/M/1$ queue to
Bob by altering the timings of the packets going from Jack to Steve. First,
Alice builds a codebook, with each codeword consisting of a sequence of packet
timings to be employed for conveying the information associated with that
codeword. However, to successfully employ this codebook, Alice must always have
a packet to send at the appropriate time. Hence, leveraging our result from the
first scenario, we propose a construction where Alice covertly slows down the
packet stream so as to buffer packets to use during a succeeding codeword
transmission phase. Using this approach, Alice can covertly and reliably
transmit $\mathcal{O}(\lambda T)$ covert bits to Bob in time period $T$ over an
$M/M/1$ queue with service rate $\mu > \lambda$.
