It is well known that opportunistic scheduling algorithms are throughput
optimal under full knowledge of channel and network conditions. However, these
algorithms achieve a hypothetical achievable rate region which does not take
into account the overhead associated with channel probing and feedback required
to obtain the full channel state information at every slot. We adopt a channel
probing model where $\beta$ fraction of time slot is consumed for acquiring the
channel state information (CSI) of a single channel.
Energy consumption of a wireless sensor node mainly depends on the amount of
time the node spends in each of the high power active (e.g., transmit, receive)
and low power sleep modes. It has been well established that in order to
prolong node's lifetime the duty-cycle of the node should be low. However, low
power sleep modes usually have low current draw but high energy cost while
switching to the active mode with a higher current draw.
We consider the problem of cross-layer resource allocation in time-varying
cellular wireless networks, and incorporate information theoretic secrecy as a
Quality of Service constraint. Specifically, each node in the network injects
two types of traffic, private and open, at rates chosen in order to maximize a
global utility function, subject to network stability and secrecy constraints.
The secrecy constraint enforces an arbitrarily low mutual information leakage
from the source to every node in the network, except for the sink node.
In this paper, we consider the standard discrete-time slotted ALOHA with a
finite number of terminals with infinite size buffers. In our study, we jointly
consider the stability of this system together with the physical layer
security. We conduct our studies on both dominant and original systems, where
in a dominant system each terminal always has a packet in its buffer unlike in
the original system. For N = 2, we obtain the secrecy-stability regions for
both dominant and original systems. Furthermore, we obtain the transmission
probabilities, which optimize system throughput.