  In this paper, we investigate a network of N interfering links contending for
the channel to send their data by employing the well-known Carrier Sense
Multiple Access (CSMA) scheme. By leveraging the notion of stochastic hybrid
systems, we find a closed form of the total average age of the network in this
setting. Armed with this expression, we formulate the optimization problem of
minimizing the total average age of the network by calibrating the back-off
time of each link. By analyzing its structure, the optimization problem is then
converted to an equivalent convex problem that can be solved efficiently to
find the optimal back-off time of each link. Insights on the interaction
between the links is provided and numerical implementations of our optimized
CSMA scheme in an IEEE 802.11 environment is presented to highlight its
performance. We also show that, although optimized, the standard CSMA scheme
still lacks behind other distributed schemes in terms of average age in some
special cases. These results suggest the necessity to find new distributed
schemes to further minimize the average age of any general network.
