  We investigate the age-of-information (AoI) in the context of random access
networks, in which transmitters need to send a sequence of information packets
to intended receivers over shared spectrum. We establish an analytical
framework that accounts for the key features of a wireless system, including
the fading, path loss, network topology, as well as the spatial interactions
amongst the queues. A closed-form expression is derived to quantify the network
average AoI and its accuracy is verified via simulations. Our analysis unveils
several unconventional behaviors of AoI in such a setting. For instance, even
when the packet transmissions are scheduled in a last-come first-serve (LCFS)
order whereby the newly incoming packets can replace the undelivered ones, the
network average AoI may not monotonically decline with respect to the packet
arrival rates, if the infrastructure is densely deployed. Moreover, the ALOHA
protocol is shown to be instrumental in reducing the AoI when the packet
arrival rates are high, yet it cannot contribute to decreasing the AoI in the
regime of infrequent packet arrivals.
