  This letter analyzes a class of information freshness metrics for large IoT
systems in which terminals employ slotted ALOHA to access a common channel.
Considering a Gilbert-Elliot channel model, information freshness is evaluated
through a penalty function that follows a power law of the time elapsed since
the last received update, generalizing the age of information metric. By means
of a signal flow graph analysis of Markov processes, we provide exact closed
form expressions for the average penalty and for the peak penalty violation
probability.
