Information Freshness Analysis of Slotted ALOHA in Gilbert-Elliot Channels

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.