On the Average and Distribution of Age of Information for Frameless ALOHA

Frameless ALOHA (FA) is a slotted-time random access protocol for collision channels that uses successive interference cancellation (SIC) techniques to improve decoding performance. In this letter, we characterize the average and distribution of age of information (AoI) for FA with M users. Transmissions in FA are organized into rounds of random length. We compare different round termination methods and observe that the average AoI is minimum for a method where the round terminates when a single user transmits in a slot. We then obtain a novel numerical characterization of the packet decoding probability for FA under the above method to terminate a round. The characterization of the packet decoding probability is then used to obtain novel characterizations of the average AoI as well as the distribution of AoI for any M. These characterizations match with simulations and can be utilized in optimizing FA protocol parameters for average AoI or any general function of AoI.