On Age of Information for Discrete Time Status Updating System With Infinite Size

In this paper, for discrete time status updating system with infinite size, we derive the explicit expression of average age of information (AoI) and its stationary distribution. Notice that there is no packet loss in an infinite size system, we successfully characterize the random dynamics of discrete AoI using a two-dimensional state vector, which simultaneously tracks the value of AoI and the age of packet currently under service. A two-dimensional stochastic process is constituted and we completely solve all the stationary probabilities. Then, as one of the marginal distributions the stationary distribution of AoI is obtained, with which the average AoI is also determined.