Analysis of Age of Information for a Discrete-Time Dual-Queue System

Using multiple sensors to update the status process of interest is promising in improving the information freshness. The unordered arrival of status updates at the monitor end poses a significant challenge in analyzing the timeliness performance of parallel updating systems. This work investigates the age of information (AoI) of a discrete-time dual-sensor status updating system. Specifically, the status update is generated following the zero-waiting policy. The two sensors are modeled as a geometrically distributed service time queue and a deterministic service time queue in parallel. We derive the analytical expressions for the average AoI and peak AoI using the graphical analysis method. Moreover, the connection of average AoI between discrete-time and continuous-time systems is also explored. It reveals that in dual-queue systems, the AoI results of continuous-time systems with exponential time distribution can be extended from the limit cases of discrete-time systems with geometric distribution. Numerical results validate the effectiveness of our analysis and further show that randomness of service time contributes more AoI reduction than determinacy of service time in dual-queue systems in most cases, which is different from what is known about the single-queue system.