Age of Information Analysis of Ber/Geo/1/1 Queue With On-Off Service

The Age of Information (AoI), which measures the time since the generation of the latest update, quantifies information freshness in timeliness-critical systems. Minimizing AoI and characterizing it precisely are crucial for system efficiency and decision-making. This work investigates AoI under external interference modeled as an On-Off process, providing a foundation for future research in more complex scenarios. We consider a discrete-time remote status-updating system with a monitor and a sensor, where the sensor observes a physical process, generates timestamped updates, and sends them to the monitor. Both inter-arrival and service times follow geometric distributions, with service interrupted according to a two-state On-Off process. We analyze AoI under two queuing disciplines: 1) non-preemptive, where arriving updates are discarded if the server is occupied, and 2) preemptive, where in-service updates are replaced with new ones during the Off state. For both, we derive closed-form expressions for average AoI and peak AoI (PAoI). We also explore the relationship between discrete-time and continuous-time systems, showing that the latter is the limiting case of the former. Numerical results validate the theoretical analysis, revealing a linear relationship between the relative normalized increase in average PAoI and AoI and the proportion of Off state time. Frequent On-Off switching and higher service rates under the same system load help mitigate freshness deterioration caused by interruptions. The On-Off process is shown to have a large impact on the average AoI (resp. PAoI) of systems with relatively high (resp. low) arrival and service rates.