Age of Information: The Multi-Stream M/G/1/1 Non-Preemptive System

This work investigates a remote status updating system where the transmission process is modeled as a multi-stream M/G/1/1 non-preemptive system. We derive the closed-form expression of the average AoI of each stream in a heterogeneous case, where the distributions of service time are different for streams. To obtain more insights, we apply the results in a homogeneous system, where the service time distributions are identical, and find that preemption of packets would not always lead to the reduction of AoI, especially when the variance coefficient of the service time is small. We further optimize the generation rate to minimize the sum of average AoI. The results in heterogeneous cases show that given the same average service time for all streams, a higher generation rate should be allocated to the stream with a small service time variance. For the homogeneous cases with different AoI urgency weights for each stream, a higher generation rate should be reserved for the stream with more urgent AoI requirements for timeliness improvement. Besides, a lower bound on sum of average AoI is also provided, which only depends on the service rate and the number of data streams in homogeneous systems. Numerical results validate our theoretical analysis.