Status Updates in a multi-stream M/G/1/1 preemptive queue

We consider a source that collects a multiplicity of streams of updates and sends them through a network to a monitor. However, only a single update can be in the system at a time. Therefore, the transmitter always preempts the packet being served when a new update is generated. We consider Poisson arrivals for each stream and a common general service time, and refer to this system as the multi-stream M/G/1/1 queue with preemption. Using the detour flow graph method, we compute a closed form expression for the average age and the average peak age of each stream. Moreover, we deduce that although all streams are treated equally from a transmission point of view (they all preempt each other), one can still prioritize a stream from an age point of view by simply increasing its generation rate. However, this will increase the sum of the ages which is minimized when all streams have the same update rate.