On the age of information for non-preemptive queues in tandem

Abstract

A monitoring system operates over a network of first-come, first-served queues in tandem, in which a source is transmitting its status to a monitor at the end of the tandem. To characterize the freshness performance of this monitoring system, we analyze the average Age of Information for this system, in which the status update arrivals are Poisson distributed and each queue is served by a non-preemptive, memoryless server. We first study the case of single-capacity queues that are modeled as a stochastic hybrid system, and we derive the average age for two queues with different service rates and three queues with equal service rate. We then study the infinite capacity queue case and use the graphical approach to derive the average age for two queues in tandem with equal service rates. Finally, we simulate the average age for intermediate cases of k capacity queues, which fall in between the two extreme cases of k = 1 and k = ∞.