Effect of Message Transmission Path Diversity on Status Age

This paper focuses on status age, which is a metric for measuring the freshness of a continually updated piece of information (i.e., status) as observed at a remote monitor. In paper, we study a system in which a sensor sends random status updates over a dynamic network to a monitor. For this system, we consider the impact of having messages take different routes through the network on the status age. First, we consider a network with plentiful resources (i.e., many nodes that can provide numerous alternate paths), so that packets need not wait in queues at each node in a multihop path. This system is modeled as a single queue with an infinite number of servers, specifically as an M/M/∞ queue. Packets routed over a dynamic network may arrive at the monitor out of order, which we account for in our analysis for the M/M/∞ model. We then consider a network with somewhat limited resources, so that packets can arrive out of order but also must wait in a queue. This is modeled as a single queue with two servers, specifically an M/M/2 queue. We present the exact approach to computing the analytical status age, and we provide an approximation that is shown to be close to the simulated age. We also compare both models with M/M/1, which corresponds to severely limited network resources, and we demonstrate the tradeoff between the status age and the unnecessary network resource consumption.