Non-linear Information Freshness in Large Scale Random Access Networks

We consider a random access network where source nodes generate and transmit timely status updates to their intended receivers. Instead of the conventionally adopted Age of Information (AoI) metric, we employ a non-linear function of AoI, referred to as the Cost of Update Delay (CoUD) that captures the sensitivity to information staleness based on different ageing properties. We derive an analytical expression for the CoUD under general cost functions by leveraging tools from stochastic geometry. We provide several closed-form results for a family of cost functions. The accuracy of our analytical results is verified through simulations. We observe that in densely deployed networks there exists an optimal update rate that minimizes the CoUD. Conversely, if the network is sparse, increasing the update rate always benefits the average information freshness of the network. In addition, we simulate the sensitivity of CoUD to the networking parameters under different cost functions, providing insights on how to choose the cost functions and the design network parameters.