An Algorithm for Exact Numerical Age-of-Information Evaluation in Multi-Agent Systems

We present an algorithm for the numerical evaluation of the state-space distribution of an Age-of-Information network. Given enough computational resources, the evaluation can be performed to an arbitrary high precision. An Age-of-Information network is described by a vector of natural numbers, that track how outdated status information from various agents is. Our algorithm yields the means to determine any moment of the corresponding stochastic process. This can be extremely valuable for cases in which the network consists of controllers that communicate with one another, as it potentially allows for less conservative control behavior. It also enables the comparison of different policies regarding their performance (minimizing the average Age-of-Information) to a much more accurate degree than was possible before. This is illustrated using the conventional MaxWeight policy and the optimal policy. We also validate and compare the algorithm with Monte-Carlo-Simulations.