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We consider a node-monitor pair, where updates are generated stochastically(according to a known distribution) at the node that it wishes to send to themonitor. The node is assumed to incur a fixed cost for each transmission, andthe objective of the node is to find the update instants so as to minimize alinear combination of AoI of information and average transmission cost. First,we consider the Poisson arrivals case, where updates have an exponentialinter-arrival time for which we derive an explicit optimal online policy. Next,for arbitrary distributions of inter-arrival time of updates, we propose asimple randomized algorithm that transmits any newly arrived update with afixed probability (that depends on the distribution) or never transmits thatupdate. The competitive ratio of the proposed algorithm is shown to be afunction of the variance and the mean of the inter-arrival time distribution.For some of the commonly considered distributions such as exponential, uniform,and Rayleigh, the competitive ratio bound is shown to be 2.

Minimizing the Sum of Age of Information and Transmission Cost under Stochastic Arrival Model