Age-optimal multi-flow status updating with errors: A sample-path approach

In this paper, we study an age of information minimization problem in continuous-time and discrete-time status updating systems that involve multiple packet flows, multiple servers, and transmission errors. Four scheduling policies are proposed. We develop a unifying sample-path approach and use it to show that, when the packet generation and arrival times are synchronized across the flows, the proposed policies are (near) optimal for minimizing any time-dependent, symmetric, and non-decreasing penalty function of the ages of the flows over time in a stochastic ordering sense.