The Age of Information in Networks: Moments, Distributions, and Sampling
EVENT CALENDAR CATEGORY
LIDS Seminar Series
We examine a source providing status updates to monitors through a network with state defined by a continuous-time finite Markov chain. Using an age of information (AoI) metric, we characterize timeliness by the vector of ages tracked by the monitors. Based on a stochastic hybrid systems (SHS) approach, we derive first-order linear differential equations for the temporal evolution of both the age moments and a moment generating function (MGF) of the age vector components. We show that the existence of a non-negative fixed point for the first moment is sufficient to guarantee convergence of all higher-order moments as well as a region of convergence for the stationary MGF vector of the age. The stationary MGF vector is then found for the age on a line network of preemptive memoryless servers. It is found that the age at a node is identical in distribution to the sum of independent exponential service times. This observation is then generalized to linear status sampling networks in which each node receives samples of the update process at each preceding node according to a renewal point process. For each node in the line, the age is shown to be identical in distribution to a sum of independent renewal process age random variables.
Roy Yates is a Distinguished Professor with the Wireless Information Networks Laboratory (WINLAB) and the Electrical and Computer Engineering (ECE) department at Rutgers University. He received the B.S.E. degree in 1983 from Princeton University, and the S.M. and Ph.D. degrees in 1986 and 1990 from M.I.T., all in Electrical Engineering. He is an author of three editions of the John Wiley textbook “Probability and Stochastic Processes: A Friendly Introduction for Electrical Engineers.” An IEEE Fellow in 2011, Dr. Yates is a past associate editor of the IEEE Journal on Selected Areas of Communication Series in Wireless Communication and also a past Associate Editor for Communication Networks of the IEEE Transactions on Information Theory.
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