Age-optimal Sampling and Transmission Scheduling in Multi-Source Systems
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In this paper, we consider the problem of minimizing the age of information in a multi-source system, where sources communicate their update packets to a destination via a channel with random delay. Due to interference, only one source can be scheduled at a time. We consider the problem of finding a decision policy that controls the packet sampling times and schedules source transmissions to minimize the total average peak age (TaPA) and the total average age (TaA) of the sources. Our investigation of this problem results in an important separation principle: The optimal scheduling strategy and the optimal sampling strategy are independent of each other. In particular, we prove that, given the sampling times of the update packets, the Maximum Age First (MAF) scheduling strategy provides the best age performance among all scheduling strategies. This transforms our overall optimization problem into an optimal sampling problem, given that the decision policy follows the MAF scheduling strategy. Interestingly, we show that the zero-wait sampler (in which a packet is generated once the channel is idle) is optimal for minimizing the TaPA, while it does not always minimize the TaA. We use Dynamic Programming (DP) to investigate the optimal sampler for minimizing the TaA. Finally, we provide an approximate analysis of Bellman's equation to approximate the TaA-optimal sampler by a water-filling solution and demonstrate its efficacy through numerical evaluations.
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