Abstract-In this work, we study how to optimally manage the freshness of information updates sent from a source node to a destination via a channel. A proper metric for data freshness at the destination is the age-of-information, or simply age, which is defined as how old the freshest received update is since the moment that this update was generated at the source node (e.g., a sensor). A reasonable update policy is the zero-wait policy, i.e., the source node submits a fresh update once the previous update is delivered and the channel becomes free, which achieves the maximum throughput and the minimum delay. Surprisingly, this zero-wait policy does not always minimize the age. This counter-intuitive phenomenon motivates us to study how to optimally control information updates to keep the data fresh and to understand when the zero-wait policy is optimal. We introduce a general age penalty function to characterize the level of dissatisfaction on data staleness and formulate the average age penalty minimization problem as a constrained semiMarkov decision problem (SMDP) with an uncountable state space. We develop efficient algorithms to find the optimal update policy among all causal policies, and establish sufficient and necessary conditions for the optimality of the zero-wait policy. Our investigation shows that the zero-wait policy is far from the optimum if (i) the age penalty function grows quickly with respect to the age, (ii) the packet transmission times over the channel are positively correlated over time, or (iii) the packet transmission times are highly random (e.g., following a heavy-tail distribution).

Non-radiative modes widely exist in the perfect electric conductor systems whose boundaries are closed surfaces, and have had many engineering applications. However, the non-radiative modes cannot be constructed by traditional electric field integral equation (EFIE)-based characteristic mode theory (CMT). The EFIE-based CMT is generalised, such that it can efficiently construct non-radiative characteristic modes (CMs), and it is found out that the non-radiative CMs and traditional internal resonant eigenmodes are one-to-one correspondence.

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Traditionally, all working modes of a perfect electric conductor are classified into capacitive modes, resonant modes, and inductive modes, and the resonant modes are further classified into internal resonant modes and external resonant modes. In this paper, the capacitive modes are further classified into intrinsically capacitive modes and nonintrinsically capacitive modes; the resonant modes are alternatively classified into intrinsically resonant modes, which are further classified into nonradiative intrinsically resonant modes and radiative intrinsically resonant modes, and nonintrinsically resonant modes; the inductive modes are further classified into intrinsically inductive modes and nonintrinsically inductive modes. Based on the modal expansion corresponding to these new modal classifications, an alternative modal decomposition method is proposed. In addition, it is also proved that all intrinsically resonant modes and all nonradiative intrinsically resonant modes constitute linear spaces, respectively, but other kinds of resonant modes cannot constitute linear spaces; by including the mode 0 into the intrinsically capacitive mode set and the intrinsically inductive mode set, these two modal sets become linear spaces, respectively, but other kinds of capacitive modes and inductive modes cannot constitute linear spaces.

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