Energy or time-efficient scheduling is of particular interest in wireless communications, with applications in sensor network design, cellular communications, and more. In many cases, wireless packets to be transmitted have deadlines that upper bound the times before their transmissions, to avoid staleness of transmitted data. In this paper, motivated by emerging applications in security-critical communications, age of information, and molecular communications, we expand the wireless packet scheduling framework to scenarios which involve strict limits on the time after transmission, in addition to the conventional pre-transmission delay constraints. As a result, we introduce the scheduling problem under two-sided individual deadlines, which captures systems wherein transmitting too late (stale) and too early (fresh) are both undesired. Subject to said two-sided deadlines, we provably solve the optimal (energy-minimizing) offline packet scheduling problem. Leveraging this result and the inherent duality between rate and energy, we propose and solve the completion-time-optimal offline packet scheduling problem under the introduced two-sided framework. Overall, the developed theoretical framework can be utilized in applications wherein packets have finite lifetimes both before and after their transmission (e.g., security-critical applications), or applications with joint strict constraints on packet delay and information freshness.

翻译：能量或时间高效调度在无线通信中备受关注，广泛应用于传感器网络设计、蜂窝通信等领域。许多情况下，待传输无线数据包具有截止时间约束，该约束限定了传输前的最大允许时间，以避免数据过期。本文受安全关键通信、信息年龄及分子通信等新兴应用启发，将无线数据包调度框架扩展至同时包含传统传输前延迟约束与传输后严格时间限制的场景。由此，我们提出具有双边个体截止时间的调度问题，该问题刻画了系统中传输过晚（陈旧）与传输过早（新鲜）均不可取的特性。在所述双边截止时间约束下，我们以可证明方式求解了最优（能量最小化）离线数据包调度问题。基于该结果及速率与能量之间的内在对偶性，我们进一步提出并求解了在双边框架下的完成时间最优离线数据包调度问题。总体而言，所发展的理论框架可应用于数据包在传输前后均具有有限生命周期（如安全关键应用）或同时对数据包延迟与信息新鲜度存在严格限制的应用场景。