Reliability and latency are two key performance indicators of communications. This paper investigates the tradeoff between them over a random packet erasure channel in the absence of feedback. In contrast to the instant feedback case where guaranteed reliability with low latency can be achieved by simple automatic repeat query (ARQ), we show that in the absence of feedback, the reliability increases with the coding window size, at the cost of the degraded latency performance. Specifically, we propose a sliding window network coding (SWNC) scheme that works in the absence of feedback and achieves various reliability and latency tradeoff by adjusting the coding window size. The tradeoff between the reliability and latency are investigated by deriving the achievable performance of the proposed SWNC scheme as a function of the coding window size. We further show that the proposed scheme degenerates to the existing benchmark schemes that are superior in either latency or reliability, and it has much higher flexibility.

Inspired by a definition of the closed-form instantaneous cross-correlation Wigner distribution (Zhang, 2019), we generalize the notion of Wigner distribution to the so-called free metaplectic Wigner distribution (FMWD) through three free metaplectic transforms, in order to tackle a challenge in high-dimensional complex features information processing. We provide some representative special cases for this general form, including the$N$-dimensional nonseparable affine characteristic Wigner distribution, kernel function Wigner distribution, convolution representation Wigner distribution and instantaneous cross-correlation Wigner distribution. We establish the standard Heisenberg’s uncertainty principles (HUPs) of the real-valued function for the FMWD. We also establish the standard HUPs of the complex-valued function for some specific (i.e., the orthogonal, the orthonormal, the minimum eigenvalue commutative and the maximum eigenvalue commutative) FMWDs. In view of the one-dimensional case of our results, we solve a burning question regarding the limit of time-frequency superresolution triggered by the linear canonical transform free parameters.

Maintenance optimization has been extensively studied in the past decades. However, most of the existing maintenance models focus on single-component systems and are not applicable to complex systems consisting of multiple components, due to various interactions among the components. The multicomponent maintenance optimization problem, which joins the stochastic processes regarding the failures of components with the combinatorial problems regarding the grouping of maintenance activities, is challenging in both modeling and solution techniques, and has remained an open issue in the literature. In this paper, we study the multicomponent maintenance problem over a finite planning horizon and formulate the problem as a multistage stochastic integer program with decision-dependent uncertainty. There is a lack of general efficient methods to solve this type of problem. To address this challenge, we use an alternative approach to model the underlying failure process and develop a novel two-stage model without decision-dependent uncertainty. Structural properties of the two-stage problem are investigated, and a progressive-hedging-based heuristic is developed based on the structural properties. Our heuristic algorithm demonstrates a significantly improved capacity to handle large-size two-stage problems comparing to three conventional methods for stochastic integer programming, and solving the two-stage model by our heuristic in a rolling horizon provides a good approximation of the multistage problem. The heuristic is further benchmarked with a dynamic programming approach and a structural policy, which are two commonly adopted approaches in the literature. Numerical results show that our heuristic can lead to significant cost savings compared with the benchmark approaches.

Preventive maintenance has received considerable attention in industries and the literature. Conventional preventive maintenance models often assume that equipment is always available for maintenance activities. However, in many mission-critical industries, equipment may not be available for scheduled maintenance due to busy operational schedules. Forced shutdown of the equipment may incur extra costs that cannot be offset by the benefits from preventively maintaining the equipment. In this paper, we propose innovative preventive maintenance policies to address the challenges caused by equipment unavailability. Maintenance models with possible rescheduling are developed for both time-based and condition-based maintenance policies, and the objective is to minimize the long-run cost rate of all maintenance activities. The proposed policies, with consideration of equipment unavailability for prescheduled PM, are compared with the policies that ignore this unavailability. Numerical examples are provided to illustrate the proposed policies.