Minimizing and maximizing a linear objective function under a fuzzy max⁡−∗\max -\ast relational equation and an inequality constraint

summary:This paper provides an extension of results connected with the problem of the optimization of a linear objective function subject to $\max-\ast$ fuzzy relational equations and an inequality constraint, where $\ast$ is an operation. This research is important because the knowledge and the algorithms presented in the paper can be used in various optimization processes. Previous articles describe an important problem of minimizing a linear objective function under a fuzzy $\max-\ast$ relational equation and an inequality constraint, where $\ast$ is the $t$-norm or mean. The authors present results that generalize this outcome, so the linear optimization problem can be used with any continuous increasing operation with a zero element where $\ast$ includes in particular the previously studied operations. Moreover, operation $\ast$ does not need to be a t-norm nor a pseudo-$t$-norm. Due to the fact that optimal solutions are constructed from the greatest and minimal solutions of a $\max-\ast$ relational equation or inequalities, this article presents a method to compute them. We note that the linear optimization problem is valid for both minimization and maximization problems. Therefore, for the optimization problem, we present results to find the largest and the smallest value of the objective function. To illustrate this problem a numerical example is provided

In-network quality optimization for adaptive video streaming services

HTTP adaptive streaming (HAS) services allow the quality of streaming video to be automatically adapted by the client application in face of network and device dynamics. Due to their advantages compared to traditional techniques, HAS-based protocols are widely used for over-the-top (OTT) video streaming. However, they are yet to be adopted in managed environments, such as ISP networks. A major obstacle is the purely client-driven design of current HAS approaches, which leads to excessive quality oscillations, suboptimal behavior, and the inability to enforce management policies. Moreover, the provider has no control over the quality that is provided, which is essential when offering a managed service. This article tackles these challenges and facilitates the adoption of HAS in managed networks. Specifically, several centralized and distributed algorithms and heuristics are proposed that allow nodes inside the network to steer the HAS client's quality selection process. The algorithms are able to enforce management policies by limiting the set of available qualities for specific clients. Additionally, simulation results show that by coordinating the quality selection process across multiple clients, the proposed algorithms significantly reduce quality oscillations by a factor of five and increase the average delivered video quality by at least 14%