Exact convex formulations of network-oriented optimal operator placement

Abstract

Data processing tasks are increasingly spread across the internet to account for the spatially distributed nature of many data sources. In order to use network resources efficiently, subtasks need to be distributed in the network so data can be filtered close to the data sources. Previous approaches to this operator placement problem relied on various heuristics to constrain the complexity of the problem. In this paper, we propose two generic integer constrained problem formulations: a topology aware version which provides a placement including the specific network links as well as an end-to-end delay aware version which relies on the routing capabilities of the network. A linear programming relaxation for both versions is provided which allows exact and efficient solution using common solvers.

Robust Distributed Linear Programming

“…On the technical side, our study of the iISS properties of (15) in Section V-B builds on a Converse Lyapunov Theorem [27] which requires the equilibrium set to be compact (the question of whether the Converse Lyapunov Theorem holds when the equilibrium set is not compact and the dynamics is discontinuous is an open problem). On the practical side, one can add box-type constraints to (4), ensuring that (A) holds.…”

“…Literature review. Linear programs play an important role in a wide variety of applications, including perimeter patrolling [1], task allocation [2], [3], operator placement [4], process control [5], routing in communication networks [6], and portfolio optimization [7]. This relevance has historically driven the design of efficient methods to solve linear optimization problems, see e.g., [8], [9], [10].…”