Robust Fluid Processing Networks

Fluid models provide a tractable and useful approach in approximating multiclass processing networks. However, they ignore the inherent stochasticity in arrival and service processes. To address this shortcoming, we develop a robust fluid approach to the control of processing networks. We provide insights into the mathematical structure, modeling power, tractability, and performance of the resulting model. Specifically, we show that the robust fluid model preserves the computational tractability of the classical fluid problem and retains its original structure. From the robust fluid model, we derive a (scheduling) policy that regulates how fluid from various classes is processed at the servers of the network. We present simulation results to compare the performance of our policies to several commonly used traditional methods. The results demonstrate that our robust fluid policies are near-optimal (when the optimal can be computed) and outperform policies obtained directly from the fluid model and heuristic alternatives (when it is computationally intractable to compute the optimal).National Science Foundation (U.S.) (Grant CNS-1239021)National Science Foundation (U.S.) (Grant IIS-1237022)United States. Army Research Office (Grant W911NF-11-1-0227)United States. Army Research Office (Grant W911NF-12-1-0390)United States. Office of Naval Research (Grant N00014-10-1-0952

Optimal Control of Multiclass Fluid Queueing Networks: A Machine Learning Approach

We propose a machine learning approach to the optimal control of multiclass fluid queueing networks (MFQNETs) that provides explicit and insightful control policies. We prove that a threshold type optimal policy exists for MFQNET control problems, where the threshold curves are hyperplanes passing through the origin. We use Optimal Classification Trees with hyperplane splits (OCT-H) to learn an optimal control policy for MFQNETs. We use numerical solutions of MFQNET control problems as a training set and apply OCT-H to learn explicit control policies. We report experimental results with up to 33 servers and 99 classes that demonstrate that the learned policies achieve 100\% accuracy on the test set. While the offline training of OCT-H can take days in large networks, the online application takes milliseconds

Recensione dell'articolo:(Bertimas, Dimitris; Nasrabadi, Ebrahim; Paschalidis, Ioannis - " Robust fluid processing networks. " - IEEE Trans. Automat. Control 60 (2015), no. 3, 715-728.) MR3318398 MathSciNet ISSN 2167-5163

In this paper, the authors present a general framework for the fluid control of multiclass processing networks. They present a tractable approach to address uncertainty in networks of this type. The proposed approach treats the uncertainty in a deterministic manner using the framework of robust optimization. It relies on modeling the fluid control problem as a separated continuous linear program (SCLP) and characterizing its robust counterpart. Specifically, the authors formulate a fluid control problem of multiclass processing networks as an SCLP. They consider uncertainty on arrival and service processes and investigate its robust counterpart. The authors propose two methods to translate an optimal solution for the robust fluid control problem to implementable sequencing policies. Then, they develop a polynomial-time algorithm to derive an optimal solution for the robust fluid control problem of single-server processing networks