Multi-Class Processing Networks describe a set of servers that perform multiple classes of jobs on different items. A useful and tractable way to find an optimal control for such a network is to approximate it by a fluid model, resulting in a Separated Continuous Linear Programming (SCLP) problem. Clearly, arrival and service rates in such systems suffer from inherent uncertainty. A recent study addressed this issue by formulating a Robust Counterpart for SCLP models with budgeted uncertainty which provides a solution in terms of processing rates. This solution is transformed into a sequencing policy. However, in cases where servers can process several jobs simultaneously, a sequencing policy cannot be implemented. In this paper, we propose to use in these cases a a resource allocation policy, namely, the proportion of server effort per class. We formulate Robust Counterparts of both processing rates and server-effort uncertain models for four types of uncertainty sets: box, budgeted, one-sided budgeted, and polyhedral. We prove that server-effort model provides a better robust solution than any algebraic transformation of the robust solution of the processing rates model. Finally, to get a grasp of how much our new model improves over the processing rates robust model, we provide results of some numerical experiments.
Optimal Energy-Efficient Policies for Data Centers through Sensitivity-Based Optimization
School of Economics and Management Sciences, Yanshan University（燕山大学经济管理学院）；Center for Intelligent and Networked Systems (CFINS), Department of Automation, TNList, Tsinghua University（清华大学自动化系智能与网络系统中心）
Xerox Research Centre India（印度施乐研究中心）；Tepper School of Business, Carnegie Mellon University（卡内基梅隆大学泰珀商学院）；Marshall School of Business, University of Southern California（南加州大学马歇尔商学院）；Department of Computing and Mathematical Sciences, California Institute of Technology（加州理工学院计算与数学科学系）
