October 2012, Volume 24, Issue 4, pp 477503,
Open Access
This content is freely available online to anyone, anywhere at any time.
Date:
11 Apr 2012
Designs of optimal switching feedback decentralized control policies for fluid queueing networks
 V. Feoktistova,
 A. Matveev,
 E. Lefeber,
 J. E. Rooda
 … show all 4 hide
Abstract
The paper considers standard fluid models of multiproduct multipleserver production systems where setup times are incurred whenever a server changes product. We consider a general approach to the problem of optimizing the longrun average cost per unit time that consists of first determining an optimal steady state (periodic) behavior and then to design a feedback scheduling protocol ensuring convergence to this behavior as time progresses. In this paper, we focus on the latter part and introduce a systematic approach. This approach gives rise to protocols that are cyclic and distributed: the servers do not need information about the entire system state. Each of them proceeds basically from the local data concerning only the currently served queue, although a fixed finite number of onebit notification signals should be exchanged between the servers during every cycle. The approach is illustrated by simple instructive examples concerning polling systems, single server systems with processor sharing scheme, and the reentrant twoserver manufacturing network with nonnegligible setup times introduced by Kumar and Seidman. For the last network considered in the analytical form, some cases of optimal steadystate (periodic) behavior are first recalled. For all examples, based on the desired steady state behavior and using the presented theory, we designed simple distributed feedback switching control laws. These laws not only give rise to the required behaviors but also make them globally attractive, irrespective of the system parameters and initial state.
This work was supported by the Netherlands Organization for Scientific Research (NWOVIDI grant 639.072.072; NWO visitors grant 040.11.131), the Russian Foundation for Basic Research (grant 090800803), the Russian Federal Program (grant N 1.1111128033) and the Russian Federal Program “Research and Teaching Cadres” (contract N 16.740.11.0042).
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 Title
 Designs of optimal switching feedback decentralized control policies for fluid queueing networks
 Open Access
 Available under Open Access This content is freely available online to anyone, anywhere at any time.
 Journal

Mathematics of Control, Signals, and Systems
Volume 24, Issue 4 , pp 477503
 Cover Date
 20121001
 DOI
 10.1007/s004980120086y
 Print ISSN
 09324194
 Online ISSN
 1435568X
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Hybrid dynamical systems
 Optimal switched control
 Control of networks
 Fluid models
 Queueing
 Authors

 V. Feoktistova ^{(1)}
 A. Matveev ^{(1)}
 E. Lefeber ^{(2)}
 J. E. Rooda ^{(2)}
 Author Affiliations

 1. Department of Mathematics and Mechanics, Saint Petersburg University, Universitetskii 28, Petrodvoretz, St. Petersburg, 198504, Russia
 2. Department of Mechanical Engineering, Eindhoven University of Technology, 5600 MB, Eindhoven, The Netherlands