Real-Time Management of Resource Allocation Systems: A Discrete Event Systems Approach (International Series in Operations Research & Management Science)

255 Pages·2004·7.22 MB·English

by  Spyros A. Reveliotis

Real-Time Management of
Resource Allocation Systems
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REAL-TIME MANAGEMENT OF
RESOURCE ALLOCATIONS SYSTEMS
A Discrete Event Systems Approach
SPYROS A. REVELIOTIS
School of Industrial & Systems Engineering
Georgia Institute of Technology
Atlanta, GA 30032
Springer
eBookISBN: 0-387-23967-7
Print ISBN: 0-387-23960-X
©2005 Springer Science + Business Media, Inc.
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Contents
Preface vii
1. RESOURCE ALLOCATION SYSTEMS: CONCEPTS AND
PROBLEMS 1
1 Some example resource allocation systems 1
2 Sequential RAS and their Supervisory Control problem 12
3 The proposed SC framework 19
4 The book organization and an outline of the key results 23
5 Historical and bibliographical notes 26
2. LOGICAL CONTROL OF DISJUNCTIVE / CONJUNCTIVE
RESOURCE ALLOCATION SYSTEMS 31
1 Finite State Automaton-based modelling of the RAS behavior 32
2 State Reachability, Safety, and Nonblocking Supervision 36
3 The computational complexity of the Optimal Nonblocking
SCP 43
4 Practical approaches to the RAS logical control problem 50
5 Some extensions of the RAS logical control problem 51
6 Historical and bibliographical notes 55
3. RAS ADMITTING OPTIMAL NONBLOCKING SUPERVISION
OF POLYNOMIAL COMPLEXITY 59
1 RAS with no deadlock-free unsafe states 60
2 Optimal “greedy” search for a process terminating sequence 69
3 Historical and bibliographical notes 73
vi REAL-TIME MANAGEMENT OF RESOURCE ALLOCATION SYSTEMS
4. POLYNOMIAL-KERNEL NONBLOCKING SCP’S FOR SINGLE-
UNIT RAS 75
1 Polynomial-Kernel SCP’s for LIN-SU-RAS 76
2 Efficiency Considerations 92
3 AGV RAS and the AGV Banker’s Algorithm 97
4 Accommodating Operational Contingencies 106
5 Historical and bibliographical notes 113
5. LOGICAL CONTROL OF RAS WITH COMPLEX PROCESSES 117
1 Petri net-based modelling of the RAS behavior 118
2 RAS deadlock in the PN-based modelling framework 129
3 Liveness-enforcing supervision for process-resource nets 142
4 PK-SCP’s for DIS-CON-RAS 150
5 PK-SCP’s for RAS with Uncontrollable Behavior 162
6 Historical and bibliographical notes 169
6. PERFORMANCE-ORIENTED MODELLING AND CONTROL
OF LOGICALLY CONTROLLED RAS 173
1 RAS performance-oriented modelling and control 174
2 The thinning problem revisited 204
3 Approximating the optimal scheduling policy 211
4 Historical and bibliographical notes 215
7. EPILOGUE 219
References 225
Index 235
Preface
This book deals with the problem of managing the resource allocation that
takes place in the operational context of various contemporary technological
applications, including flexibly automated production systems, automated rail-
way and/or monorail transportation systems, electronic workflow management
systems and business transaction supporting systems. A distinguishing trait
of all the aforementioned applications, is that they seek to limit the role of
the human element to remote high-level supervision, while placing the burden
of the real-time monitoring and coordination of the ongoing activity upon a
computerized control system. This development is justified by a number of
technical, economic and safety considerations, and it is facilitated by the ad-
vent of modern computing and sensing technologies. On the other hand, a
challenging task for the effective deployment of these target applications, is
the synthesis of the control logic that will manage the allocation of the lim-
ited system resources to the concurrently running processes; this logic must
guarantee the correct and expedient execution of all the active processes, while
minimizing the need for external human intervention. The resulting problem
is rather novel for the developers of these systems, since, in the past, many of
its facets were left to the jurisdiction of the present human intelligence. It is
also complex, due to the high levels of choice – otherwise known as flexibility
– inherent in the operation of these environments. As a result, most of the re-
sourceallocation controllers currently developed for the automated versions of
the aforementioned applications, are based on ad-hoc and simplistic solutions;
unable to deal systematically with the behavioral complexity of the underlying
system, these solutions, in their effort to ensure correct and robust operation,
constrain unnecessarily the inherent operational flexibility, and eventually, they
compromise the overall efficiency and productivity.
Yet, the last 10-15 years have seen the development of a series of results,
coming primarily from the burgeoning area of Discrete Event Systems (DES),
that have enhanced our understanding of the behavioral properties of the afore-
viii
mentioned applications with respect to the underlying resource allocation func-
tion, and they offer a solid theoretical basis towards the formal representation,
analysis and control of this function. The main objective of this book is the
systematic exposition of these results, and their orchestration in a complete
control framework, appropriate for the aforementioned environments. Hence,
the book opens with an introductory description of (some of) the target ap-
plication environments, and the underlying resource allocation function. This
description leads to the specification of the control requirements, and the outline
of a control framework that can provide a viable solution to theserequirements.
A notable feature of the proposed control framework is the emphasis that it
places on (i) the robustness of the deployed control function with respect to the
system stochasticities and the various operational contingencies, (ii) the scal-
ability of the proposed solutions, so that they apply to the large-scale context
of the target technological applications, and (iii) the operational efficiency of
the resulting controlled system. These three properties are supported through
the adoption of a “closed-loop” structure for the proposed control scheme, and
also, through a pertinent decomposition of the overall control function, to one
component seeking the logical correctness and consistency of the system be-
havior, and another component addressing performance considerations; the first
of these components is characterized as the logical controller of the underlying
resource allocation function, while the second component is characterized as
the performance-oriented controller. The rest of the book is devoted to a rig-
orous study of the control problems addressed by each of these two controllers,
and their integration to a unified control function. A notion of optimal control
is formulated for each of these problems, but it turns out that the corresponding
optimal policies are computationally intractable. Hence, a large part of the book
is devoted to the development of effective and computationally efficient approx-
imations for these optimal control policies, especially for that corresponding to
the more novel logical control problem.
The above paragraphs have outlined the “utilitarian” aspects of the book
content. However, the book is intended to play a number of additional roles,
eachdefined with respect to a different audience: Hence, for the Industrial En-
gineering / Operations Research-oriented student, researcher and sophisticated
practitioner, the book offers an introduction to the broader area of Discrete Event
Systems, and familiarization with an array of its main modelling frameworks,
concepts and algorithms. Furthermore, this material is provided through im-
plementation on a practical application context, that reveals the potential of this
fairly novel area, and expands our analysis and design capability for a class of
problems that traditionally has belonged to the domain of the IE/OR disciplines.
For the student and researcher of the area of Discrete Event Systems itself, the
book offers a contextual, in-depth application of many concepts and algorithms
developed by DES theory, but even more importantly, it stresses the complica-
PREFACE ix
tions arising from the non-polynomial complexity that is inherent in many of
these concepts and algorithms, and addresses the issue of developing effective
and computationally efficient / polynomial approximations. Indeed, a major
contribution of this book is that it epitomizes a significant body of results, that
were developed over the last 12 years, and concern the design of provably cor-
rect and computationally efficient solutions for the considered logical control
problem. Finally, a lastintention of the book is to highlight the missing links
in the presented developments, and to motivate, in this way, further research
activity by the interested communities.
From a presentational standpoint, there has been an effort to keep the book
development as independent as possible, but the reader is expected to be familiar
with somefundamental mathematical concepts, like the concepts of a graph or
a probability distribution. In each chapter, an opening section summarizes
all the background material necessary for the subsequent developments, and it
provides a number of citations for readers that would like to have a more in-depth
or leisurely treatment of this material. On the other hand, the development of the
main results of each chapter has placed the emphasis on the rigor, conciseness,
and also, the lucidity of the exposition. The selection of the material included
in each chapter has been aligned with and supports the posed specifications
of robustness, scalability and efficiency for the proposedsolution; however, a
closing section at each chapter overviews the broader set of available results on
the problems considered in it, and it provides a “historical perspective” for the
presenteddevelopments. The book can function as the basis for a senior-level
undergraduate or graduate-level course on resource allocation systems and their
real-time management, or some more “concrete” version of this problem defined
in the context of the aforementioned targetapplication environments. It would
alsoconstitute a good supplement for any introductory course on Discrete Event
Systems theory.
Concluding this expository discussion of the book and its content, I would
like to take the opportunity to acknowledge and thank a number of parties that
havebeen valuable in the development of this work. Hence, first I would like to
thank Placid Ferreira, Mark Lawley,Jonghun Park and Jin Young Choi, whose
collaboration and friendship have been very instrumental in the development
of many of the results presented in this book. I would also like to extendmany
thanks to all my colleagues who, through personal communication, conference
participation, or simply through their own personal contributions, have been
great inspiration and partners in the entire journey that has culminated to the
writing of this book. I am particularly indebted to Elzbieta Roszkowska who
readmany parts of the manuscript and provided valuable feedback during the
book development. The School of Industrial Engineering at Georgia Tech, and
especially, the Virtual Factory Lab in it, have been a very supportive environment
for the research activity that has led to many of the results reported in this book.