Briefly, this approach recog-nizes that the set of safe states of a given SU-RAS, Q corresponds to the reachability set of a “co-system,” Q system Q remark, this sample set consists of s
Trang 1the coverability of the safe space Ss by the policy-admissible subspace, S(P) More formally, consider the
the policy admissible subspace Then, a viable policy efficiency measure is provided by the ratio
(4.12)
where denotes the cardinality number of set S
Because of the typically large size of the S(H) and Ss subspaces, their explicit enumeration will not be possible and, therefore, we must resolve simulation and statistical sampling techniques Such a technique, known as the co-space simulation technique, is developed in Reference [62] Briefly, this approach
recog-nizes that the set of safe states of a given SU-RAS, Q corresponds to the reachability set of a “co-system,” Q
system Q
remark, this sample set consists of safe states of the original system In continuation, the condition H defining the evaluated DAP is applied on the extracted sample set and the portion of the sample states admitted by the policy is determined This portion expresses the policy coverability of the extracted sample
set, and constitutes a point estimate for index I Application of this technique to the polynomial-kernel
DAPs of Section 4.5, and experimental evaluation results can be found in References [58], [59], and [62]
In the rest of this section, we discuss some properties of polynomial-kernel DAPs which can be used to enhance the operational flexibility of these policies when implemented on any given FMS configuration
Policy Disjunctions and Essential Difference
The first way to improve the efficiency of an FMS structural controller employing polynomial-kernel DAPs, with respect to the metric of Eq (4.12) is based on the following proposition
Proposition 4.4 Given two conditions H1( ) and H2( ) defining correct polynomial-kernel DAPs, the policy defined by the disjunction H1( ) H2( ) is another correct polynomial-kernel DAP
To see this, simply notice that acceptance of a state s by the policy disjunction implies that at least one of
the two policy defining conditions, H1( ), H2( ), evaluates to TRUE at s and, therefore, state s is safe Further-more, if state s S(Hi), i {1, 2}, then the correctness of the corresponding policy implies the existence of
at least one feasible event e, which is enabled by that policy, and s i) (cf Theorem 4.2) Then,
s 1 H2), and according to Theorem 4.2, the policy defined by H1( ) H2( ) is correct
It is also easy to see that the subspace admitted by the policy disjunction is the union of the subspaces admitted by the two constituent policies If it happens that
(4.13) then S(H1) S(H2) is richer in states than any of its constituents Therefore, the resulting policy is more
efficient with respect to index I.
Two polynomial-kernel policies based on conditions H1 and H2 that satisfy Eq (4.13) are characterized
as essentially different The essential difference of the polynomial-kernel policies presented in Section 4.5 is analyzed in Reference [59] It turns out that RUN and the FMS Banker’s algorithm are essentially different, while RO is subsumed by Banker’s
Optimal and Orthogonal Orderings for RUN and RO DAPs
A second opportunity for improving the efficiency of RUN and RO DAPs is provided by the fact that the defining logic of these two policies essentially leads to entire families of policies for a given FMS configu-ration As we saw in Section 4.5, each member of these families is defined by a distinct ordering of the system resource set Hence, a naturally arising question is which of these orderings leads to the most efficient
S H( ){s iS : H(s i) is TRUE},
I S H( )
S s
-
S
∨
S H ( ) S H1 ( )2
( )∧(S H ( ) S H2 ( )1 )
© 2001 by CRC Press LLC
Trang 2The Design of Human-Centered Manufacturing Systems
of Human-Centered Systems
The Concept of Human-Centered Systems • Human-Centered Systems in Practice: Some Observations • Designing and Evaluating Human-Centered Systems • Simulation as an Evaluation Strategy
of Complex Shapes
The Scope of the MATRAS Project • NC Kernel Improvement
• A New NC Programming Data Interface • Conclusions
User-Oriented Shop Floor Software
The Concept of Shop Floor Software Development • The Software System to Support Work Planning • The Software Tool to Support Group Communication • Conclusion
Production Planning System for Groupwork
The Need for Computer–Supported Cooperative Work
• Human-Centered CIM • Workflows for Shop Floor PPC
• Conclusions
and Its Application to the Process Industry
The Concept of Human-Process Communication
• Characteristics of Operational Situations • Presenting Human-Process Communication • Integration of Operational Experience • Conclusions
of Complex Software Systems
Problems of Software Reengineering: The Example of a Tourism Network • The Reengineering of a Tourism Booking and Information Software System • The Methodological Approach to the Software Reengineering Project • Conclusions
Technology: The Example of Slovenia
The Concept of Success Factors • The Importance of Human Orientation as a Success Factor • How to Integrate New
Dietrich Brandt
University of Technology (RWTH)
Inga Tschiersch
University of Technology (RWTH)
Klaus Henning
University of Technology (RWTH)
© 2001 by CRC Press LLC