This note first identifies a problem with the correctness of the RUN DAP for Conjunctive RAS, presented in the above paper, 1 and it, subsequently, proceeds to the problem correction through an appropriate policy modification. More specifically, the first part of this note provides a counter example to the policy correctness (i.e., deadlock freedom of the controlled system) claimed in, 1 while the second part introduces the proposed correction, and briefly argues the correctness of the modified

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... DAP. A more detailed mathematical treatment of RUN DAP in the Petri net formalism, and its redefinition so that it covers the broader class of Conjunctive/Disjunctive RAS, can be found in [1] . For the sake of brevity, it is presumed in the following that the reader is familiar with the material of 1 . The Counter-Example Consider a conjunctive RAS with four resources, < = fR1;R2;R3; R4g and supporting a single job with process plan JT : Furthermore, suppose that the resource capacities satisfy the following inequalities: C1 2 (2) Manuscript C4 2": The reader can verify that using the natural ordering of the system resources i.e., o(R i ) = i; i = 1; . . . ; 4; the RUN definition of 1 results in the following stage nominal requirements: However, it can then be easily checked that, under the assumptions of (2)-(5), state s = h2;0; 0i is a reachable induced-deadlock state, when the aforementioned RAS is controlled by the considered RUN implementation. The Policy Correction The problem exposed in the above example is resolved, and a correct RUN definition for Conjunctive RAS is obtained, when equation 10 in the original policy definition 1 , is modified as in (7) , shown at the bottom of the page. The reader can verify that the above modification resolves the induced deadlock constructed in the introductory example, since the new nominal stage requirements are: It is also noticed that the modification of (7) incidentally enhances the policy flexibility. A proof for the correctness of the modified policy can still be based on the argument of Appendix B in 1 , with Rmin, in Case 3 of that argument, denoting a minimally ordered resource that has some of its units allocated, under the resource reservation scheme established by the (modified) policy definition. 2 Finally, as it was mentioned in the opening paragraph, a more detailed mathematical treatment of RUN DAP in the Petri net formalism in an extended form that covers the broader class of Conjunctive/Disjunctive RAS, can be found in [1]. REFERENCES [1] J. Park and S. A. Reveliotis, "Deadlock avoidance in sequential resource allocation systems with multiple resource acquisitions and flexible routings," IEEE Transactions on Automatic Control, 2000, to be published. 2 It is this italicized part that was confounded in the original argument. JT P ik [q] = maxfJT il [q] : JT il 2 N ik g; if o(Rq) minfo(Rj ) : JT ik [Rj ] > 0g 0; otherwise :