Deadlock Prevention Policy with Behavioral Optimality or Suboptimality Achieved by the Redundancy Identification of Constraints and the Rearrangement of Monitors
Algorithm 3
A liveness-enforcing policy.
Input: An S3PR , with .
Output: A liveness-enforcing net , with .
(1) begin
(2) ; . and denote the sets of constraints in the MIP problem and monitors obtained
at the first phase, respectively
(3) Apply MIP to to obtain a maximal unmarked siphon.
(4) if {there exists such a siphon} then
(4.1) Obtain a minimal siphon from the maximal one.
(4.2) Enforce a constraint , , to the MIP problem of ; ; go to step (3).
(5) ifthen ; ; go to step (17).
(6) Apply Algorithm 1 to , obtain a set of necessary constraints .
(7) foreach ,
(7.1) Add a corresponding monitor to by Definition 9.
(7.2) .
(8) Obtain (, ) and .
(9) ; . and denote the sets of constraints in the MIP problem and monitors obtained
at the second phase, respectively
(10) Apply MIP to to obtain a maximal unmarked siphon.
(11) if {there exists such a siphon} then
(11.1) Obtain a minimal siphon from the maximal one.
(11.2) Enforce a constraint , , to the MIP problem of ;
; go to step (10).
(12) ifthen ; ; go to step (17).
(13) Apply Algorithm 1 to to obtain a set of necessary constraints .
(14) foreach ,
(14.1) Add a corresponding monitor to by Definition 17.
