Abstract
This paper derives an iterative deadlock prevention policy for systems of simple sequential processes with resources (S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> PRs) based on structural analysis, which consists of two stages. The first stage is called siphons control. Strict minimal siphons (SMSs) in an S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> PR net are computed and control places are added by imposing P-invariants associated with the complementary sets of the SMSs, which restricts no legal system behavior. The original resource places are removed and the newly added control places are regarded as resource places, resulting in a new net, which needs to add control places for its SMSs if deadlocks persist. Repeat this step until a new net without SMSs is obtained. Then, an S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> PR, called the first-controlled net, is obtained by integrating all added control places into the original net. The second stage, called non-max-marked siphons control, is performed in an iterative way if the system is not live yet. At each iteration, a mixed integer linear programming (MILP) problem is formulated to compute a non-max-marked siphon, and a control place is added for the siphon to the first-controlled net, resulting in an augmented net. The iteration is executed until a final-augmented net generates no new non-max-marked siphon. In general, based on the above two stages, this paper can obtain a supervisor with more behavior permissiveness compared to the previous studies. Moreover, an optimal supervisor can be found if a first-controlled net has no non-max-marked siphon, implying that the second stage is not necessary. Finally, some examples are provided to demonstrate the proposed policy.
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