Abstract
Liveness is very important for resource allocation systems (RASs) as it means that no deadlock can arise in the system operation. By applying the approach of allocating resources, this paper focuses on enforcing the liveness of RASs that allow for the general resource allocation and flexible routs. These considered RASs can be modeled by a subcalss of systems of sequential systems with shared resources, named as S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> PRs. Deadlocks in S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> PR can be characterized by the saturation of a kind of activity-circuits. Based on these circuits, we study the relationship between the number of initial tokens or marking of resource place and the non-saturation of some involved activity-circuits. Further, a liveness condition for S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> PR is derived which is associated with the numbers of initial tokens or markings of all resource places. An algorithm is proposed to allocate the initial number of resources so that the considered S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> PR is live. Finally the proposed method is illustrated by examples.
Highlights
Resource allocation systems (RASs) [1] can model well a majority of contemporary applications such as automated manufacturing systems, transport systems, and workflow management systems
We study the relationship between the number of initial tokens or marking of resource place and the non-saturation of some involved activity-circuits
Our previous paper [3] points out that deadlocks in S4PR are caused by saturated PA-circuit
Summary
Resource allocation systems (RASs) [1] can model well a majority of contemporary applications such as automated manufacturing systems, transport systems, and workflow management systems. The initial marking configuration methods have the major benefit that no supervisors are added, and the control cost is saved It is well-known that deadlock in RAS is caused by improper allocation of resources. 1) Based on the saturation of PA-circuits that would lead to deadlock in S4PR [3], the relation between the initial markings of a resource place and the non-saturation of involved PA-circuits is established This is the foundation of this work.
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