Holt's model of resource allocation

1. I'd like to start with a quick overview of the resource allocation model described in the paper by Holt.
2. If nothing else was clear, about Holt's model, it should still be clear that it is entirely based on using directed graphs to describe the aspects of systems involving resource allocation. I'll assume general familiarity with the notion of a directed graph, but I will remind you that a:

   Bipartite Graph

   is a graph whose vertices can be partitioned into two sets in such a way that all the graph's edges connect elements from different sets.

3. The graphs used in Holt's model are all bipartite directed graphs. The vertices of the graph correspond to the processes and resources in a computer system. The partition (that makes the graph bipartite) is formed by viewing the resource vertices as one set and the process vertices as another set.
4. To completely represent the state of a system the graph must be augmented with some additional specifications:
   • the set of vertices associated with resources is further partitioned into vertices corresponding to reusable resources and consumable resources
   • for each reusable resource, the total number of units of the resource available must be specified.
5. The interpretation of edges in one of Holt's graphs depends on their direction.
   • An edge directed from a process vertex to a resource vertex indicates that the process has requested (and not yet been granted) one unit of the resource (multiple unit requests are indicated by multiple edges or by edge weights).
   • An edge directed from a resource vertex to a process vertex indicates that the process is capable of releasing one or more units of the resources. The precise meanings of these edges depends on the type of resource involved:
     • If the resource is reusable, then in order to release a unit, the process which is the target of the edge must be currently allocated use of a unit of the resource. In other words, the number of edges between a reusable resource node and a process indicates the number of units of the resource allocated to the process.
     • If the resource is consumable, an edge to a process indicates that the process is a producer of the resource.
6. A particular instance of one of Holt's graphs is intended to represent the state of a "General resource system" at some point in time. The states of such systems change over time, and Holt attempts to capture the possible changes in terms of transformations that can be performed on his graphs. He identifies three such transformations:

   Requests

   A process which currently has no requests outstanding can request one or more units of one or more distinct resource classes. In the graph model, this is accomplished by adding edges pointing from the node to one or more resource nodes.

   Acquisitions

   A process with outstanding requests can be allocated the resources requested if sufficient units are available of all the resource classes requested by the process. In the system graph, this is accomplished by reversing all edges that point to reusable resource nodes and deleting edges pointing to consumable resource nodes.

   Releases

   A process:

   • to which resusable resources have been allocated, or
   • which is a producer of consumable resources

   which has no resource requests outstanding can release the some or all of the reusable resources allocated to it and/or units of any consumable resources it produces. In the graph, this is accomplished by deleting one or more of the request edges directed toward the process node (in the case of a reusable resource) or increasing the available count (in the case of a consumable resource).