1. Resource Allocation Graphs
Lecture 4
Introduction to
Resource Allocation Graphs

2. Resource-Allocation Graphs
Squares
Represent processes
Large circles
Represent classes of identical resources
Small circles drawn inside large circles
Indicate separate identical resources of each class

3. Resource-Allocation Graphs
Resource-allocation and request graphs.

4. Reduction of Resource-Allocation Graphs
Graph reductions
If a process’s resource requests may be granted, the graph may be reduced by that process
If a graph can be reduced by all its processes, there is no deadlock
If a graph cannot be reduced by all its processes, the irreducible processes constitute the set of deadlocked processes in the graph

5. Reduction of Resource-Allocation Graphs
Graph reductions determining that no deadlock exists.

6. Resource Allocation Graphs and Deadlock Prevention
We have learned that resource alloction graphs can be used to detect deadlock in a set of processes in contention for shared resources by simplifying the graph and then searching for irreducible cycles.  In this exercise we will investigate a procedure for preventing deadlock by setting limits on the number of resources of each type that can be requested by a process and then providing a sufficient total number of resources evenly distributed across the resource types.
We want to know the minimum number of resources required to prevent deadlock for a given number of processes and resource types.  Our goal is to devise a mathematical formula to compute this minimal number.  To prepare for this task, answer the following questions about the resource allocation graphs provided.

7. Is a condition of deadlock exhibited in this resource allocation graph?

8. Is a condition of deadlock exhibited in this resource allocation graph?

9. Is a condition of deadlock exhibited in this resource allocation graph?

10. Given P processes, and R resource types, and assuming that each process can request at most m of each type of resource, find an expression for N(P,R,m) that computes the minimum total number of resources evenly distributed over the R resource types that will prevent deadlock.                  N(P,R,m) =
Note:  For resources to be "evenly distributed" over the R resource types means that no resource type may have more than 1 more resource that any other resource type.  For example, given R=3 and N = 8 we could allocate resources in any of the following ways,
while the following are not "evenly distributed".