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Assumptions
1) Multiple instances of resources
2) Each process must claim the maximum use a priori
3) When a process requests a resource it may have to wait
4) When a process gets all its resources it must return them in a finite amount of time
Consists of safety algorithm and resource request algorithm.
Let n = number of processes and m = number ofresourcetypes 1)Available: vector of length m. If available [j] = k, k instances of resource type are available. 2)Max: n x m matrix. If Max[i, j] = k, process may request at most k in instances of resources types 3)Allocation: n x m matrix. If Need[i, j] = k, then Pi may need k more instances of to complete its task Need[i, j] =Max[i, j] - Allocation[i, j]. |
1) Let Work and Finish be vectors of length m and n, respectively. Initialize,
Work = Available
Finish [i] = false for i = 0, 1,..., n-1
2) Find process i such that:
a) Finish [i] == false; and
b) ≤ Work
If no such i exists, go to step 4
3) Work = work + ≤ Work
Finish [i] = true
go to step 2
4) If Finish [i] = = true for all i, then the system is in a safe state. Otherwise, it is in an unsafe state.
Request = request vector for process. If [j] = k then process Pi wants k instances of resource type
1) If <= go to step 2. Otherwise, raise error condition, since process has exceeded its maximum claim.
2) If <= Available, go to step 3. Otherwise must wait, since resources are not available.
3) Pretend to allocate requested resources to by modifying the state as follows:
Available = Avalable – ;
= + ;
= – ;
Call safety algorithm
5 process P0 through P4; 3 resource type A(10 instances), B(5 instances), and C (7 instances) and Snapshot at time T0:
| Allocation | Max | Available | |||||||
| A | B | C | A | B | C | A | B | C | |
| P0 | 0 | 1 | 0 | 7 | 5 | 3 | 3 | 3 | 2 |
| P1 | 2 | 0 | 0 | 3 | 2 | 2 | |||
| P2 | 3 | 0 | 2 | 9 | 0 | 2 | |||
| P3 | 2 | 1 | 1 | 2 | 2 | 2 | |||
| P4 | 0 | 0 | 2 | 4 | 3 | 3 | |||
The content of the matrix. Need is defined to be Max- Allocation.
Need
| A | B | C | |
| P0 | 7 | 4 | 3 |
| P1 | 1 | 2 | 2 |
| P2 | 6 | 0 | 0 |
| P3 | 0 | 1 | 1 |
| P4 | 4 | 3 | 1 |
The system is in a safe state since the sequence < P1, P3, P4, P2, P0 satisfies safety criteria.
P1 request (1, 0, 2)
- Check that request <= Available (that is, (1, 0, 2) <= (3, 3, 2)) => true
| Allocation | Need | Available | |||||||
| A | B | C | A | B | C | A | B | C | |
| P0 | 0 | 1 | 0 | 7 | 4 | 3 | 2 | 3 | 0 |
| P1 | 3 | 0 | 2 | 0 | 2 | 0 | |||
| P2 | 3 | 0 | 1 | 6 | 0 | 0 | |||
| P3 | 2 | 1 | 1 | 0 | 1 | 1 | |||
| P4 | 0 | 0 | 2 | 4 | 3 | 1 | |||
- Executive safety algorithm shows that sequence < P1, P3, P4, P0, P2> satisfies safety requirement.
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