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## Banker’s Algorithm:

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.

### Data Structures for the Banker's algorithm

 Let n = number of processes and m = number ofresourcetypes1)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 taskNeed[i, j] =Max[i, j] - Allocation[i, j].

## Banker's algorithm- safety procedure

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.

### Banker's Algorithm- Resource Request algorithm for process

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

1. If sae => the resources are allocated to .
2. If unsafe =>  must wait, and the old resource- allocation state is restored

### Example of Banker's 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.