Bankers Resource Allocating Algorithm

Banker’s Algorithm: A Brief Overview

The Banker’s Algorithm is a deadlock avoidance algorithm used in operating systems to manage resource allocation in a way that prevents deadlocks. It ensures that the system remains in a safe state, where there is always a sequence of processes that can complete and release their resources.

Key Concepts:

Safe State: A state where there exists a sequence of processes that can finish executing without causing a deadlock.
Work and Finish Arrays: Work simulates the available resources, and Finish tracks whether a process can complete execution.
Need Matrix: Calculated as Need = Max - Allocation, representing the additional resources a process may request.

How It Works:

Initialization: Set Work to the available resources and Finish to false for all processes.
Resource Allocation: For each process, check if its Need is less than or equal to Work. If so, allocate resources and update Work and Finish.
Safety Check: Continue allocating resources until all processes can complete, ensuring the system remains in a safe state.

The Banker’s Algorithm is particularly useful in environments where resource allocation must be carefully managed to avoid deadlocks, ensuring that processes can always complete their execution.

Example of Banker’s Algorithm

Number of processes: 5 ( $P_{1}$ through $P_{5}$ )
Resource types:
- $A$ (10 instances)
- $B$ (5 instances)
- $C$ (7 instances)

Snapshot at time $T_{c}$ :

Process	Allocation	Max	Available	Need (Calculated by students)
	A B C	A B C	A B C	A B C
$P_{1}$	1 0 5	7 5 3	3 3 2	6 5 3
$P_{2}$	0 1 0	7 5 3		7 4 3
$P_{3}$	2 0 0	3 2 2		1 2 2
$P_{4}$	3 0 2	9 0 2		6 0 0
$P_{5}$	0 0 2	4 3 3		4 3 1
Available			3 3 2

Key Definitions:

Allocation: The resources currently allocated to each process.
Max: The maximum resources each process may need.
Available: The resources available in the system at the given time.
Need: The remaining resources required by each process to complete, calculated as: $Need = Max - Allocation$

Work and Finish Arrays:

Work: Initially set to the Available resources, i.e., Work = Available = [3, 3, 2].
Finish: An array of boolean values, initially set to false for all processes. A value of true will indicate that a process can finish its execution and release resources.
- Finish[i] becomes true if the need of process $P_{i}$ is less than or equal to the current Work resources.

Algorithm Steps:

Initialization: Set Work = Available = [3, 3, 2], and Finish[i] = false for all $i$ .
Find a process with unmet needs: Check each process for which Finish[i] = false. If the Need of that process is less than or equal to Work, it means the process can execute and release its allocated resources.
Process Execution:
- Start with $P_{1}$ . The Need for $P_{1}$ is [6, 5, 3], which is greater than the available resources [3, 3, 2]. Therefore, $P_{1}$ cannot be allocated.
- Move to $P_{2}$ . The Need for $P_{2}$ is [7, 4, 3], which is greater than the available resources [3, 3, 2]. Thus, $P_{2}$ cannot be allocated either.
- Check $P_{3}$ . The Need for $P_{3}$ is [1, 2, 2], which is less than the available resources [3, 3, 2]. Hence, $P_{3}$ can be allocated.
  
  After allocating $P_{3}$ :
  - Update Work = Work + Allocation[P_3] = [3, 3, 2] + [2, 0, 0] = [5, 3, 2].
  - Set Finish[3] = true (since $P_{3}$ has completed).
  - Go back to step 2.
Continue the process:
- Now, check if any other process can be allocated. Since the resources available are now [5, 3, 2], move to $P_{1}$ , $P_{2}$ , $P_{4}$ , and $P_{5}$ and check their Need values relative to Work.
- Eventually, if all processes can be allocated and finished in a safe sequence, the system is in a safe state.

Dry Run:

Initial State:
- Work = [3, 3, 2]
- Finish = [false, false, false, false, false]
Check $P_{1}$ :
- Need = [6, 5, 3]
- Need > Work, so $P_{1}$ cannot be allocated.
Check $P_{2}$ :
- Need = [7, 4, 3]
- Need > Work, so $P_{2}$ cannot be allocated.
Check $P_{3}$ :
- Need = [1, 2, 2]
- Need ≤ Work, so $P_{3}$ can be allocated.
- Update Work = [5, 3, 2]
- Set Finish[3] = true
Check $P_{4}$ :
- Need = [6, 0, 0]
- Need ≤ Work, so $P_{4}$ can be allocated.
- Update Work = [8, 3, 4]
- Set Finish[4] = true
Check $P_{5}$ :
- Need = [4, 3, 1]
- Need ≤ Work, so $P_{5}$ can be allocated.
- Update Work = [8, 6, 6]
- Set Finish[5] = true
Check $P_{1}$ again:
- Need = [6, 5, 3]
- Need ≤ Work, so $P_{1}$ can be allocated.
- Update Work = [14, 11, 11]
- Set Finish[1] = true
Check $P_{2}$ again:
- Need = [7, 4, 3]
- Need ≤ Work, so $P_{2}$ can be allocated.
- Update Work = [14, 15, 11]
- Set Finish[2] = true

Final State:

All processes have been allocated and finished successfully.
The system is in a safe state.

Final Remarks:

The Banker’s Algorithm ensures that the system avoids unsafe states by checking if there is always a way to allocate resources such that every process can eventually finish and release its resources. If such a sequence exists, the system is in a safe state.

Resource Allocation Algorithm

First, let’s examine the table:

Process ID	Allocation	Max	Available	Need = $M a x - A ll oc a t i o n$
P0	0 1 0	7 5 3	3 3 2	7 4 3
P1	2 0 0	3 2 2		1 2 2
P2	3 0 2	9 0 2		6 0 0
P3	2 1 1	2 2 2		0 1 1
P4	0 0 2	4 3 3		4 3 1

Steps to Determine Resource Allocation:

If the request is greater than the need, go to step 2.
If the request is less than or equal to Available:
- Update the allocation: allocation = allocation + request.
- Update the need: Need = Need - request.

Dry Run:

Initial State:
- Work = [3, 3, 2]
- Finish = [false, false, false, false, false]
Check $P_{0}$ :
- Need = [7, 4, 3]
- Need > Work, so $P_{0}$ cannot be allocated.
Check $P_{1}$ :
- Need = [1, 2, 2]
- Need ≤ Work, so $P_{1}$ can be allocated.
- Update Work = [5, 3, 2]
- Set Finish[1] = true
Check $P_{2}$ :
- Need = [6, 0, 0]
- Need ≤ Work, so $P_{2}$ can be allocated.
- Update Work = [8, 3, 4]
- Set Finish[2] = true
Check $P_{3}$ :
- Need = [0, 1, 1]
- Need ≤ Work, so $P_{3}$ can be allocated.
- Update Work = [8, 4, 5]
- Set Finish[3] = true
Check $P_{4}$ :
- Need = [4, 3, 1]
- Need ≤ Work, so $P_{4}$ can be allocated.
- Update Work = [12, 7, 6]
- Set Finish[4] = true
Check $P_{0}$ again:
- Need = [7, 4, 3]
- Need ≤ Work, so $P_{0}$ can be allocated.
- Update Work = [19, 11, 9]
- Set Finish[0] = true

Final State:

Process ID	Allocation	Max	Available	Need = $M a x - A ll oc a t i o n$
P0	0 1 0	7 5 3	3 3 2	7 4 3
P1	2 0 0	3 2 2		1 2 2
P2	3 0 2	9 0 2		6 0 0
P3	2 1 1	2 2 2		0 1 1
P4	0 0 2	4 3 3		4 3 1

Mermaid Diagram and Complete answer

flowchart TD
    A[Start] --> B[Initialize Work and Finish]
    B --> C{Check each process}
    C --> D{Is Finish false?}
    D -- Yes --> E{Is Need[i] <= Work?}
    E -- Yes --> F[Allocate resources to process i]
    F --> G[Update Work = Work + Allocation[i]]
    G --> H[Set Finish[i] to true]
    H --> C
    E -- No --> C
    D -- No --> I{Are all processes checked?}
    I -- No --> C
    I -- Yes --> J[End: Safe State]

Safety Index
- $P_{1}$ , $P_{3}$ , $P_{4}$ , $P_{2}$ , $P_{0}$
All processes have been allocated and finished successfully.
The system is in a safe state.

This detailed dry run demonstrates how both the Banker’s Algorithm and the Resource Allocation Algorithm work step-by-step to ensure safe resource allocation.

References

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date: 2025.03.01
time: 12:34

🪴 TJ's Notes 1.0

Explorer

Bankers Resource Allocating Algorithm

Bankers Resource Allocating Algorithm

Banker’s Algorithm: A Brief Overview

Key Concepts:

How It Works:

The Banker’s Algorithm is particularly useful in environments where resource allocation must be carefully managed to avoid deadlocks, ensuring that processes can always complete their execution.

Example of Banker’s Algorithm

Key Definitions:

Work and Finish Arrays:

Algorithm Steps:

Dry Run:

Final State:

Final Remarks:

Resource Allocation Algorithm

Steps to Determine Resource Allocation:

Dry Run:

Final State:

Mermaid Diagram and Complete answer

References

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