Consider a system which has 28 instances of a resource P such that 4 ...
28 > 4 × (5 × 1) + (5 – 1) × n
28 > 20 – 4 + 5n – n
28 > 16 + 4n
12 > 4n
3 > n
Maximum value of n is 3 – 1 = 2
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Consider a system which has 28 instances of a resource P such that 4 ...
To determine the maximum value of n such that the system is in a safe state, we need to apply the Banker's Algorithm. The Banker's Algorithm is used to check if a system can allocate resources to processes in a safe manner.
Given:
- There are 28 instances of resource P available.
- 4 processes share these instances.
- 4 processes request 5 instances of resource P.
We can determine the maximum value of n by simulating the allocation of resources using the Banker's Algorithm and checking if the system remains in a safe state.
The steps to apply the Banker's Algorithm are as follows:
1. Initialization:
- Set the available resources vector to the total number of instances of resource P (28 in this case).
- Set the maximum matrix to represent the maximum resource requirement of each process.
- Set the allocation matrix to represent the resources currently allocated to each process.
- Set the need matrix to represent the remaining resource requirements of each process.
2. Request Resources:
- When a process requests resources, check if the requested resources can be allocated by comparing the requested resources with the available resources.
- If the requested resources can be allocated, update the allocation, need, and available matrices accordingly.
- If the requested resources cannot be allocated, the process must wait until sufficient resources become available.
3. Safety Check:
- After each resource allocation or request, perform a safety check to determine if the system is in a safe state.
- The safety check involves simulating the allocation of resources to all processes and checking if there exists a safe sequence.
- A safe sequence is a sequence of processes where each process can acquire its required resources and complete execution.
- If a safe sequence exists, the system is in a safe state. Otherwise, it is in an unsafe state.
In this case, since 4 processes request 5 instances of resource P, the maximum value of n can be determined by incrementing n until the system is in an unsafe state. Using the Banker's Algorithm, we find that the system remains in a safe state for n=2, but becomes unsafe for n=3. Therefore, the maximum value of n such that the system is in a safe state is 2 (option B).