Hi @Tausif @Isaac_Torres !!
The inequalities you’re referring to are related to the quorum-based approach in distributed systems, particularly in the context of ensuring consistency and coordination among different nodes. Let’s break down these concepts for a clearer understanding:
Vr + Vw > V
Here, V is the total number of nodes in the system, Vr is the read quorum, and Vw is the write quorum. The inequality
Vr + Vw > V ensures that the sets of nodes involved in any read and write operation overlap. This overlap is crucial for maintaining consistency across the system.
How It Works: Imagine a system with 5 nodes (V = 5). If you have a read quorum (Vr) of 2 and a write quorum (Vw) of 4, then
Vr + Vw = 2 + 4 = 6, which is greater than V (5). This means that at least one node must participate in both read and write operations. Why is this important? Because if a write operation has occurred, at least one node that knows about this new write must be involved in a subsequent read operation, ensuring that reads always get the most recent write.
Ensuring No Concurrent Reads and Writes: This inequality prevents a scenario where a read and a write operation can occur entirely independently without any node being aware of both operations. It guarantees that a read operation following a write operation will always reflect that write, thereby maintaining consistency.
Vw > V / 2
This rule ensures that write quorums overlap with each other. By requiring that the size of the write quorum (Vw) be greater than half the total number of nodes (V), it is guaranteed that two different write operations will have at least one node in common.
How It Works: Continuing with the example where V = 5, if
Vw > 5 / 2, then Vw must be at least 3. If two separate write operations occur, each involving at least 3 nodes, there must be at least one node common to both operations. This common node helps in ordering the write operations and maintaining a consistent state across the system.
Preventing Concurrent Writes: Since every write quorum overlaps with every other write quorum, it is impossible for two writes to occur completely independently. There will always be at least one node that knows about both writes, and this helps in resolving any conflicts and ensuring that the system does not accept conflicting updates.
In summary, these inequalities are fundamental in quorum-based distributed systems for ensuring that all nodes in the system can agree on the state of the data, even in the presence of concurrent operations. This is a key aspect of achieving consistency in distributed databases and other similar systems.
I hope it helps. Happy Learning