Part 1 In A Two-Phase Total Order Multicast System Messages

Part 1in Atwo Phase Total Ordermulticast System Messages Are Sent I

Part 1: In a two-phase, total-order multicast system, messages are sent in the following sequence from node S to G1 and G2. G1 and G2 are the members of the group. S sends m1 to G1, S sends m1 to G2, S sends m2 to G2, S sends m2 to G1. Use the basic implementation of the Lamport clock. The clock s at each node start at: S: 4, G1: 6, G2: 1. Show the exchange of messages and their acknowledgments in a clock diagram using the basic implementation of Lamport’s clock. In which order and at what times are m1 and m2 delivered?

Part 2: Draw a state diagram of Maekawa’s voting algorithm on the slide “Maekawa’s algorithm” in the “Distributed mutual exclusion” slide set. Note that the state diagram is from the point of view of any one of the nodes, called "this" node below. The state diagram cannot show the states of other nodes. i) Start with the basic case where "this" node wants the lock, gets it, and then releases it, and no other node wants the lock at the same time. In this case, "this" node goes through all the states in this order: Released and not voted, Wanted and not voted, Wanted and voted, Held and voted, Released and voted, and then back to Released and not voted. Events are: acquire when “this” node wants the lock, and release when “this” node releases the lock.

Paper For Above instruction

Understanding the operational mechanics of distributed systems is fundamental to ensuring efficient coordination and synchronization among nodes. This paper explores two critical aspects: the implementation of message ordering via the Lamport clock in a two-phase total order multicast system, and the state transitions in Maekawa’s voting algorithm for distributed mutual exclusion. By delving into these topics, we aim to clarify the mechanisms that underpin reliable message delivery and mutual exclusion in distributed architectures.

Part 1: Lamport Clock in Two-Phase Total Order Multicast System

In distributed systems, ensuring total ordering of messages is essential, especially in applications like replicated databases, where consistency must be maintained across nodes. The two-phase total order multicast system achieves this by employing synchronized logical clocks, such as the Lamport clock, which assign timestamps to messages to preserve the causality and order of events.

Given nodes S, G1, and G2, with initial Lamport clock values of 4, 6, and 1 respectively, the sequence of message transmissions unfolds as follows:

  • Node S initiates by sending message m1 to G1 and G2. Before sending, S increments its clock from 4 to 5, timestamping m1 with 5.
  • Simultaneously or shortly afterward, S sends m1 to G2, which receives the message with its clock at 1. G2 updates its clock to max(1,5)+1=6, acknowledging receipt.
  • Next, S sends message m2 to G2. S increments its clock from 5 to 6, and sends m2 with timestamp 6 to G2.
  • G2 receives m2, updates its clock to max(6,6)+1=7, and acknowledges receipt. In parallel, S sends m2 to G1, which receives it with its clock at 6, updating it to max(6,6)+1=7 if necessary.

The clocks at each node after message exchanges are:

  • S: final clock 6
  • G1: clock updated upon receipt of m1 and m2, resulting in 7
  • G2: clock updated upon receipt of m1 and m2, resulting in 7

The delivery order based on timestamps will be:

  1. G1 receives m1 at timestamp 5; it delivers m1 immediately.
  2. G2 receives m1 at timestamp 5; it delivers m1 shortly after.
  3. G2 receives m2 at timestamp 6; it delivers m2 after processing m1.
  4. G1 receives m2 at timestamp 6; it delivers m2 accordingly.

Thus, message m1 is delivered first at G1 and G2, followed by m2 at both nodes, respecting the total order dictated by the Lamport timestamps.

Part 2: Maekawa’s Voting Algorithm State Diagram

Maekawa’s algorithm reduces the number of votes each node needs to grant to acquire a lock in distributed mutual exclusion. The state diagram from a node's perspective describes the node's transitions when requesting, obtaining, and releasing a lock without conflicting requests.

The states include:

  • Released and not voted: The default state where the node is not holding the lock and has not voted for another’s request.
  • Wanted and not voted: When the node desires to acquire the lock but has not yet voted for any request.
  • Wanted and voted: The node requests the lock and has granted its vote to itself or others.
  • Held and voted: The node has received votes and is currently holding the lock.
  • Released and voted: The node releases the lock but still retains its vote if needed or resets its state.

Transitions occur as:

  • Acquire: A request to lock, moving from Released and not voted to Wanted and not voted.
  • Vote granted: When the node grants the lock, it transitions to Wanted and voted, then to Held and voted when acquiring the lock.
  • Release: Releasing the lock transitions the node back from Held and voted to Released and voted, then eventually to Released and not voted.

The diagram captures the sequential states as the node requests, acquires, holds, and releases the lock, illustrating the protocol’s flow to prevent deadlocks and ensure mutual exclusion.

Conclusion

Understanding Lamport clocks’ role in ordering messages and the state transitions in Maekawa’s algorithm is crucial for designing robust distributed systems. Lamport clocks facilitate consistent message ordering across nodes, essential for system-wide consistency, while Maekawa’s voting algorithm optimizes resource access, reducing message complexity without sacrificing safety. Analyzing these mechanisms helps improve fault tolerance, efficiency, and scalability in distributed computing environments.

References

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