Maekawa’s Algorithm for Mutual Exclusion in Distributed System

Prerequisite – Mutual exclusion in distributed systems
Maekawa’s Algorithm is quorum based approach to ensure mutual exclusion in distributed systems. As we know, In permission based algorithms like Lamport’s Algorithm, Ricart-Agrawala Algorithm etc. a site request permission from every other site but in quorum based approach, A site does not request permission from every other site but from a subset of sites which is called quorum.

In this algorithm:

• Three type of messages ( REQUEST, REPLY and RELEASE) are used.
• A site send a REQUEST message to all other site in its request set or quorum to get their permission to enter critical section.
• A site send a REPLY message to requesting site to give its permission to enter the critical section.
• A site send a RELEASE message to all other site in its request set or quorum upon exiting the critical section.

The construction of request set or Quorum:
A request set or Quorum in Maekawa’s algorithm must satisfy the following properties:

1. ∀i ∀j : i ≠ j, 1 ≤ i, j ≤ N :: Ri ⋂ Rj ≠ ∅ 

   i.e there is at least one common site between the request sets of any two sites.

2. ∀i : 1 ≤ i ≤ N :: Si ∊ Ri 

3. ∀i : 1 ≤ i ≤ N :: |Ri| = K 

4. Any site S_i is contained in exactly K sets.

5. N = K(K - 1) +1 and |Ri| = √N 

Algorithm:

• To enter Critical section:
  • When a site S_i wants to enter the critical section, it sends a request message REQUEST(i) to all other sites in the request set R_i.
  • When a site S_j receives the request message REQUEST(i) from site S_i, it returns a REPLY message to site S_i if it has not sent a REPLY message to the site from the time it received the last RELEASE message. Otherwise, it queues up the request.

  .

• To execute the critical section:
  • A site S_i can enter the critical section if it has received the REPLY message from all the site in request set R_i
• To release the critical section:
  • When a site S_i exits the critical section, it sends RELEASE(i) message to all other sites in request set R_i
  • When a site S_j receives the RELEASE(i) message from site S_i, it send REPLY message to the next site waiting in the queue and deletes that entry from the queue
  • In case queue is empty, site S_j update its status to show that it has not sent any REPLY message since the receipt of the last RELEASE message

Message Complexity:
Maekawa’s Algorithm requires invocation of 3√N messages per critical section execution as the size of a request set is √N. These 3√N messages involves.

• √N request messages
• √N reply messages
• √N release messages

Drawbacks of Maekawa’s Algorithm:

• This algorithm is deadlock prone because a site is exclusively locked by other sites and requests are not prioritized by their timestamp.

Performance:

• Synchronization delay is equal to twice the message propagation delay time
• It requires 3√n messages per critical section execution.

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