Question

Discuss how the Lamport’s algorithm achieves clock synchronization, using 4 clocks of
different machines. Here, also compute the time taken for synchronizing the clocks
(consider the clock with lowest time and compute the time with respect to this clock). Can
this algorithm be used in a real time system.

Answer 1

Lamport’s Distributed Mutual Exclusion Algorithm is a permission based algorithm proposed by Lamport as an illustration of his synchronization scheme for distributed systems.
In permission based timestamp is used to order critical section requests and to resolve any conflict between requests.

In Lamport’s Algorithm critical section requests are executed in the increasing order of timestamps i.e a request with smaller timestamp will be given permission to execute critical section first than a request with larger timestamp.

In this algorithm:

• Three type of messages ( REQUEST, REPLY and RELEASE) are used and communication channels are assumed to follow FIFO order.
• A site send a REQUEST message to all other site 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 upon exiting the critical section.
• Every site S_i, keeps a queue to store critical section requests ordered by their timestamps.
  request_queue_i denotes the queue of site S_i
• A timestamp is given to each critical section request using Lamport’s logical clock.
• Timestamp is used to determine priority of critical section requests. Smaller timestamp gets high priority over larger timestamp. The execution of critical section request is always in the order of their timestamp.

Algorithm:

• To enter Critical section:

  .

  • When a site S_i wants to enter the critical section, it sends a request message Request(ts_i, i) to all other sites and places the request on request_queue_i. Here, Ts_i denotes the timestamp of Site S_i
  • When a site S_j receives the request message REQUEST(ts_i, i) from site S_i, it returns a timestamped REPLY message to site S_i and places the request of site S_i on request_queue_j
• To execute the critical section:
  • A site S_i can enter the critical section if it has received the message with timestamp larger than (ts_i, i) from all other sites and its own request is at the top of request_queue_i
• To release the critical section:
  • When a site S_i exits the critical section, it removes its own request from the top of its request queue and sends a timestamped RELEASE message to all other sites
  • When a site S_j receives the timestamped RELEASE message from site S_i, it removes the request of S_i from its request queue

Message Complexity:
Lamport’s Algorithm requires invocation of 3(N – 1) messages per critical section execution. These 3(N – 1) messages involves