Explain how timestamps and logical clocks are utilized in Maekawa's algorithm to ensure mutual exclusion. Analyze the message complexity and scalability of this algorithm
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Each process is assigned a set of other processes to communicate with, forming a voting group. The algorithm relies on timestamps and logical clocks to determine the order of requests and to ensure that processes can make decisions based on the most recent Show more…
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(a) Prove or disprove the following statement: Lamport's mutual exclusion algorithm will work correctly even if channels are not FIFO. (b) Illustrate with an example that under Lamport's mutual exclusion algorithm, a process may not have to wait until its request reaches other processes to access critical section. (c) Prove that under Ricart Agrawala's mutual exclusion algorithm, request for accessing critical section will be satisfied in ascending order of the timestamps of the requests of the processes. (d) Prove or disprove the following statement: Ricart-Agrawla's mutual exclusion algorithm allows a process to access critical section more than once while other processes are waiting to access critical section. (e) Prove or disprove the following statement: Under Suzuki-Kasami's algorithm, a process may enter critical section more than once while other processes are waiting to access critical section (i.e., other processes have pending requests).
Akash M.
(a) (6 marks) Consider the schedule below. Here, R(·) and W(·) stand for ‘Read’ and ‘Write’, respectively. T₁, T₂, T₃ and T₄ represent four transactions and tቢ represents a time slot. Time | t₁ | t₂ | t₃ | t₄ | t₅ | t₆ | t₇ | t₈ | t₉ --- | --- | --- | --- | --- | --- | --- | --- | --- | --- T₁ | | W(Y) | | | R(X) | | | | T₂ | | | | | | R(Y) | W(Z) | | T₃ | | | | R(Z) | | | | R(Y) | R(X) T₄ | W(Y) | | W(X) | | | | | | 1. Give the precedence graph of this schedule. (3 marks) 2. Is this schedule conflict serializable? If your answer is ‘‘yes’’, please providing the equivalent serial schedule. If your answer is ‘‘no’’, convert it to a conflict serializable schedule with the minimum change in the scheduling while preserving the given ordering of operations in each transaction. (3 marks) (b) (6 marks) Consider the lock request sequence given below. RL() and WL() stand for ‘‘read lock’’ and ‘‘write lock’’, respectively. T₁, T₂, T₃ and T₄ represent four transactions. Time | t₁ | t₂ | t₃ | t₄ | t₅ | t₆ | t₇ | t₈ --- | --- | --- | --- | --- | --- | --- | --- | --- T₁ | | | | WL(B) | | RL(A) | | T₂ | | | WL(A) | | WL(C) | | | T₃ | WL(C) | | | | | | | RL(B) T₄ | | RL(B) | | | | | WL(C) | 1. Determine whether there exists a deadlock in the lock requests and justify your answer. (3 marks) 2. For the four transactions, construct a serializable but non-serial schedule using two-phase locking mechanism. If this is impossible, please justify your answer. (3 marks)
Suppose there are three processes A, B, and C. All clocks run at the same rate, but initially A's clock reads 10, B's clock reads 0, and C's clock reads 5. At time 10 by A's clock, A sends a message to B. This message takes 4 units of time to reach B. B then waits one unit of time and then sends a message onto C, which takes 2 units of time to reach C. a. Assuming that the system implements Lamport's timestamps, draw a picture illustrating the timestamps for the messages and explain how the timestamps are obtained. b. What does it mean for two events to be concurrent, and what is the relation of the Lamport timestamps of the two events.
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