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Algorithm description

Let n {\displaystyle n} be the number of processes. Each process is identified by an integer in 1 , . . . , n {\displaystyle 1,...,n} .

Data structures

Each process maintains one data structure:

• an array R N i [ n ] {\displaystyle RN_{i}[n]} (for Request Number), i {\displaystyle i} being the ID of the process containing this array, where R N i [ j ] {\displaystyle RN_{i}[j]} stores the last Request Number received by i {\displaystyle i} from j {\displaystyle j}

The token contains two data structures:

• an array L N [ n ] {\displaystyle LN[n]} (for Last request Number), where L N [ j ] {\displaystyle LN[j]} stores the most recent Request Number of process j {\displaystyle j} for which the token was successfully granted
• a queue Q {\displaystyle Q} , storing the ID of processes waiting for the token

Algorithm

Requesting the critical section (CS)

When process i {\displaystyle i} wants to enter the CS, if it does not have the token, it:

• increments its sequence number R N i [ i ] {\displaystyle RN_{i}[i]}
• sends a request message containing new sequence number to all processes in the system

Releasing the CS

When process i {\displaystyle i} leaves the CS, it:

• sets L N [ i ] {\displaystyle LN[i]} of the token equal to R N i [ i ] {\displaystyle RN_{i}[i]} . This indicates that its request R N i [ i ] {\displaystyle RN_{i}[i]} has been executed
• for every process k {\displaystyle k} not in the token queue Q {\displaystyle Q} , it appends k {\displaystyle k} to Q {\displaystyle Q} if R N i [ k ] = L N [ k ] + 1 {\displaystyle RN_{i}[k]=LN[k]+1} . This indicates that process k {\displaystyle k} has an outstanding request
• if the token queue Q {\displaystyle Q} is not empty after this update, it pops a process ID j {\displaystyle j} from Q {\displaystyle Q} and sends the token to j {\displaystyle j}
• otherwise, it keeps the token

Receiving a request

When process j {\displaystyle j} receives a request from i {\displaystyle i} with sequence number s {\displaystyle s} , it:

• sets R N j [ i ] {\displaystyle RN_{j}[i]} to m a x ( R N j [ i ] , s ) {\displaystyle max(RN_{j}[i],s)} (if s < R N j [ i ] {\displaystyle s<RN_{j}[i]} , the message is outdated)
• if process j {\displaystyle j} has the token and is not in CS, and if R N j [ i ] == L N [ i ] + 1 {\displaystyle RN_{j}[i]==LN[i]+1} (indicating an outstanding request), it sends the token to process i {\displaystyle i}

Executing the CS

A process enters the CS when it has acquired the token.

Performance

• Either 0 {\displaystyle 0} or N {\displaystyle N} messages for CS invocation (no messages if process holds the token; otherwise N − 1 {\displaystyle N-1} requests and 1 {\displaystyle 1} reply)
• Synchronization delay is 0 {\displaystyle 0} or N {\displaystyle N} ( N − 1 {\displaystyle N-1} requests and 1 {\displaystyle 1} reply)

Notes on the algorithm

• Only the site currently holding the token can access the CS

• All processes involved in the assignment of the CS

• Request messages sent to all nodes

• Not based on Lamport’s logical clock
• The algorithm uses sequence numbers instead

• Used to keep track of outdated requests
• They advance independently on each site

The main design issues of the algorithm:

• Telling outdated requests from current ones
• Determining which site is going to get the token next

References

1. Ichiro Suzuki, Tadao Kasami, [1], ACM Transactions on Computer Systems, Volume 3 Issue 4, Nov. 1985 (pages 344 - 349) https://dl.acm.org/doi/pdf/10.1145/6110.214406 ↩

2. Ricart, Glenn, and Ashok K. Agrawala. "An optimal algorithm for mutual exclusion in computer networks." Communications of the ACM 24.1 (1981): 9-17. https://apps.dtic.mil/sti/pdfs/ADA083268.pdf ↩