Suzuki–Kasami algorithm

The Suzuki–Kasami algorithm^[1] is a token-based algorithm for achieving mutual exclusion in distributed systems. The process holding the token is the only process able to enter its critical section. ***

This is a modification to Ricart–Agrawala algorithm^[2] in which a REQUEST and REPLY message are used for attaining the critical section, but in this algorithm, a method was introduced in which a seniority vise and also by handing over the critical section to other node by sending a single PRIVILEGE message to other node. So, the node which has the privilege it can use the critical section and if it does not have one it cannot. If a process wants to enter its critical section and it does not have the token, it broadcasts a request message to all other processes in the system. The process that has the token, if it is not currently in a critical section, will then send the token to the requesting process. The algorithm makes use of increasing Request Numbers to allow messages to arrive out-of-order.

Algorithm description

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

Data structures

Each process maintains one data structure:

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

The token contains two data structures:

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

Algorithm

Requesting the critical section (CS)

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

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

Releasing the CS

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

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

Receiving a request

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

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

Executing the CS

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

Performance

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