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 they introduced a method 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 $n$ be the number of processes. Each process is identified by an integer in $1,...,n$ .

Data structures

Each process maintains one data structure:

an array $RN[n]$ (for Request Number), where $RN_{i}[j]$ stores the last Request Number received from $j$

The token contains two data structures:

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

Algorithm

Requesting the critical section (CS)

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

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

Releasing the CS

When process $i$ leaves the CS, it:

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

Receiving a request

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

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RN_{i}[j]$ , the message is outdated)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

Executing the CS

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

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

Data structures used to deal with these two aspects:

Each site Si has an array RNi[1..N] to store the sequence
Number of the latest requests received from other sites

The token contains two data structures:

The token array LN[1..N] keeps track of the request executed most recently on each site
The token queue Q is a queue of requesting sites

Requesting the CS

If the site does not have the token, then it increases its sequence number RNi[i] and sends a request(i, sn) message to all other sites (sn= RNi[i])
When a site Sj receives this message, it sets RNj[i] to max(RNj[i], sn). If Sj has the idle token, them it sends the token to Si if RNj[i] = LN[i]+1

Executing the CS

Site Si executes the CS when it has received the token

Releasing the CS

When done with the CS, site Si sets LN[i] = RNi[i]
For every site Sj whose ID is not in the token queue, it appends its ID to the token queue if RNi[j] =LN[j]+1
If the queue is not empty, it extracts the ID at the head of the queue and sends the token to that site

Performance

either 0 or n messages for CS invocation (no messages if process holds the token; otherwise $N-1$ requests and $1$ reply)
Synchronization delay is 0 or N

References

↑ Ichiro Suzuki, Tadao Kasami, A distributed mutual exclusion algorithm, ACM Transactions on Computer Systems, Volume 3 Issue 4, Nov. 1985 (pages 344 - 349)
↑ Ricart, Glenn, and Ashok K. Agrawala. "An optimal algorithm for mutual exclusion in computer networks." Communications of the ACM 24.1 (1981): 9-17.

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