Lecture 6

Fall 2000: CS 771/871 Operating Systems

Lecture 6 - Distributed Mutual Exclusion

Clock Based Consistent Cache

Why Cache?
Distinguish read and write caches
If want to write, have to invalidate all read caches even if not in use.
Unless readers have a lease time, old readers cannot trust cache consistency
Can renew leases if no one else has requested a write lease.
Server can break lease for priority writer.
If client has crashed, time out by lease value (or network partition).

Mutual Exclusion

Only one process can access a shared resource at a time (e.g. printer, file, data record).

Can be implemented as critical region.
Question: what is difference between critical section and resource lock?

Desirable Characteristics of Mutual Exclusion algorithm:

Freedom from deadlock
Freedom from starvation
Fairness
Fault Tolerance

Measuring performance

Number of messages
Synchronization delays
Response time
system throughput

Also high/low load and best/average/worst case performance

Centralized Mutual Exclusion Algorithm

Centralized algorithm:

Send request to enter critical section to coordinator
If no one already in, mark in use and grant request
If in use, queue request.
When process leaves critical region, send message to coordinator to release
If processes queued, pick one and grant request.

Centralized is not always inappropriate.
A single shared resource is inherently centralized - co-locate coordinator.

System Throughput is 1/(2T+E) where T is average message delay and E is the average CS time

Distributed Mutual Exclusion Algorithm (Ricart and Agrawala)

Totally order all events.
build message containing, critical region, process number and current time.
Send to all processes reliably
Question: how can this be determined?
A process replies as follows:
- If not in and does not want, reply OK
- If in, queues request (no reply)
- If wants to enter, compare timestamp in request to its own. If lower sends OK. otherwise queue
- requesting process waits until everyone sends it an OK message
- When exiting dequeues all processes and sends OK.

How many messages?
What about failures? before, during and after
What about load (CPU and network)?
Is distributed better?

Correctness of Ricart-Agrawala Algorithm

Proof by contradiction: Assume that two sites Si and Sj are executing the critical section (CS) concurrently and that Si's request has a smaller timestamp than Sj (timestamps are totally ordered). Si must have receieved Sj's request after it made its own request. But Sj can only be in the CS if Si returned a reply to it before Si finishes the CS. But this is not possible since Sj has lower priority than Si's request.

Distributed Mutual Exclusion Algorithm (Token Ring)

Form LOGICAL ring
circulate token around ring
If token holder, can enter critical region if desired else pass token on.

Is this fair?
what is max wait?
What if token is lost?
What is machine crashes?

Comparison of Mutual Exclusion Algorithms

algorithm	Messages/critical region	Delay to enter	Problems
Centralized	3	2	coordinator crash
Distributed	2(n-1)	2(n-1)	process crash
Token Ring	1 to unbounded	0 to n-1	lost token or process crash

Can also measure throughput, utilization, etc.

Generalized Non-Token-Based Algorithm

Sanders realized that what each process knows about the global state can be used to generalize Non-token based algorithms.

The knowledge of the global state for each site Si is kept in an information structure containing:

Ri: request set
Ii: inform set
STi: status set
CSSTATi: this site's knowledge of the status of the CS
Queue of Requests message ordered by timestamp

If Si is in Ij then Sj is in STi

Theorem 6.4: If for all i, Si is in Ii, then to guarantee mutual exclusion

G1: Forall i, Ii is a subset of Ri

G2: forall i,j :: The UNION of Ii and Ij is not empty OR Si is in Rj AND Sj is in Ri)

Algorithm:

Requesting the critical section:

Site wishing to enter CS sends timestamped REQUEST messages to all sites in its request set.

On receipt of a REQUEST message, a site Si does

Places request in its queue (ordered by timestamp)

If CSSTAT indicates CS is free, send GRANT request to site at top of the queue, removing it.
If the recipient of a GRANT message is in STi, then CSSTAT is set to indicate that the site is in the CS

Executing the critical section

after receiving a GRANT message for all sites in its request set.

Releasing the critical section

Send RELEASE message to all sites in the inform set.
Upon receiving a RELEASE message do

CSSTAT is set to free

If the queue is non-empty, thens a GRANT request to the site on the top
If the recipient of a GRANT message is in STi, then CSSTAT is set to indicate that the site is in the CS

Repeat previous until CSSTAT indicated that a site is in its CS or queue is empty

Ricart-Agrawala algorithm says it does not object to another site entering the CS but does not have the authority by itself in granting permission.

Maekawa's algorithm says all sites in my status set agree that you can enter your CS.

Generalized combines these two. If first predicate of G2 is false for all Si and Si, then it is Ricart-Agrawala. if second predicate is false it is Maekawa.