Bully algorithm: Difference between revisions

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TheIn [[distributed computing]], the '''bully algorithm''' is a method infor dynamically [[distributedLeader computingelection|electing]] for dynamically electing a [[Distributed Computingcomputing#Coordinator Election|coordinator]] byor processleader IDfrom numbera group of distributed computer processes. The process with the highest process ID number from amongst the non-failed processes is selected as the [[Distributed Computing#Coordinator Election|coordinator]].

==Assumptions==

The algorithm assumes that:<ref>{{cite book |last1=Coulouris |first1=George |last2=Dollimore |first2=Jean |last3=Kindberg |first3=Tim |title=Distributed Systems: Concepts and Design |date=2000 |publisher=Addison Wesley |isbn=978-0201619188 |edition=3rd}}</ref>

* The system is synchronous and uses timeout for identifying process failure

* Assumes thatthe system is synchronous .

* Allow processes tomay crashfail at any time, including during exectionexecution of the algorithm.

* Message delivery between processes should be reliable

* a process fails by stopping and returns from failure by restarting.

* Prior information about other process id's must be known

* there is a failure detector which detects failed processes.

* Messagemessage delivery between processes should beis reliable.

* each process knows its own process id and address, and that of every other process.

==Message typesAlgorithm==

The [[algorithm]] uses the following message types:

* Election Message : Sent to announce the election .

* Answer Message(Alive) Message: RespondResponds to the electionElection message.

* Coordinator (Victory) Message: Sent by winner of the election to announce victory.

When a process {{var|P}} recovers from failure, or the failure detector indicates that the current coordinator has failed, {{var|P}} performs the following actions:

* Election Message : Sent to announce the election

* Answer Message : Respond to the election message

* Coordinator message: sent to announce the identity elected process

# If {{var|P}} has the highest process ID, it sends a Victory message to all other processes and becomes the new Coordinator. Otherwise, {{var|P}} broadcasts an Election message to all other processes with higher process IDs than itself.

Compare with Ring algorithm:

# If {{var|P}} receives no Answer after sending an Election message, then it broadcasts a Victory message to all other processes and becomes the Coordinator.

* Assumes that system is synchronous

# If {{var|P}} receives an Answer from a process with a higher ID, it sends no further messages for this election and waits for a Victory message. (If there is no Victory message after a period of time, it restarts the process at the beginning.)

* Uses timeout to detect process failure/crash

# If {{var|P}} receives an Election message from another process with a lower ID it sends an Answer message back and if it has not already started an election, it starts the election process at the beginning, by sending an Election message to higher-numbered processes.

* Each processor knows which processor has the higher identifier number and communicates with that<ref>Jean Dollimore, Tim Kindberg, George F. Coulouris, "Distributed systems : concepts and design (Third Edition)," in ''Distributed systems : concepts and design (Third Edition)''. Addison-Wesley, 2003.</ref>

# If {{var|P}} receives a Coordinator message, it treats the sender as the coordinator.

===Analysis===

When a process P determines that the current coordinator is down because of message timeouts or failure of the coordinator to initiate a handshake, it performs the following sequence of actions:

====Safety====

# P broadcasts an election message (inquiry) to all other processes with higher process IDs, expecting an "I am alive" response from them if they are alive.

The safety property expected of [[leader election]] protocols is that every non-faulty process either elects a process {{var|Q}}, or elects none at all. Note that all [[process (computing)|processes]] that elect a leader must decide on the same process {{var|Q}} as the leader. The Bully algorithm satisfies this property (under the system model specified), and at no point in time is it possible for two processes in the group to have

# If P hears from no process with a higher process ID than it, it wins the election and broadcasts victory.

a conflicting view of who the leader is, except during an election. This is true because if it weren't, there are two processes {{var|X}} and {{var|Y}} such that both sent the Coordinator (victory) message to the group. This means {{var|X}} and {{var|Y}} must also have sent each other victory messages. But this cannot happen, since before sending the victory message, Election messages would have been exchanged between the two, and the process with a lower process ID among the two would never send out victory messages. We have a contradiction, and hence our initial assumption that there are two leaders in the system at any given time is false, and that shows that the bully algorithm is safe.

# If P hears from a process with a higher ID, P waits a certain amount of time for that process to broadcast itself as the leader. If it does not receive this message in time, it re-broadcasts the election message.

# If P gets an election message (inquiry) from another process with a lower ID it sends an "I am alive" message back and starts new elections.

====Liveness====

Note that if P receives a victory message from a process with a lower ID number, it immediately initiates a new election. This is how the algorithm gets its name - a process with a higher ID number will bully a lower ID process out of the coordinator position as soon as it comes online.

[[Liveness]] is also guaranteed in the [[synchronous]], crash-recovery model. Consider the would-be leader failing after sending an Answer (Alive) message but before sending a Coordinator (victory) message. If it does not recover before the set timeout on lower ID processes, one of them will become leader eventually (even if some of the other processes crash). If the failed process recovers in time, it simply sends a Coordinator (victory) message to all of the group.

====Network bandwidth utilization====

{{see also|network bandwidth}}

Assuming that the bully algorithm messages are of a fixed (known, invariant) sizes, the most number of messages are exchanged in the group when the process with the lowest ID initiates an election. This process sends (N−1) Election messages, the next higher ID sends (N−2) messages, and so on, resulting in <math>\Theta\left(N^2\right)</math> election messages. There are also the <math>\Theta\left(N^2\right)</math> Alive messages, and <math>\Theta\left(N\right)</math> co-ordinator messages, thus making the overall number messages exchanged in the worst case be <math>\Theta\left(N^2\right)</math>.

== See also ==

*[[Leader election]]

*[[Distributed Computing#Coordinator Election]]

*[[Chang and Roberts algorithm]]

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{{reflist}}

* Witchel, Emmett (2005). [http://www.cs.utexas.edu/users/witchel/372/lectures/25.DistributedCoordination.ppt "Distributed Coordination"]. Retrieved May 4, 2005.

* Hector Garcia-Molina, Elections in a Distributed Computing System, IEEE Transactions on Computers, Vol. C-31, No. 1, January (1982) 48-5948–59

* L. Lamport, R. Shostak, and M. Pease, [http://research.microsoft.com/en-us/um/people/lamport/pubs/byz.pdf "The Byzantine Generals Problem"] ACM Transactions on Programming Languages and Systems, Vol. 4, No. 3, July 1982.

==External links==

*{{Commonscatinline}}

[[Category:Distributed algorithms]]

[[Category:Graph algorithms]]