load balancing algorithms
irving cordova
what is heroku?
- platform as a service
- in reality a quick way to deploy apps
- all you need to do is
. git commit git push heroku master
platform as a service
heroku's popularity
it even got acquired
why am i talking about it?
heroku broke
its load balancing
algorithm
changes...
results...
load balancing is hard
what have others done?
it turns out a lot
(unsurprisingly)
Parallel Randomized Load Balancing (1995)
Parallel Randomized Load Balancing (1995)
Parallel Randomized Load Balancing (1995)
Balanced Allocations (1999)
if the balls choose sequentially from d > 2 u.i.r. bins greedily the currently least loaded one, the maximum load is
They prove that this bound is stochastically optimal in the sense that any other strategy to assign the balls majorizes their approach.
Tight Bounds for Parallel Randomized Load Balancing (2011)
Comparison of efficiency
implementing
the algorithm
how to simulate the environment?
- it must be parallel
- must have message passing
- concurrency is hard
actors!
what are actors?
Wikipedia:
The Actor model adopts the philosophy that everything is an actor. This is similar to the everything is an object philosophy used by some object-oriented programming languages, but differs in that object-oriented software is typically executed sequentially, while the Actor model is inherently concurrent.
results
Balls: 300 x producer
Producers: 20
Bins: 20
the naive algorithm
tights bound algorithm
problems
- high cpu usage
- eventually the stack was blown
- tasks take too long to be taken
improving the
tights bound algorithm
the algorithm is already parallel and randomized
sample and modify
this technique can still be used
if the bin is already known to be busy
let's not query it again
in effect the working set is reduced
the stack is still being blown
still being blown....
simplify
final algorithm
-
Set k(1) = 1, i = i, available bins = all bins.
-
Balls contact k(1) bins requesting permission to be placed in them, selected u.i.r from the set of available bins.
-
Each bin admits permission to one of the requesting balls (if it received any) and declines all other requests.
- Removed bins that declined requests from the set of available bins.
- Any ball receiving at least one permission chooses and arbitrary set of the bins to be placed into, informs it, and terminates
- If i>= 10 set k(i) = sqrt ( log ( n )) else set k(i) = k(i) e ^ (k(i)/5)
- If the set of available bins == 0 sleep k(i), restart algorithm
demo
results
compare
where to go from here?
- mathematically model the new approach
- test with extended loads
- have good implementations
questions?
sources
- M. Adler, S. Chakrabarti, M. Mitzenmacher, and L. Rasmussen. Parallel Randomized Load Balancing. In Proc. 27th Symposium on Theory of Computing (STOC), pages 238{247, 1995
- Y. Azar, A. Z. Broder, A. R. Karlin, and E. Upfal. Balanced Allocations. SIAM Journal on Computing, 29(1):180–200, 1999.
-
C Lenzen, R. Wattenhofer, Tight Bounds for Parallel Randomized Load Balancing, STOC'11 June 6-8 2011
images
- http://outre-monde.com/2012/04/12/keep-on-asking-questions/
- http://www.root-image-analysis.org/wp-content/uploads/2011/09/choice.jpg
- http://letitcrash.com/post/29044669086/balancing-workload-across-nodes-with-akka-2
- http://www.essex1.com/pages/paul/Uh-oh-title.gif
- http://spin.atomicobject.com/2011/10/27/generic-memoization-in-c/
- http://www.google.com
- http://3.bp.blogspot.com/-bxj9LtU6bJE/UGl0Idls8_I/AAAAAAAAAFo/ld8Pk5OWGGE/s1600/heroku-logo-white.jpg
- http://www.heroku.com
- http://techcrunch.com/2010/12/08/breaking-salesforce-buys-heroku-for-212-million-in-cash/
- http://rapgenius.com/James-somers-herokus-ugly-secret-lyrics
- http://www.myconfinedspace.com/2010/04/07/go-ask-alice-jefferson-airplane/tell-you-where-to-go-jpg/
load balancing
By Irving Cordova
