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by Dianne Foreback Advanced Operating Systems Kent State University November 2013. Corona Linearization Analysis. Linearization Algorithm Model. Peer-to-peer overlay network of N processes Each peer has a unique ID non-FIFO message passing system - PowerPoint PPT Presentation
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Corona Linearization Analysisby
Dianne Foreback
Advanced Operating SystemsKent State University
November 2013
2
Linearization Algorithm Model
Peer-to-peer overlay network of N processes Each peer has a unique ID non-FIFO message passing system copy-store-forward (stores id of right & left neighbor) all IDs are known Weakly connected channel connectivity graph (CC) and message based
links channel process graph (CP)--locally stored neighboring ids CC/CP--message links
Goal to Linearize the system Consequent processes cnsq(a, b), if ( c : c N : (c < a) (b < c))∀ ∈ ∨
3
Corona Linearization Algorithm Example
Example taken directly from reference.[1]
4
Linearization Algorithm (2 actions)
linearize—remove message from channel and process
timeout—reintroduce p to left and right (omits sending to infinities)
5
Experimental Model I (random strongly conn components)
CC \ CP
CP
a t m
a' t’ m’
k e s
k' e’ s’
100 randomly placed nodes Varying graph diameters ranging from 10 to 100 in increments of 10 Timeout action and Linear action not equally executed
Diameter Components Nodes per component10 5 2020 10 1030 15 6 Remainder of 1040 20 550 25 460 30 3 Remainder 1070 35 2 Remainder 3080 40 2 Remainder 2090 45 2 Remainder 10
100 100 1
6
Results I (random strongly conn components)
Analysis As diameter increases, processing of linear messages decreases (“speed” of linearization
increases) . Same a Results I. As diameter increases, less timeout actions exec (due to more messages in channel). Differs
from Results II.
10 20 30 40 50 60 70 80 90 1000
5000
10000
15000
20000
25000
30000
BothLinearTimeout
Diameter
Actio
ns E
xecu
ted
Measurement: # of actions
7
Experimental Model II (linear strongly conn components)
100 Nodes Varying Graph Diameters ranging from 10 to 100 in increments of 10 Timeout execution
CC \ CP
CP
a b c
a' b’ c’
d e f
d' e’ f’
Diameter Components Nodes per component10 5 2020 10 1030 15 6 Remainder of 1040 20 550 25 460 30 3 Remainder 1070 35 2 Remainder 3080 40 2 Remainder 2090 45 2 Remainder 10
100 100 1
8
Results II (linear strongly conn components)
Analysis As diameter increases, processing of linear messages decreases (“speed” of linearization
increases) . Same a Results I. As diameter increases, more timeout actions exec (due to fewer messages in channel)
10 20 30 40 50 60 70 80 90 1000
1000
2000
3000
4000
5000
6000
7000
Linear Strongly Connected Components
BothLinearTimeout
Diameter
Actio
ns E
xec
Measurement: # of actions
9
Challenges
CC \ CP
CP
a m t
a' m’ t’
c e s
c' e’ s’
Randomly Generate Strongly Connected Components runtime too long with timeout having equal probability as linear action
Strongly connected components do not have evenly distributed nodes Place remaining nodes in one component—no Distribute remaining nodes
Number of runs 10 (results inconclusive) 100 (better results) 1000 (best results)
10
Future Work
Timeout Action—vary the probability of executing the timeout action
Randomize number of processes in each strongly connected component (make
Vary number of nodes
11
References
Rizal Mohd Nor, Mikhail Nesterenko, and Christian Scheideler. Corona: A stabilizing deterministic message-passing skip list. In 13th. International Symposium on Stabilization, Safety and security of Distributed Systems (SSS) pages 356-370, October 2011c.
[1]
Thank You
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