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