1. Corona Linearization Analysis by Dianne Foreback Advanced Operating Systems Kent 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)) 2

3. Corona Linearization Algorithm Example 3 Example taken directly from reference. [1]

4. Linearization Algorithm (2 actions) 4 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) 5 CC \ CP CP atm a't’m’ kes 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 DiameterComponentsNodes per component 10520 10 30156 Remainder of 10 40205 50254 60303 Remainder 10 70352 Remainder 30 80402 Remainder 20 90452 Remainder 10 100 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. 6 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 7 CC \ CP CP abc a'b’c’ def d'e’f’ DiameterComponentsNodes per component 10520 10 30156 Remainder of 10 40205 50254 60303 Remainder 10 70352 Remainder 30 80402 Remainder 20 90452 Remainder 10 100 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) 8

9. Challenges 9 CC \ CP CP amt a'm’t’ ces 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 10

11. References 11 Rizal Mohd Nor, Mikhail Nesterenko, and Christian Scheideler. Corona: A stabilizing deterministic message-passing skip list. In 13 th. International Symposium on Stabilization, Safety and security of Distributed Systems (SSS) pages 356-370, October 2011c. [1]

12. Thank You