Corona Linearization Analysis by Dianne Foreback Advanced Operating Systems Kent State University November 2013

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

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

Linearization Algorithm (2 actions) 4 linearize—remove message from channel and process timeout—reintroduce p to left and right (omits sending to infinities)

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 Remainder of Remainder Remainder Remainder Remainder

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

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 Remainder of Remainder Remainder Remainder Remainder

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

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)

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

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 , October 2011c. [1]

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