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05-01-2013 3rd BCGL Conference 1/22Resilience in Transaction-OrientedNetworksDmitry Zinoviev*, Hamid Benbrahim,Greta Meszo...
05-01-2013 3rd BCGL Conference 2/22Outline Transaction­oriented networks Network model and its interpretations Simulati...
05-01-2013 3rd BCGL Conference 3/22Transaction-Oriented Networks Used to execute distributed transactions (compound opera...
05-01-2013 3rd BCGL Conference 4/22Transactions and NetworkNetworkIncomingtransactionsCommitted transactionsAbortedtransac...
05-01-2013 3rd BCGL Conference 5/22Network Model Overview Random Erdös–Rényi network, N=1,600 identical nodes representin...
05-01-2013 3rd BCGL Conference 6/22Opportunistic Routing The node for the next subtransaction is chosen uniformly at rand...
05-01-2013 3rd BCGL Conference 7/22Node Shutdown When a node is overloaded (load > C), it shuts down. A node may fail ra...
05-01-2013 3rd BCGL Conference 8/22Simulation Framework Custom­built network simulator in C++ In each experiment, the ne...
05-01-2013 3rd BCGL Conference 9/22Failing by Overloading Start with a fully functional network. Gradually increase the ...
05-01-2013 3rd BCGL Conference 10/22Phase Transition Injection Ratesr1, smaller dr0, smaller ddense
05-01-2013 3rd BCGL Conference 11/22Quadratic Amplification Both r0(C) and r1(C) can be approximated by a power function:...
05-01-2013 3rd BCGL Conference 12/22Failing by Internal Faults Start with a fully functional network. Gradually increase...
05-01-2013 3rd BCGL Conference 13/22Phase Transition Fault Ratesmaller ddense
05-01-2013 3rd BCGL Conference 14/22Faulty Nodes Effect Estimation of m0: For the dense networks, A tends to [0...0.23]...
05-01-2013 3rd BCGL Conference 15/22Failing by Overloading and InternalFaults Start with a fully functional network. Gra...
05-01-2013 3rd BCGL Conference 16/22Phase Space Summary (C=4, d=.2)dielectricresistivesuperconductive
05-01-2013 3rd BCGL Conference 17/22Equivalence of Excessive Traffic andNode Failuresdense
05-01-2013 3rd BCGL Conference 18/22Equivalence of Excessive Traffic andNode Failures To a first approximation, the relat...
05-01-2013 3rd BCGL Conference 19/22A Closer Look at the Resistive Phaser1r0???
05-01-2013 3rd BCGL Conference 20/22What Happens around the “knee”? The “knee” is visible only in sparse networks Networ...
05-01-2013 3rd BCGL Conference 21/22How Many Nodes Are in the GC? Percentage of faulty (red) and healthy (blue) nodes in ...
05-01-2013 3rd BCGL Conference 22/22Conclusion Random transactional networks can stay in four phases of interest: “superc...
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Resilience in Transactional Networks

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Resilience in Transactional Networks

  1. 1. 05-01-2013 3rd BCGL Conference 1/22Resilience in Transaction-OrientedNetworksDmitry Zinoviev*, Hamid Benbrahim,Greta Meszoely+, Dan Stefanescu**Mathematics and Computer Science Department+Sawyer School of ManagementSuffolk University, Boston
  2. 2. 05-01-2013 3rd BCGL Conference 2/22Outline Transaction­oriented networks Network model and its interpretations Simulation results: Dense and sparse networks Throughput amplification Equivalence of excessive traffic and faulty nodes Network as a four­phase matter Conclusion and future work
  3. 3. 05-01-2013 3rd BCGL Conference 3/22Transaction-Oriented Networks Used to execute distributed transactions (compound operations that succeed or fail atomically) Interpretations: Distributed database transactions (original, HPC­related interpretation) Financial transactions (e.g., loans) Transportation (e.g., multi­leg flights) How resilient are these networks to externally and internally induced failures?
  4. 4. 05-01-2013 3rd BCGL Conference 4/22Transactions and NetworkNetworkIncomingtransactionsCommitted transactionsAbortedtransactions
  5. 5. 05-01-2013 3rd BCGL Conference 5/22Network Model Overview Random Erdös–Rényi network, N=1,600 identical nodes representing network hosts, density d. Each node can simultaneously execute up to C almost independent subtransactions. Each subtransaction takes constant time 0 to complete. The network is simulated for the duration of S0. Each node can be used for injecting transactions into the network and for terminating transactions. Transactions are injected uniformly across the network. The delays between subsequent transactions are drawn from the exponential distribution E(1/r). Each transaction has L=N(10,4) subtransactions.
  6. 6. 05-01-2013 3rd BCGL Conference 6/22Opportunistic Routing The node for the next subtransaction is chosen uniformly at random from all neighbors of the current node. If the next node is disabled, then another neighbor is chosen. If all neighbors are disabled, the subtransaction is aborted, and the master transaction rolls back. If a transaction is aborted, all other transactions that crossed path with it in the past T time units (T=100), are also aborted with probability p0=.01. We observed very little dependence of the simulated network measures on p0.
  7. 7. 05-01-2013 3rd BCGL Conference 7/22Node Shutdown When a node is overloaded (load > C), it shuts down. A node may fail randomly after an initial delay drawn from the exponential distribution E(Tf). Once disabled, a node is not restarted. All subtransactions currently executed at a disabled node are aborted.
  8. 8. 05-01-2013 3rd BCGL Conference 8/22Simulation Framework Custom­built network simulator in C++ In each experiment, the network has been simulated for a variety of combinations of node capacities and densities (C, d): d  {0.01, 0.011, 0.015, 0.025, 0.04, 0.055, 0.075, 0.1, 0.2, 0.3, 0.5, 0.6, 0.75, 0.85, 0.99} C  {2, 3, 4, ... 22} Red color indicates sparse networks (they behave diferently from the dense networks)
  9. 9. 05-01-2013 3rd BCGL Conference 9/22Failing by Overloading Start with a fully functional network. Gradually increase the injection rate from 0 to r0 until at least 10­6 of all transactions abort (superconductive mode ⇒ resistive mode). The fraction of aborted transactions monotonically increases, until at some rate r1  the network chokes (resistive mode ⇒ dielectric mode).  Define 0 = r0 / r1. r0 and r1 slightly depend on the simulation running time. Our results have been obtained for S=84,6000 (“one day”).
  10. 10. 05-01-2013 3rd BCGL Conference 10/22Phase Transition Injection Ratesr1, smaller dr0, smaller ddense
  11. 11. 05-01-2013 3rd BCGL Conference 11/22Quadratic Amplification Both r0(C) and r1(C) can be approximated by a power function: The exponents i for the dense networks are ~1.7 and ~2.1, respectively. Both is tend to 1 as d tends to 0. The mantissas Ai for the dense networks are ~0.7 and ~2.8, respectively. Both Ai increase and possibly diverge as d tends to 0. Doubling node capacity almost quadruples the throughput.r0,1C ≈A0,1C−20,1
  12. 12. 05-01-2013 3rd BCGL Conference 12/22Failing by Internal Faults Start with a fully functional network. Gradually increase the injection rate from 0 to r0. At the fixed injection rate, fail random nodes after random delays.  Let m0 be the smallest fraction of failed nodes that causes the network to choke.
  13. 13. 05-01-2013 3rd BCGL Conference 13/22Phase Transition Fault Ratesmaller ddense
  14. 14. 05-01-2013 3rd BCGL Conference 14/22Faulty Nodes Effect Estimation of m0: For the dense networks, A tends to [0...0.23] That is, it takes no more 23% of internally faulty nodes to choke a dense network with infinite buffer space in the presence of the highest superconductive injection rate.m0C≈ A−1erf logC−2/− A12
  15. 15. 05-01-2013 3rd BCGL Conference 15/22Failing by Overloading and InternalFaults Start with a fully functional network. Gradually increase the injection rate from 0 to r () and simultaneously fail random nodes after random delays, until the network chokes.
  16. 16. 05-01-2013 3rd BCGL Conference 16/22Phase Space Summary (C=4, d=.2)dielectricresistivesuperconductive
  17. 17. 05-01-2013 3rd BCGL Conference 17/22Equivalence of Excessive Traffic andNode Failuresdense
  18. 18. 05-01-2013 3rd BCGL Conference 18/22Equivalence of Excessive Traffic andNode Failures To a first approximation, the relationship between the network resilience parameters 0 and m0 is almost linear, with the slope of ­1 Tolerating additional superconductive traffic 0is equivalent to disabling extra network nodes m0 due to internal faults:≈−m0
  19. 19. 05-01-2013 3rd BCGL Conference 19/22A Closer Look at the Resistive Phaser1r0???
  20. 20. 05-01-2013 3rd BCGL Conference 20/22What Happens around the “knee”? The “knee” is visible only in sparse networks Network state at the end of the simulation run: red circles correspond to faulty nodes, cyan circles—to healthy nodes
  21. 21. 05-01-2013 3rd BCGL Conference 21/22How Many Nodes Are in the GC? Percentage of faulty (red) and healthy (blue) nodes in the respective giant component for various rs The phase transition happens when all faulty nodes join the giant component Two “resistive” phases: “resistive­A” (truly “resistive”) and “resistive­B” (“resistive­dielectric”)0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.50%20%40%60%80%100%rAll faulty nodes join the giant component!
  22. 22. 05-01-2013 3rd BCGL Conference 22/22Conclusion Random transactional networks can stay in four phases of interest: “superconductive” (no transactions fail), “resistive­A and ­B (some transactions fail), and “dielectric” (all transactions fail) Injection rates associated with the phase transitions, scale almost quadratically with respect to the node capacity At the resistive­to­dielectric phase transition, the effects of excessive network load and internal, spontaneous, and irreparable node faults are equivalent and almost perfectly anticorrelated The phase transition between two “resistive” phases can be attributed to the evolution of the giant component of faulty nodes

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