Resilience in Transactional Networks
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This document summarizes a presentation on the resilience of transaction-oriented networks. It describes a model of a random transaction network and simulations examining how the network's performance is affected by node capacity, density, and failures from overloading or faulty nodes. The key findings are that the network exhibits four phases depending on traffic load and failures, and that doubling node capacity can nearly quadruple throughput. Additionally, excessive traffic and node failures have an almost linear and equivalent impact on resilience.
![05-01-2013 3rd BCGL Conference 14/22
Faulty 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.
m0C≈
A−1erf logC−2/− A1
2](https://image.slidesharecdn.com/05-2013-130430230616-phpapp02/85/Resilience-in-Transactional-Networks-14-320.jpg)
Resilience in Transactional Networks
- 1. 05-01-2013 3rd BCGL Conference 1/22 Resilience in Transaction-Oriented Networks Dmitry Zinoviev*, Hamid Benbrahim, Greta Meszoely+ , Dan Stefanescu* *Mathematics and Computer Science Department + Sawyer School of Management Suffolk University, Boston
- 2. 05-01-2013 3rd BCGL Conference 2/22 Outline 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. 05-01-2013 3rd BCGL Conference 3/22 Transaction-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. 05-01-2013 3rd BCGL Conference 4/22 Transactions and Network Network Incoming transactions Committed transactions Aborted transactions
- 5. 05-01-2013 3rd BCGL Conference 5/22 Network 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. 05-01-2013 3rd BCGL Conference 6/22 Opportunistic 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=100 ), are also aborted with probability p0 =.01. We observed very little dependence of the simulated network measures on p0 .
- 7. 05-01-2013 3rd BCGL Conference 7/22 Node 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. 05-01-2013 3rd BCGL Conference 8/22 Simulation 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. 05-01-2013 3rd BCGL Conference 9/22 Failing 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=84,6000 (“one day”).
- 10. 05-01-2013 3rd BCGL Conference 10/22 Phase Transition Injection Rates r1 , smaller d r0 , smaller d dense
- 11. 05-01-2013 3rd BCGL Conference 11/22 Quadratic 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 i 's 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. r0,1C ≈A0,1C−2 0,1
- 12. 05-01-2013 3rd BCGL Conference 12/22 Failing 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. 05-01-2013 3rd BCGL Conference 13/22 Phase Transition Fault Rate smaller d dense
- 14. 05-01-2013 3rd BCGL Conference 14/22 Faulty 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. m0C≈ A−1erf logC−2/− A1 2
- 15. 05-01-2013 3rd BCGL Conference 15/22 Failing by Overloading and Internal Faults 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. 05-01-2013 3rd BCGL Conference 16/22 Phase Space Summary (C=4, d=.2) dielectric resistive superconductive
- 17. 05-01-2013 3rd BCGL Conference 17/22 Equivalence of Excessive Traffic and Node Failures dense
- 18. 05-01-2013 3rd BCGL Conference 18/22 Equivalence of Excessive Traffic and Node 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 0 is equivalent to disabling extra network nodes m0 due to internal faults: ≈−m0
- 19. 05-01-2013 3rd BCGL Conference 19/22 A Closer Look at the Resistive Phase r1 r0 ???
- 20. 05-01-2013 3rd BCGL Conference 20/22 What 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. 05-01-2013 3rd BCGL Conference 21/22 How Many Nodes Are in the GC? Percentage of faulty (red) and healthy (blue) nodes in the respective giant component for various r's The phase transition happens when all faulty nodes join the giant component Two “resistive” phases: “resistiveA” (truly “resistive”) and “resistiveB” (“resistive dielectric”) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 0% 20% 40% 60% 80% 100% r All faulty nodes join the giant component!
- 22. 05-01-2013 3rd BCGL Conference 22/22 Conclusion 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