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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
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
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?
05-01-2013 3rd BCGL Conference 4/22
Transactions and Network
Network
Incoming
transactions
Committed transactions
Aborted
transactions
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.
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=100
), are also aborted with probability p0
=.01.
 We observed very little dependence of the simulated network measures on p0
.
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.
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)
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=84,6000
 (“one day”).
05-01-2013 3rd BCGL Conference 10/22
Phase Transition Injection Rates
r1
, smaller d
r0
, smaller d
dense
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.
r0,1C ≈A0,1C−2
0,1
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.
05-01-2013 3rd BCGL Conference 13/22
Phase Transition Fault Rate
smaller d
dense
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.
m0C≈
 A−1erf logC−2/− A1
2
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.
05-01-2013 3rd BCGL Conference 16/22
Phase Space Summary (C=4, d=.2)
dielectric
resistive
superconductive
05-01-2013 3rd BCGL Conference 17/22
Equivalence of Excessive Traffic and
Node Failures
dense
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
05-01-2013 3rd BCGL Conference 19/22
A Closer Look at the Resistive Phase
r1
r0
???
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
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!
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

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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=100 ), 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=84,6000  (“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. r0,1C ≈A0,1C−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. m0C≈  A−1erf logC−2/− A1 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