Presentation by Iva Bojic at the 2nd FoCAS Workshop on the Fundamentals of Collective Adaptive Systems at SASO 2014.

1. Scalability Issues of Firefly-Based
Self-Synchronization in Collective Adaptive Systems
Iva Bojic*, Tomislav Lipic and Mario Kusek
*Department of Urban Studies and Planning
Massachusetts Institute of Technology
Cambridge, MA, US
FoCAS 2014
September 8, 2014, London, UK

2. Heterogeneous Collective Adaptive Systems Machine-to-Machine systems
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3. Problem no global notion of time
In distributed systems each node has its own internal clock and its own notion of time
In practice these clocks drift apart
accumulating errors over time
Global notion of time is prerequisite for:
common resource sharing (e.g., channel)
depend events tracking (e.g., consistency
of distributed databases)
simultaneous events detection (e.g., data collection)
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4.  If oscillators are not coupled, their state variables change
following only their own excitations
 xi denotes state variable
xi(t) = fi(t)
 ti
* denotes a moment when
i-th oscillator flashes
R. E. Mirollo and S. H. Strogatz. Synchronization of pulse-coupled biological oscillators. SIAM J. Appl. Math. 50: pp.1645-1662 (1990)
Pulse coupled oscillators model
one firefly
0
1
t
xi
threshold
excitation
flash flash
= T 2T * ti
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5.  If oscillators are coupled
 state variable xi is adjusted upon the
reception of flashes from the others
 xi(t) = fi(t) + ϵij gij(t)
 ϵij is a coupling constant
 gij(t) is a coupling function between
i-th and j-th oscillators
R. E. Mirollo and S. H. Strogatz. Synchronization of pulse-coupled biological oscillators. SIAM J. Appl. Math. 50: pp.1645-1662 (1990)
Pulse coupled oscillators model
two fireflies
0
1
t
xi
threshold
flash flash
T 2T
0
1
t
xj
T 2T
εij
ti *
tj *
εij
εji εji
flash flash flash
threshold
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6. Pulse coupled oscillators model assumptions
oscillators are the same (i.e., have same frequencies)
oscillators are connected in a fully-connected network
no delays in the message exchange among oscillators
no oscillators with a faulty behavior that desynchronizes the network
oscillators cannot join or leave the network nor change their positions in the network (i.e., no mobility)
Pulse coupled oscillators model limitations
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7. Synchrony – ”firing” in unison
Phase locking – differences between state variable values are constant and nonzero
Frequency locking – differences between state variable values are not constant because of frequency fluctuations
Forms of time synchronization synchrony, phase locking and frequency locking
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8. Rate of successful synchronization outcomes
synchronization precision is acceptable
Time to synchronization
time needed to achieve synchronization of desired precision
Network traffic
number of messages exchanged during synchronization process
The goal of this paper is to reduce network traffic
Frequency locking time to synchronization and network traffic
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9. Results of simulations
all-to-all connectivity is not the best one considering both time to synchronization and network traffic [1, 2]
smaller transmission radius leads to lower energy consumption [3]
Constraints in testbeds
calculation and memory costs of finding neighbors
time cost of sending multicast messages [1] I. Bojic, et al. “A Self-Optimizing Mobile Network: Auto-Tuning the Network with Firefly-Synchronized Agents”, Information Sciences, vol. 182, no. 1, pp. 77– 92 (2012) [2] I. Bojic and M. Kusek, “Comparing Different Overlay Topologies and Metrics in Pulse-Coupled Multi-Agent Systems,” in Proceedings of the 6th KES International Conference on Agent and Multi-Agent Systems: Technologies and Applications, 2012, pp. 464–473 [3] Y. Niu, et a. “Selective Pulse Coupling Synchronicity for Sensor Network,” in Proceedings of the 2nd International Conference on Sensor Technologies and Applications, 2008, pp. 123–128
Network traffic reduction overlay network topologies
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10. Selective coupling implemented on the sender side
at the end of each synchronization cycle before sending the synchronization messages
Proposed solution
mechanism for selective coupling implemented on the sender side
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11. Selective coupling implemented on the receiver side
selective coupling leads to faster synchronization convergence [4]
halving the probability to send synchronization messages meant doubling time to synchronization [5]
selective reduction of transmitted information saves energy and improves the convergence rate of desired synchronization precision [6] [4] Y. Niu, et a. “Selective Pulse Coupling Synchronicity for Sensor Network,” in Proceedings of the 2nd International Conference on Sensor Technologies and Applications, 2008, pp. 123–128. [5] I. Scholtes, J. Botev, M. Esch, and P. Sturm, “Epidemic Self-Synchronization in Complex Networks of Kuramoto Oscillators,” Advances in Complex Systems, vol. 13, no. 1, pp. 33–58, 2010 [6] J. Degesys, P. Basu, and J. Redi, “Synchronization of Strongly Pulse-Coupled Oscillators with Refractory Periods and Random Medium Access,” in Proceedings of the ACM Symposium on Applied Computing, 2008, pp. 1976–1980
Related work
mechanism for selective coupling implemented on the receiver side
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12. Multi-Agent Simulator Of Neighborhoods
Graphs generated by Watts/Strogatz model [7]
reconnection probability = 0.5
number of nearest neighbors in initial ring lattice = 10
Future work – graphs generated by Barabasi/Albert model
synchronization benefits from networks in which high degree devices are connected to low degree devices [8] [7] I. Scholtes, J. Botev, M. Esch, and P. Sturm, “Epidemic Self-Synchronization in Complex Networks of Kuramoto Oscillators,” Advances in Complex Systems, vol. 13, no. 1, pp. 33–58, 2010 [8] M. di Bernardo, F. Garofalo, and F. Sorrentino, “Effects of Degree Correlation on the Synchronization of Networks of Oscillators,” International Journal of Bifurcation and Chaos, vol. 17, no. 10, pp. 3499–3506, 2007.
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Simulation environment
mechanism for selective coupling implemented on the receiver side
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Simulation results
relative difference of exchanged messages and time to synchronization
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14. M2M systems with 10000 devices (0.1 for thresholdSyn and 0.3 for thresholdProbability)
2.5 million (i.e., 52 %) less messages are exchanged
around 1300 (i.e., 53 %) less steps are needed to achieve synchronization
indications that this mechanism can improve the synchronization rate
Open issues
lack of the practical implementation in real-world environments
can Watts/Strogatz model represent heterogeneous M2M systems?
communication latency and different distributions of device frequencies
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Conclusions and open issues
mechanism for selective coupling implemented on the receiver side
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15. Thank you for your attention Questions?
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