Scalability Issues of Firefly-Based Self-Synchronization in Collective Adaptive Systems

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

Heterogeneous Collective Adaptive Systems Machine-to-Machine systems

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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)


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

excita

tion

flash flash

= T 2T*ti


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 flashflash

threshold


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


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


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


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


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


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


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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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

8 September 2014

Thank you for your attention Questions?

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