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University of Zagreb, Croatia
Synchronization inspired by fireflies
Iva BojićUniversity of Zagreb, Croatia
Faculty of Electrical Engineering and ComputingDepartment of Telecommunications
Summer School of Science 2012 August 7, 2012, Višnjan, Croatia
University of Zagreb, Croatia
Round of applauseuse your hands and move your body
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University of Zagreb, Croatia
Group of peoplesame rhythmus
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University of Zagreb, Croatia
Heterogeneous Machine-to-Machine Systemssame time
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University of Zagreb, Croatia
Logical questionscan we go home?
April 21, 2023
1. How hard it is to synchronize different clocks?
2. Why do we need time synchronization?
3. How can we achieve time synchronization?
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University of Zagreb, Croatia
Outlinetry to give logical answers…
Research motivation
Biologically-inspired computing
Firefly-inspired synchronization
Results from the laboratory setting
ConclusionApril 21, 2023S3++ 2012 6 of 19
University of Zagreb, Croatia
Computer clockhow does it work?
How is this possible?
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Quartz crystals are manufactured for frequencies from a few tens of kHz to tens of MHz
A clock is an electronic device that counts oscillations in a crystal at a particular frequency
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University of Zagreb, Croatia
Problemno global notion of time
In distributed systems each
node has its own clock and
its own notion of time
In practice these clocks
drift apart accumulating
errors over time (1 second
every 11 days)
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University of Zagreb, Croatia
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)
Need for (speed?)time
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Frequency division multiple access Time division multiple access
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University of Zagreb, Croatia
Time synchronizationdifferent algorithms
Time synchronization provides a common time scale for local clocks of nodes in distributed systems
B. Sundararaman, U. Buy and A. D. Kshemkalyani: Clock synchronization for wireless sensor networks: A Survey, Ad Hoc Networks 3, pp. 281-323 (2005)
April 21, 2023S3++ 2012 10 of 19
University of Zagreb, Croatia
Biologically-inspired computingbiology applied in distributed systems
Nature is a enormous and a highly complex system
processes are done without any centralized control
processes are self-sustainable and self-organized
Self-organization is a process where some form of global
order arises out of the local interactions between the
components of an initially disordered system
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Self-synchronizationin nature
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a) fireflies b) neurons c) heart cells
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Self-synchronizationin humans
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University of Zagreb, Croatia
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 modelone firefly
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0
1
t
xi
threshold
flash flash
= T 2T*ti
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University of Zagreb, Croatia
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 modeltwo fireflies
April 21, 2023
0
1
t
xi
threshold
flash flash
T 2T
0
1
t
xj
T 2T
εij
ti*
tj*
εij
εji εji
flash flashflashthreshold
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University of Zagreb, Croatia
Pulse coupled oscillators model assumptions
no oscillators with a faultyfaulty behavior that desynchronizes the network
oscillators are connected in a fully-connected networkfully-connected network
oscillators cannot join or leave the network nor change their positions in the network (i.e. no mobilitymobility)
oscillators are the same (i.e. have same frequenciessame frequencies)
no delaysdelays in the message exchange among oscillators
Pulse coupled oscillators modellimitations
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We embedded a cryptographic mechanism in the pulse coupled oscillators model to ensure robustness
We used the logical operation exclusive disjunction (i.e. XOR)
provides protection from an attack
does not have a negative effect on the time needed for synchronization
Robustnesswith oscillators with faulty behavior
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Resultsrobustness
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Conclusionscan we go home? NOW WE CAN!!!!!!!!!!!!!!!!!!!
April 21, 2023
1. How hard it is to synchronize different clocks?
2. Why do we need time synchronization?
3. How can we achieve time synchronization?
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University of Zagreb, Croatia
Questions?
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University of Zagreb, Croatia
Summationexclusive disjunction
Input Output
A B
0 0 0
0 1 1
1 0 1
1 1 0
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