Permissionbased Distributed Mutual Exclusion: RicartAgrawala

1
Permission-based Distributed Mutual Exclusion
Ricart-Agrawala Maekawa Algorithms
By Sherenaz W. Al-Haj Baddar
2
Outline

• Introduction
• Experiments Setup
• Results and Analysis
• Further Elaboration
• Code snapshots features problems
• Conclusion
• References

3
Introduction

• Permission-based DMX
• Accessing Critical Section (CS), via gaining
  permission from some(or all) other processes in
  the system.
• Ricart-Agrawala Algorithm(RA)
• Process requires permission from all OTHER
  processes in the system.
• If a process P receives a request to enter CS
  from process Q, while it doesnt want to enter CS
  or has a lower priority request, then P sends
  reply to CS Q
• Else
• P queues Qs request, replies after exiting
  CS
• When all OTHER processes reply to P, P enters CS

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Introduction

• Maekawas Algorithm (quorums)
• Each process communicates with a limited number
  of adjacent nodes (quorum).
• For every two quorums p and q pnq ltgt?
• When P wants to enter CS it gains permission from
  all q members
• Quorum member Q, has one permission to give, if
  given, then queue Ps request.
• After exiting CS, P sends release to all q
  members, allowing q members to send reply to
  queued requests

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Experiments Setup

• Number of nodes4-40 (before msgs get swallowed)
• Duration
• 30000 TOSSIM Clock Ticks (neither short nor
  long)(PART1)
• 50000-130000 TOSSIM Clock Ticks (neither short
  nor long)(PART2)
• Metrics considered
• Synchronization delay
• Message complexity
• Responsiveness the amount of time that elapses
  since P requests CS until it enters it for the
  first time.
• record system time (getLow32(),
  SimpleTimeInterface), after initiating request to
  CS
• record system time just after entering CS
• accumulate the difference in some global
  variable.
• Assuming LL (msgs being swallowed)
• Delay Timers were used to control the frequency
  and duration of accessing CS (basically, every
  1024 Tick).

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Experiments Setup

• RA algorithm
• Fully connected topology CS requests
  broadcasted, replies unicasted
• MK algorithm
• Assumes a connected topology(as long as quorum
  members can access each other)
• In TOSSIM the underlying Topology is Fully
  Connected
• Quorum formation Using Billiard Quorums
• Number of nodes Quorum size
• 4,6,8 ? 3
• 10,12 ? 5
• 24,28 ? 7
• 34,40 ? 9
• With elaboration on the relationship between
  quorum size and msg complexity responsiveness)

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Billiard QuorumsAgrawal, Egecioglu, and Abbadi

• Assumes system nodes arranged into a 2-D grid.
• Meakawas quorum for N1/2XN1/2 grids are of size
  2N1/2.
• Billiard Quorums are of size 21/2 N1/2.
• Assumes number of nodes N(q2-1)/2 and assumes
  that q is odd (maintain symmetry).
• Let P be located in cell(i,j), and denoted by
  R(i,j) then its quorum members can be found along
  the lines
• R(i-1,jj) R(i,j)-(q-1)/2
• R(i1,j1) R(i,j)(q1)/2
• R(i1,j-1) R(i,j)(q-1)/2
• R(i-1,j-1) R(i,j)-(q1)/2

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Results AnalysisSynchronization Delay
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Results AnalysisMessage Complexity

• Message complexity RA has significantly higher
  message complexity when number of nodes gt 6. As
  Expected.
• Unified quorum size reduces sensitivity to System
  size.

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Results AnalysisResponsiveness

• According to responsiveness definition
• More nodes to contact ? More delay
• Expectation RA has SLOWER responsiveness than
  MK.

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Results AnalysisResponsiveness
Two major points - MK has SLOWER
responsiveness!!! WHAT WENT WRONG??? -RAs
responsiveness less sensitive towards system size
increase (quorum size effect).
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Results AnalysisResponsiveness

• The unexpected behavior is due to the nature of
  the implementation environment.
• To communicate with everybody else, in RA, mote
  sends one sndMsg.send to the broadcast address,
  if returns true, then responsiveness timing
  starts.
• To communicate with your quorum Q, you are
  supposed to send a unicast message to each quorum
  member, after all contacted successfully (request
  initiated successfully), then responsiveness
  timing starts.
• To overcome this anomaly
• Start measuring responsiveness after contacting
  first member (semantics not exact).
• Broadcast requests, ignore request when
  necessary(back to RA!!
• Use a platform that supports multicast ?!

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Results Analysisquorum size and message
complexity

• Larger quorum size? higher message complexity

14
Results Analysisquorum size and responsiveness

• Larger quorum size ? slower responsiveness

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Further Elaboration

• Overcome message loss due to high contention to
  be able to measure pure HL.
• Implement the DL free version of MK (extra msg
  loss overhead).
• Investigate the issue of assigning quorum members
  such that DL possibility is reduced (i.e. NO DL
  implementation).
• Extend these two algorithms for Multi-hop
  networks??
• Extend these two algorithms for generalized DMX
  scenarios??

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Conclusion

• Permission based DMX induce relatively high
  message complexity.
• Permission based DMX induce relatively low
  synchronization overhead.
• Permission based DMX exhibit less sensitivity to
  system load.
• RA has higher message complexity and lower
  synchronization delay than MK
• RA is supposed to have slower responsiveness than
  MK. However, the implementation platform may
  enforce different sort of relations.
• Larger quorum size ? slower responsiveness and
  higher msg complexity.

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Code SnapShot
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References

• D. Agrawal, O. Egecioglu, A. El Abbadi, "Billiard
  Quorums on the Grid," Information Processsing
  Letter 64 (1997) 9-16.
• TOSSIM User Manual, http//deneb.cs.kent.edu/mikh
  ail/classes/aos.f06/aos_tos_tutorial/tos_tutorial.
  html,2006.
• D. Gay, Lives, P., and Behren R.,The nesC
  Language A Holistic Approach to Networked
  Embedded Systems, http//nescc.sourceforge.net.
• D. Gay, Lives, P., and Behren, R., nesC 1.1
  Language Reference Manual David Gay, Philip
  Levis, David Culler, Eric Brewer, May 2003.
• TinyOs mailing Archive, http//deneb.cs.kent.edu/
  mikhail/classes/aos.f06/aos_tos_tutorial/tos_tutor
  ial.html