Performance of Fair Distributed Mutual Exclusion Algorithms

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Performance of Fair Distributed Mutual Exclusion
Algorithms Kandarp Jani Ajay D.
Kshemkalyani University of Illinois at Chicago
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Presentation Plan

• Introduction to fair distributed mutual exclusion
• Previous fair algorithms
• Lamport 78 3(n-1) msgs/CS
• Ricart-Agrawala (RA) 81 2(n-1) msgs/CS
• Lodha-Kshemkalyani (LK) TPDS00 n, 2n-1
  msgs/CS
• Simulation expts study improvement of LK over RA
• Conclusion LK has fewer messages, lower
  waiting time, w/o compromising message size or
  other metrics

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Model and Metrics

• Asynchronous distributed message-passing system
• d time for a message hop
• Metrics for mutual exclusion algorithms
• number of messages/CS
• response time O(2dcss)
• synchronization delay O(d)
• waiting time O(2d)
• throughput 1/ response time
• fairness
• message size O(1)
• Single request outstanding at a time

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Relating CSS, ?, NCSS, wait time
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Fair Mutual Exclusion

• Popular definition of fairness requests must be
  answered in the order of their causality-based
  scalar clock values
• If clk(Req1) lt clk(Req2)
• Req1 has higher priority
• If clk(Req1) clk(Req2)
• Use requestors PIDs as tie-breaker (i.e., define
  a lexicographic order)
• Only Lamport, RA, and LK algorithms are fair

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Ricart-Agrawala Algorithm (1983)
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LK Algorithm (messages)

• REQUEST, REPLY, FLUSH messages
• REQUEST contains timestamp of request
• REPLY, FLUSH contain timestamp of last completed
  CS access by sender of message
• Local Request Queue (LRQ) at each process, LRQ
  tracks concurrent requests

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LK Algorithm (concurrency set)

• Message overhead 2n - Cset msgs/CS
• (n-1) REQUEST messages
• n - Cset REPLY messages
• 1 FLUSH message

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LK algorithm (REQUEST)

• Multiple uses of REQUEST
• to seek permission to enter CS
• if requesting concurrently, the REQUEST acts as
  a REPLY from the lower priority requestor (i) to
  the higher priority requester (j)
• j remembers is request in its LRQ
• i remembers js request in its LRQ
• After j finishes CS, i will eventually get
  logical permission from j via a chain of REPLY
  and FLUSH messages

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LK algorithm (REPLY)

• REPLY message has timestamp of last completed CS
  request of sender of REPLY
• Multiple uses of REPLY
• Sender gives individual permission
• Sender gives collective permission on behalf of
  all processes with higher priority requests
• It acts as multiple logical reply messages

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LK algorithm (FLUSH)

• FLUSH sent after exiting CS, to the concurrently
  requesting process with the next highest priority
  
• FLUSH timestamped w/timestamp of just completed
  CS request of sender of FLUSH
• Multiple uses of FLUSH
• Sender gives individual permission
• Sender gives collective permission on behalf of
  all processes with higher priority requests
• It acts as multiple logical reply messages

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Simulation Parameters (on OPNET)

• Input parameters
• Number of processes n (10-40)
• Inter-request time exp. Distributed, mean ?
• (0.1 ms to 10 s)
• Critical Section Sitting time exp. distributed,
  mean CSS (0.1 microsec to 10 millisec)
• Propagation delay D, implicitly modeled in CSS
• Output parameters
• Normalized message complexity M
• Waiting time T

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Experiments

• Experiment 1
• M f(?), for multiple settings of (n, CSS)
• Experiment 2
• M f(n), for multiple settings of (CSS, ?)
• Experiment 3
• T f(n), for multiple settings of (CSS, ?)
• compared LK and RA algorithms

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Impact of ? on Msg. Ovhd (Expt 1, n10)
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Impact of ? on Msg. Ovhd (Expt 1, n20)
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Impact of ? on Msg. Ovhd (Expt 1, n30)
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Impact of ? on Msg. Ovhd (Expt 1, n40)
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Impact of n on Msg. Ovhd (Expt 2, CSS0.1
microsec)
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Impact of n on Msg. Ovhd (Expt 2, CSS1 microsec)
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Impact of n on Msg. Ovhd (Expt 2, CSS0.1 ms)
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Impact of n on Msg. Ovhd (Expt 2, CSS1 ms)
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Impact of n on Wait Time (Expt 3, CSS1 microsec)
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Impact of n on Wait Time (Expt 3, CSS0.1
microsec)
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Conclusions

• LK is the best known fair mutex algorithm
• LK outperforms Ricart-Agrawala i.t.o.
• Number of messages/CS
• Waiting time/CS
• without compromising message size or any other
  metric
• Studied behaviour of LK using simulations under a
  wide range of conditions