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

2. 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) TPDS‘00: [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

3. 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: Ω(2d+css)
synchronization delay: Ω(d)
waiting time: Ω(2d)
throughput: 1/ response time
fairness
message size: O(1)
Single request outstanding at a time

4. Relating CSS, λ, NCSS, wait time

5. Fair Mutual Exclusion
Popular definition of fairness: requests must be answered in the order of their causality- based scalar clock values
If clk(Req1) < 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

6. Ricart-Agrawala Algorithm (1983)

7. 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

8. LK Algorithm (concurrency set)
Message overhead: 2n - |Cset| msgs/CS
(n-1) REQUEST messages
n - |Cset| REPLY messages
1 FLUSH message

9. 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 i’s request in its LRQ
i remembers j’s request in its LRQ
After j finishes CS, i will eventually get logical permission from j via a chain of REPLY and FLUSH messages

10. 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

11. 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

12. Simulation Parameters (on OPNET)
Input parameters:
Number of processes : n (10-40)
Inter-request time: exp. Distributed, mean λ
(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

13. Experiments Experiment 1: Experiment 2: Experiment 3:
M = f(λ), for multiple settings of (n, CSS)
Experiment 2:
M = f(n), for multiple settings of (CSS, λ)
Experiment 3:
T = f(n), for multiple settings of (CSS, λ)
compared LK and RA algorithms

14. Impact of λ on Msg. Ovhd (Expt 1, n=10)

15. Impact of λ on Msg. Ovhd (Expt 1, n=20)

16. Impact of λ on Msg. Ovhd (Expt 1, n=30)

17. Impact of λ on Msg. Ovhd (Expt 1, n=40)

18. Impact of n on Msg. Ovhd (Expt 2, CSS=0.1 microsec)

19. Impact of n on Msg. Ovhd (Expt 2, CSS=1 microsec)

20. Impact of n on Msg. Ovhd (Expt 2, CSS=0.1 ms)

21. Impact of n on Msg. Ovhd (Expt 2, CSS=1 ms)

22. Impact of n on Wait Time (Expt 3, CSS=1 microsec)

23. Impact of n on Wait Time (Expt 3, CSS=0.1 microsec)

24. 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