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

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

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

Relating CSS, λ, NCSS, wait time

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

Ricart-Agrawala Algorithm (1983)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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