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 doesn’t want to enter CS or has a lower priority request, then P sends reply to CS Q  Else P queues Q’s request, replies after exiting CS  When all OTHER processes reply to P, P enters CS

4 Introduction Maekawa’s Algorithm (quorums):  Each process communicates with a limited number of adjacent nodes (quorum).  For every two quorums p and q : p∩q <>Ф  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 P’s request.  After exiting CS, P sends release to all q members, allowing q members to send reply to queued requests

5 Experiments Setup Number of nodes:4-40 (before msgs get swallowed) Duration:  TOSSIM Clock Ticks (neither short nor long)(PART1)  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).

6 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)

7 Billiard Quorums Agrawal, Egecioglu, and Abbadi Assumes system nodes arranged into a 2-D grid. Meakawa’s quorum for N 1/2 XN 1/2 grids are of size 2N 1/2. Billiard Quorums are of size 2 1/2 *N 1/2. Assumes number of nodes N=(q 2 -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,j+j) = R(i,j)-(q-1)/2 R(i+1,j+1)= R(i,j)+(q+1)/2 R(i+1,j-1)= R(i,j)+(q-1)/2 R(i-1,j-1)= R(i,j)-(q+1)/2

8 Results & Analysis Synchronization Delay

9 Results & Analysis Message Complexity Message complexity: RA has significantly higher message complexity when number of nodes >= 6. As Expected. Unified quorum size reduces sensitivity to System size.

10 Results & Analysis Responsiveness According to responsiveness definition:  More nodes to contact  More delay  Expectation: RA has SLOWER responsiveness than MK….

11 Results & Analysis Responsiveness Two major points: - MK has SLOWER responsiveness!!! WHAT WENT WRONG??? -RA‘s responsiveness less sensitive towards system size increase (quorum size effect).

12 Results & Analysis Responsiveness 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 ?!

13 Results & Analysis quorum size and message complexity Larger quorum size  higher message complexity

14 Results & Analysis quorum size and responsiveness Larger quorum size  slower responsiveness

15 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??

16 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.

17 Code SnapShot

18 References D. Agrawal, O. Egecioglu, A. El Abbadi, "Billiard Quorums on the Grid," Information Processsing Letter 64 (1997) TOSSIM User Manual, _tutorial.html, _tutorial.html,2006 D. Gay, Lives, P., and Behren R.,The nesC Language: A Holistic Approach to Networked Embedded Systems, D. Gay, Lives, P., and Behren, R., nesC 1.1 Language Reference Manual David Gay, Philip Levis, David Culler, Eric Brewer, May TinyOs mailing Archive, _tutorial.html