Energy Analysis for ProFID

1. Energy Analysis for ProFID TUBITAK-COST Research Project Title: Energy efficiency in peer-to-peer network services Principle Investigator: Dr. ÖznurÖzkasap Ender Demirkaya, ErtemEsiner, BurakÖzaydın

2. There are two types of approaches, centralized approaches and gossip-based approaches • Energy consumption • Dynamic entrance of peers in P2P swarm • Reliability Approaches

3. Protocol for Frequent Item Set Discovery • Gossip-Based • Using pairwise averaging function which is novel in frequent item set discovery problem. State Machine ProFID description

4. User DefinedT(Threshold): is the value that we use to determine if the item is frequent or not. This value is defined by user. • Protocol relatedfanout: is the number of neighbors to whom gossip message is sent at each round.mms (maximum message size): maximum gossip message size.ui (unique item): This helps us for network size estimation. • Convergence relatedconvLimit: After one peer thinks that it converged, it must count up to convLimit. If in one round the condition is not satisfied the counter is reset.e (epsilon): value to determine if the peer is converged or not. Parameters

5. Parameter Analysis

6. T: threshold has no effect because it is used at the end of whole process (i.e. when all peers reached convLimit). It has no effect to decrease number of rounds or computation load, therefore, to energy consumption. • Fanout: has inverse proportion to number of rounds: • (Fanout, # of rounds): (1:2:3:4,16:8:6:3), (1:2:3:4,25:12:8:4). Moreover, fanout has a direct proportion to number of messages that a peer sends & receives. Parameters, in terms of energy

7. mms: mms has no effect to the energy consumption because while it increases the energy consumption in one round, it decreases the number of rounds. • ui: unique item is to check Ɛ condition, it has no effect. • convLimit: higher values of convergence limit leads to more rounds to be performed to calculate average. Since more rounds require energy, it has a direct proportion. Parameters, in terms of energycont.

8. Ɛ: epsilon is to define the accuracy of the calculation. Smaller values of Ɛ require more rounds to be performed, therefore it has a inverse effect. • Number of peers: since number of peers increase both number of rounds and number of messages sent in one round, this parameter affects the energy consumption in direct proportion. Parameters, in terms of energycont.

9. Energy consumed while local computations • Sending messages (gossip) • Receiving messages Energy Cost Model for ProFID

10. A peer of ProFID consumes energy while; • Preparing gossip • Processing incoming gossip • Sending the gossip to neighbors • Replying it back Epeer = Esend+ Ereceive + Ecomp To understand the energy load of a peer: (one round, one neighbor, one request etc.).

11. Figure 1 Effect of mms to the rounds

12. After effect of fanout: Epeer= fanout x (Esend + Ereceive + Ecomp) • After effect of mms : Epeer= fanout x mms x (Esend+ Ereceive + Ecomp ) • Effect of rounds: (R: number of rounds) Epeer= R x fanout x mms x (Esend+ Ereceive + Ecomp ) Adding other effects to the formula

13. Number of rounds depends on epsilon, N, convLimit, fanoutand mms: • epsilon has inverse proportion with 1/log(epsilon) • N has direct proportion with logN • convLimit has direct proportion with convLimit • fanout has inverse proportion with 1/fanout • mms has inverse proportion with 1/mms Number of rounds depends on…

14. R = (1/logƐ) x logN x convLimit x (1/fanout) x (1/mms) Round

15. In lights of findings above, we can formulate whole system as following: Epeer = R x fanout x mms x (Esend+ Ereceive+ Ecomp ) = (1/logƐ) x logN x convLimit x (1/fanout) x (1/mms) x fanout x mms x (Esend+ Ereceive + Ecomp ) = (1/logƐ) x logN x convLimit x (Esend+ Ereceive + Ecomp) Formulate whole system

16. For a more realistic formula, Epeer is not the value defined above. There are other factors which are also affecting energy but they are constant. Rather giving such a formula above, those constants should be added also to the formula. Then; • Epeer= k x (1/logƐ) x logN x convLimit x (Esend+ Ereceive + Ecomp) + C Epeer

17. Analysis with Numbers

18. Transmitting data • Computation 2 areas of Energy Consumption

19. Power dissipation of CPU is calculated with unit W/GHz and it changes from 15 to 200. • With a Pentium 4 CPU • power dissipation at average = 30W/GHz • For a local computation requiring K many cycles to complete, energy consumption will be following: • joule power dissipation of CPU

20. in a network, at each hop, 4.6 micro joules is consumed per bit. • For a gossip message with size B bytes and with a path having H hop: 36.8*B*H micro joules is consumed. Joules per bit.

21. According to information above, to obtain energy consumption with numbers, the followings must be answered: • In how many cycles can local computation be performed? • Which CPU technology do peers use? • How many hops exist between two nodes?

22. To model the network system with the parameters (K cycles on Pentium 4, gossips of B bytes with H hop) chosen above, we obtain the following formula. Epeer= k x (1/logƐ) x logN x convLimit x (Esend+ Ereceive + Ecomp) + C = [k x (1/logƐ) x logN x convLimit x (73.6*B*H + ) + C] joules formula

23. Open-source Java based network simulator, Peersim Simulation Results

24. Optimum values of convLimit (convergence limit) and epsilon • Deciding about the effect of N to energy consumption • Testifying newly offered weighted average algorithm for ProFID. Three main simulation models

25. Total messages (in terms of gossip): defines total number of gossips throughout the run. • Total messages (in terms of item): defines total number of item sent and received throughout the run. • Average Error: defines the difference between actual and tested frequencies • Frequency Error: defines the difference between items found as frequent and items which are actually frequent. 4 different outputs on simulation

26. Constants • number of peers = 1000 • mms = 100 • fanout = 1 • threshold = 500 as constants; ConvLimit changes from 1 to 20 epsilon from 1 to 20. Our each run has 10 experiments. Therefore, we have total 400 different run and 4000 experiments. For each run, we took average of 10 experiments for more accurate results. Optimum convLimit-epsilon value pair

27. Figure 2: Total Messages vs. convLimit x epsilon Optimum convLimit-epsilon value pair cont.

28. Figure 3: Total Messages vs. convLimit x epsilon Optimum convLimit-epsilon value pair cont.

29. As it is stated while parameter analysis, convergence limit has more effect (direct proportion with convLimit) on number of messages than epsilon (inverse proportion with 1/log epsilon) • because slope of [total messages]/[convergence limit] is greater than slope of [total messages]/[1/epsilon]

30. Figure 4: Average Error vs. convLimit x epsilon Optimum convLimit-epsilon value pair cont.

31. Figure 5: Frequency Error vs. convLimit x epsilon Optimum convLimit-epsilon value pair cont.

32. To get only list of frequent items (without frequencies), it is enough to have such a condition that epsilon <= 12 and convLimit >= 7 because, in that area, the differences on frequency error are very similar (see Figure 5). • For obtaining frequency of frequent items the result is always better for greater values of convLimit and smaller values of epsilon. However, for the area that convLimit >= 11 and epsilon <= 10, reduce on the amount of error is getting smaller (see Figure 4). Therefore, it is better to select one of high values of epsilon and one of the low values of convLimit on that area. Optimum convLimit-epsilon value pair cont.Conclusion

33. To understand the effect we set up a simulation conditions as following: • epsilon = 10 • convLimit = 10 • mms = network size/10 • fanout = 1 • threshold = 500 as constants; • network size = { 1000, 2000, 3000, 4000, 5000 } Effect of Number of Peers to Energy

34. Figure 6: Number of Peers vs. Total Messages Before test, effect of network is calculated as [N log N] because number of rounds increase with ratio log N for increasing numbers of N and in one round total energy consumption for the network is Epeer x N. It is justified with tests that increase on total messages is a little bit greater than ratio N.

35. ProFID performs an averaging algorithm by dividing the sum of item frequencies coming from two neighbor nodes by 2. • , it does not matter how many nodes contribute to this averaged value when the next average operation would be performed with a node which does not have any frequency value for that specific item. • After that operation these two nodes will have v/2 as a frequency for the item i. This situation cause immediate reduction on given frequency v. Effect of Weighted Average

36. Instead of v/2 ; Effect of Weighted Average cont.

37. However, our experiments showed that weighted average is not a good solution for averaging operations. Below is the characteristic of the weighted average operation results comparing with standard averaging operation results: Results of weighted average

38. According to the results, weighted average is always worse than standard averaging operation. Additionally for convLimit > 5 or epsilon < 4, weighted average algorithm never converges. Some reasons causing this effect can be listed as following: • Weighted average supplies quick converges for small subsets of whole network but this situation prevents network-wide converges for increasing number of rounds. • Same node may contribute to same weight multiple times that causes frequency errors. Weighted average

39. Recommendations for Parameter Selection • Recommendations for Protocol • Closer Neighbor Selection • Compressing • Temporarily Hierarchical Model Discussion

40. an algorithm can be developed to automatically find out optimum values of some crucial parameters to save energy consumption. • Recommendations for the ProFID protocol can be evaluated and tested, beneficial ones can be implemented. Future Work