Emergence of Superpeer Networks: A New Perspective

Transcription

1 Emergene o Suereer Networs: A New Persetive Bivas Mitra Deartment o Comuter Siene & Engineering Indian Institute o Tehnology, Kharagur, India

2 Peer to Peer arhiteture Node Node Node Internet Node Node All eers at as both lients and servers Any node an initiate a onnetion Provide and onsume data No entralized data soure Suereer networ (Gnutella 0.6, KaZaA, Sye) emerges as most widely used networ

3 Suereer Toologies Two Layer Toologies in ertain networs lie Sye, Gnutella To Layer --- Resoureul nodes (Suereers) High Bandwidth, Storage Sae, Comutational Power Provides Searh, Indexing and Storage Servies to the nodes in the networ Bottom Layer --- Ordinary nodes Image Soures: tehblessing.om and Lua et al. Com. Comm. 31(3), 2008

4 Dynamis in suereer networs Node joins through bootstraing rotool Node removal Node leaves the networ due to hurn and atta i Node initiated rewiring Rewiring o lins

5 Suereer networs Toology o the suereer networs are modeled by degree distribution seiies the ration o nodes having degree Degree distribution o Gnutella Suereer networ Small ration o nodes are suereers and rest are eers Can be modeled using bimodal degree distribution

6 Researh Question IEEE INFOCOM 2013 (Mini onerene) Why does bootstraing rotool result in bimodal distribution in suereer networs? Literature shows that reerential attahment o nodes results sale ree networ Inlusion o the itness and rewiring o lins do not hanges the nature But suereer networs (Gnutella, Sye) exhibit bimodal degree distribution How does the bootstraing aets networ toology Can this understanding may hel the design engineers to imrove 2 networs?

7 Outline IEEE INFOCOM 2010, IEEE INFOCOM 2013 (Mini onerene) Modeling the bootstraing rotools Develoment o an analytial ramewor to exlain the aearane o bimodal networ Investigating the eet o various bootstraing arameters on networ toology (ration o suereers et.) Study o the Gnutella networ in light o the develoed ormalism

8 Modeling the bootstraing rotools Eah node joins the networ with Node weight (roessing ower, storage sae et) Finite bandwidth (determines the uto degree) Newly arriving eers Preerentially attah to nown owerul eers (via Webahe) Powerul node is deined by the node weight and urrent node degree Random onnetions also exist (arameterized by ) Model Preerential as well as Random attahment by the nodes Attahment Probability ( + ), w = Degree o the existing node = randomness arameters w= node weight

9 Bootstraing Constraints Conet o uto degree IEEE INFOCOM 2010 Bandwidth onstraints o the nodes Imliation A node an tae at most number o onnetions Further onnetion request will be rejeted

10 Conet o inite bandwidth/uto degree =5 Cuto degree o a node is Allowed to tae inoming lins =5 =5 Not allowed to tae inoming lins

11 Bootstraing Constraints Conet o uto degree IEEE INFOCOM 2010 Two dierent assumtions Simle : All the nodes join with same uto degree Realisti : Nodes join with individual uto degree. q (j) ration o nodes joins with uto degree (j). All nodes join with degree - m

12 What do we aim to observe? Eet o bootstraing arameters (randomness ator) w (resoure) (uto degree) m (joining degree) On the networ toology Fration o suereers Fration o lowest degree nodes m and Prominene o suereers Denoted as Suereer Demaration Ratio (SDR)= /( -1)

13 Develoment o the analytial ramewor Joining o a node results the shit in the degree nodes to (+1) The shit in the (-1) degree nodes to Number o nodes o degree (-1) at t inlux Number o nodes o degree at t+1 outlux Number o nodes o degree +1 at t

14 The Degree Distribution When a new node arrives The hange in the number o -degree nodes between timestam n and n+1 is given as n = (n+1) - n = - robability that a node is o degree Asymtotially -- DD (n+1) DD n,n+1,n

15 The Degree Distribution Let ->+1 = average no. o nodes that hanges rom degree to +1. Then n = -> > 1 1 ( ) ( ) m ( ) m where 2 m and ( ) 1 (2 m )

16 The Degree Distribution m Rate equation at Rate equation at Rate equation at heavily deends on Beta untion B(a,b)

17 The Degree Distribution (Arox) Low values o ( << ) When m < < When = 1 ( 1) m m Higher values o When m < < When = m m m m m ( 1)( 0.5) ( 1) ( ) C e ( 1)( 0.5) 1 ( 1) C e For m < < and

18 The Degree Distribution For m < < and 1 Low values o ( << ) m m Higher values o m m m When m < < m m 1 ( 1) When m < < ( 1) ( 1)( 0.5) C( ) e When = m When = ( 1)( 0.5) 1 ( 1) e C

19 The Degree Distribution For m < < and 1 Low values o ( << ) m When m < < m m When = m 1 ( 1) Higher values o m m m Power law When m < < When = ( 1) ( 1)( 0.5) C( ) e ( 1)( 0.5) 1 ( 1) e C Deviates rom ower law

20 Validation: Imat o esilon m=10 = nodes 500 realizations Low model Randomness ε adds a new dimension Aroximation or low ε mathes well with simulation or ε=0 Does not it well with ε=20 Aroximation or high ε mathes well with simulation or ε=20 For all simulations number o nodes is 5000

21 Validation: Imat o esilon Imat o ε, and m On a) Fration o suereers ( ) b) Fration o lowest degree nodes ( m ) ) SDR Inrease in ε redues m Many m degree eers reeive onnetions, results m m+1, m+2, et For all simulations number o nodes is 5000

22 Validation: Imat o esilon Imat o ε, and m On a) Fration o suereers ( ) b) Fration o lowest degree nodes ( m ) ) SDR Inrease in ε redues Hene redues For all simulations number o nodes is 5000

23 Validation: Imat o esilon Deviation rom ower law Imat o esilon on m and Inrease in redues both m and The ration o intermediate degree node inreases For all simulations number o nodes is 5000

24 The Degree Distribution For m < < and 1 Low values o ( << ) m When m < < m m ( 1) Higher values o m m m When m < < ( 1) ( 1)( 0.5) C( ) e Deviates rom ower law When = m Power law When = ( 1)( 0.5) 1 ( 1) e C

25 Imat o on SDR (SP demaration) We have 1 m 2m1 1 2m Thus with inreasing esilon SDR dereases i ( -2m-1)/(2m+ ) >0 SDR inreases i ( -2m-1)/(2m+ ) < 0 Thus when < 2m+1 SDR inreases with Inset igures (Values o m and ) (5, 10), (10, 20) (15, 30)

26 Imat o on SDR We have 1 m 2m1 1 2m Thus with inreasing esilon SDR dereases i ( -2m-1)/(2m+ ) >0 SDR inreases i (inset) ( -2m-1)/(2m+ ) < 0 Thus when < 2m+1 SDR inreases with Values o m and (5, 10), (10, 20) (15, 30)

27 Imat o on SDR We have At =0 At = 1 m 2m1 1 2m m m 1 2m Range o SDR is bounded m Values o m and (5, 10), (10, 20) (15, 30)

28 Imat o and m on suereers =50 =0 The ration o suereers ( ) Dereases with inreasing values o m Ratio SDR= inreases m m

29 Imat o and m =50 =0 The ration o suereers ( ) Inreases with inreasing values o m m The ration o low degree eers ( m ) Gets high value or low m

30 Imat o and m =50 =0 The ration o suereers ( ) Dereases with inreasing values o Inreases with inreasing values o m The SDR Inreases with inreasing values o both m and

31 What do we aim to observe? Eet o bootstraing arameters (randomness ator) w (resoure) (uto degree) m (lowest degree) w ration o nodes o weight w On the networ toology Fration o suereers Fration o lowest degree nodes m and Prominene o suereers Denoted as Suereer Demaration Ratio (SDR)= /( -1)

32 Imat o node weight (w) IEEE INFOCOM 2010 Consider a bimodal weight distribution nodes join with two weights w 1 and w 2 with individual ration w 1 and w 2. We tae w 1 =10, w 1 =0.8. w 2 varied rom 10 to Observations (1) * 1. Initial inrease in w 2 inreases the amount o suereers ( ) raidly. 2. Ater a ertain threshold, stabilizes Observations (2) - Inset 1. Initial inrease in w 2 inreases. w 2 * 2. Ater reahing maximum value ( *), dereases 3. Existene o otimum w 2 (w 2 *)

33 Imat o node weight Some suggestions to the networ engineers Resoure (w) o a mahine an be exloited only uto a oint Enhaning resoure (w) is not always ost eetive to inrease the number o suereers Putting many high resoure mahines ( w2 ) in the networ an in at be detrimental May redue the suereer ration

34 Nodes joining with individual uto degree Dierent users have dierent aaity -- Dial-u, leased line, mobile broadband, DSL Model Probability that node j joins with uto degree (j) is q (j) ; (min) (j) (max)

35 Dierent ut-o degrees Nodes joined with ut-o degrees 20, 30, 40 & 50 Eah with a robability 0.25 Sies at eah ut-o degrees Power-law between eah ut-o degrees

36 Case study : Gnutella Exeriment erormed based on the real world networ data Gnutella networ snashot obtained rom the Multimedia and Internetworing researh grou, University o Oregon, USA Size o the networ 131,869 nodes Comare the theoretial degree distribution with real trae

37 Case study : Gnutella Deviation seially or the low-middle degree nodes

38 Role o Webahe IEEE INFOCOM 2013 (Mini onerene) Finite Size Cahes (new nodes ontat Webahe) Limited inormation availability about the suereers Imliation Inormation about only a small ration o nodes (mostly o high degree) are stored and roagated Peers having low degrees do not reeive onnetions rom the inoming eers Most o the low degree nodes remain in the low degree Subsequently the amount o low degree nodes in the Gnutella networ is less than the theoretial alulated value

39 Revisit the bootstraing rotool m=2 A newly arriving eer initially ontats a WebCahe The Webahe rovides a list o M eers. The eer ontats m < M eers and attemts to onnet to them A eer on reeiving a onnetion request aets the request i it has not reahed its uto degree m =3 = WebCahe 39

40 Model inite sized Webahe IEEE INFOCOM 2013 (Mini onerene) Assumtions Nodes having degree m' (m'< ) will ALWAYS be in ahe Prob. that a node having degree (m<<m' ) will be in ahe is We model the web ahe with tule {, m' } Average number o degree nodes in the web ahe aquires lins rom inoming node We tae Assume low esilon

41 Degree Distribution with Web Cahes At m m m When m < < m When = m m m( 1) m C ( m 1) m m ( 1) When m < < Cm( m 1) m ( ) m ( 1) When = All terms exet are onstant Cm( m 1) m

42 Eet o on the Degree Distribution Simulations Parameters = 0 m =7, m=2, =25 Eet on m m m m deeases slowly with Sine inreases with dereases slowly with inreasing varies inversely with

43 Eet o on the Degree Distribution Two regimes in Degree distribution 1. One at m < m ( indeendent) 2. Other at m < ( deendent) Simulations Parameters = 0, In inset =50 m =7, m=2, =25 In low, webahe is oulated by high degree nodes Nodes in this region aggressively aet new lins and move to Dereasing, rations m and both inreases The deth o the it in the in region m < inreases with the derease in Polarization eet

44 Eet o m' on the Degree Distribution Simulations Parameters =0 m=2, =25 =0.5 =0.3 Eet o m' on For m'=m or m'=, suereer ration remains same (irresetive o ) m m 1 =0.7 m = m 1 m m =

45 Degree Distribution with Web Cahes At m m m When m < < m When = m m m( 1) m C ( m 1) m m ( 1) When m < < Cm( m 1) m ( ) m ( 1) When = Substituting m =m and m = Cm( m 1) m m

46 Eet o m' on the Degree Distribution Simulations Parameters =0 m=2, =25 =0.5 =0.3 =0.7 Eet o m' on For m'=m or m'=, suereer ration remains same (irresetive o ) For m<m'<, there exists an otimal value o m' or whih is maximum

47 Eet o m' on the Degree Distribution Simulations Parameters =0 m=2, =25 =0.5 =0.3 Eet o m' on For m'=m or m'=, suereer ration remains same (irresetive o ) m m m m 1 1 =0.7 m m 1

48 Aliation o the model: Gnutella Networs Gnutella Networ Data Size Data Size 100,000 nodes (2012) Data Size 1,31,869 nodes (2004) Best it observed or =0.42, m =15 (2012) =0.37 and m =18 (2004) 2012 Webahe is mainly oulated by the high o high degree nodes (>15) Only 40% o low degree nodes resent in ahe Variable uto degrees (Inset) Data Obtained at IIT Kharagur 2004

49 Conlusion Closed orm quantitative relationshis between Various bootstraing arameters and the emergent networ roerties lie Fration o Suereers SDR Obtain ertain insights Inreasing randomness in onnetions inreases onnetion uniormity o suereers Resoure otimization (weight) Inreasing webahe size (m ) not neessarily inrease ration o suereers Otimum oint

50 Than you Contat: Comlex Networ Researh Grou (CNeRG) CSE, IIT Kharagur, India htt://se.iitg.a.in/resgr/nerg/