peer-to-peer security in wireless ad hoc networks + commonsensenet

Peer-to-Peer Security in Wireless Ad Hoc Networks+ CommonSenseNet

Jean-Pierre HubauxEPFL, Switzerland

OutlineBrief presentation of the MICS/Terminodes projectMobility helps peer-to-peer securityCooperation between nodes in multi-hop wireless networksThree more projects : Cooperation without incentivesPower-efficient broadcast in all-wireless networksWater management by means of sensor networks

National Competence Centers in ResearchInitiative of the Swiss National Science FoundationCall for proposals in late 1998, for several scientific areas (including Medicine and Physics)Proposals have to be substantial (yearly budget around 3 Mio Euros/year) and long term (from 2001 to 2010)200+ proposals have been submitted in the first round14 proposals finally selected (in 2000)The Mobile Infomation and Communication Systems or Terminodes proposal is the only selected in the area of communications; official start : November 2001

Terminal + Node = TerminodeAll network functions (packet forwarding, flow control, error control,) and terminal functions (coding/decoding, A/D and D/A, storage, ciphering,) are embedded in the terminodeA communication must be relayed by intermediate terminodesThe network is self-organized: it is operated by its users All terminodes are potentially mobile

Terminodes are the extreme (or academic) case of several concrete incarnations: multi-hop cellular networks, networks of vehicles, sensor networks, self-operated networks, distributed robots,

National Center for Competence in Research: Mobile Information and Communication Systems

Academicconsortium(in CH):EPFLUni LausanneUni BernUni St GallenUni ZurichCSEMETHZDirector of NCCR Prof. M. VetterliDeputy director of NCCR Prof. Th. GrossFribourg: CCTCIndustrial partners:

IBM Microsoft Samsung Siemens Swisscom Whitestein Technologies+ many academic partners worldwidewww.terminodes.orgAround 25 faculty membersand 80 PhD students

Main challenge and benefit of the research program : working accross layersSelected application: environmental monitoring (sensor networks) Other possible applications: crisis networks, networks of cars, networks for rural areas

Mathematical foundationInformation theorySecurityEconomicsSystem architectureCommunicating embedded systemsInformation systemsReal-time servicesNetwork layerPhysical and MAC layers

Joint work with Levente Buttyan+ and Srdjan CapkunMobility Helps Peer-to-Peer Security

Peer-to-peer Authentication and Key Establishment in Mobile Networks+ Now with Laboratory of Cryptography and Systems Security (CrySyS) Department of Telecommunications, Budapest University of Technology and Economics

Secure communication with cryptography(reminder)AlicexEK(x)DK(y)Key KyMallory (or Oscar)BobKey KSenderReceiverAttacker or opponent or intruderx: plain texty: cipher text

Symmetric cryptography: if K = KAsymmetric cryptography (or public key cryptography): if K K

DK(EK(x)) = xEncrypterDecrypterx

Digital Signature (reminder)AliceBobMessagemm= ?Signature: sig or Verification: verA certificate is an identity or a public keysigned by another entity

Does mobility increase or reduce security ?Very often, people move to increase security:Face to face meetingsTransport of assets and physical documentsAuthentication by physical presenceIn spite of the popularity of PDAs and cellular phones, this mobility has not been exploited so far to provide digital securityMobility is usually perceived as a major security challenge:Wireless channel Unpredictable location of the userSporadic availability of the userHigher vulnerability of the deviceSmaller computing capability of the deviceSo far, client-server security has been considered as the priority (e-business, cellular telephony,)Peer-to-peer security is still in its infancy

Security of cellular networksExample: GSMMobile station(key stored in The SIM card)Shared, symmetric keyBase stationAuthentication CenterChallengeResponseSetting up of the encryption key The key stored in the SIM card incarnates the contract between the subscriber and the operator It is established manually when the contract is signed Only symmetric cryptography is used

Example of security for wireless LANs: standard IEEE 802.1x (*)Supplicant(Mobile Station)Authenticator(Access Point)Authentication ServerEAPOL (over IEEE 802.11)Encapsulated EAP,Typically on RADIUSEAP: Extensible Authentication Protocol (RFC 2284, 1998)EAPOL: EAP over LANRADIUS: Remote authentication dial in user service (RFC 2138, 1997)

Features of IEEE 802.1x: - Supports a wide range of authentication schemes, thanks to the usage of EAP One-way authentication Optional encryption and data integrity(*) Notes: IEEE 802.1x is not specific to wireless LANs and was not designed specifically for them New standard: IEEE 802.11i (2003)

Wireless Transport Layer Security protocol (WTLS)WTLSWAPGatewaySSLWeb serverAuthentication classes of WTLS:Class 1: no authentication Class 2: authentication of the server only (similar to traditional SSL / HTTPS used with Web servers); the server certificateis usually signed by a Trusted Third Party (Verisign, Entrust, Smartrust,)Class 3: authentication of both server and client; requires a Public Key Infrastructure and a Wireless Identity Module (WIM);very few implementations so far(Secure Socket Layer)

Security in ad hoc networksConstraintsMobile devices limited computing capabilitiesSporadic connectivity prevents from relying on an on-line serverSolutions proposed so farSome nodes have a special role; they are entitled to perform threshold cryptography operations (Cornell, 1999)Generalization: any node can take this responsibility (UCLA, 2001)Users are all in the same location; they agree on a common password, type it into their device; the protocol creates a strong shared key (Nokia, 2001)Issue mutual certificates and build up a distributed certificate graph la PGP (EPFL, 2001)

Mobility helps securityInfrared link(Alice, PuKAlice, XYZ)(Bob, PuKBob , UVW)Visual recognition, conscious establishment of a two-way security associationSecure side channel Typically short distance (a few meters) Line of sight required- Ensures integrity- Confidentiality not required AliceBobProblem : how to bootstrap security in a mobile network without a central authority ?

Friends mechanismIRColinBob(Colins friend)Alice(Alice, PuKAlice, XYZ)(Alice, PuKAlice, XYZ)Colin and Bob are friends: They have established a Security Association at initialisation They faithfully share with each other the Security Associations they have set up with other users

Mechanisms to establish Security AssociationsFriendship : nodes know each others triplets

Exchange of triplets over the secure side channelTwo-way SA resulting from a physical encounter iji knows the triplet of j ; the triplet has been obtained from a friend of ia) Encounter and activation of the Secure Side Channelb) Mutual friendc) Friend + encounterNote: there is no transitivity of trust (beyond your friends)

Protocols

Pace of establishment of the security associations (1/2) Depends on several factors: Area size Number of communication partners: s Number of nodes: n Number of friends Mobility model and its parameters (speed, pause times, )Established security associations :Desired security associations :Convergence :

Pace of establishment of the security associations (2/2)

Chart1

0.10.10.1

0.20.20.2

0.30.30.3

0.40.40.4

0.50.50.5

0.60.60.6

0.70.70.7

0.80.80.8

0.90.90.9

0.910.910.91

0.920.920.92

0.930.930.93

0.940.940.94

0.950.950.95

0.960.960.96

0.970.970.97

0.980.980.98

0.990.990.99

111

tw - torus

tw,f - torus, bounded

tw - bounded

5m/s, 2 friends

5m/s, 0 friends

20m/s, 0 friends

s=99, f=0, pause=100 s, sr=5 m, v=5 m/s

s=99, f=2, pause=100 s, sr=5 m, v=5 m/s

s=99, f=0, pause=100 s, sr=5 m, v=20 m/s

time (s)

percentage of security associations

waypoint graphs

waypoint graphs

0.10.4481818182110.10.42488.379641294188.379641294111

0.20.500808080817.243158866417.24315886640.20.4965139.059187113139.05918711325.08546853525.085468535

0.30.600101010134.814385729934.81438572990.30.594326.5884345274326.588434527440.312358242240.3123582422

0.40.700101010148.782396410948.78239641090.40.6935498.3696145811498.369614581162.670738644962.6707386449

0.50.800909090967.055045248167.05504524810.50.792642.6782401801642.678240180167.975230326267.9752303262

0.60.9159.6186800944159.61868009440.60.891769.5194193534769.5194193534149.5501899536149.5501899536

0.70.9104040404187.1340434947187.13404349470.70.9011010.26072267771010.2607226777156.2876934036156.2876934036

0.80.9201010101203.0408182166203.04081821660.80.91051733.54455321921733.5445532192183.4598842474183.4598842474

0.90.9304040404229.45594818229.455948180.90.92053274.33785205323274.3378520532187.2601674106187.2601674106

0.910.94258.0776625443258.07766254430.910.93053739.71079646613739.7107964661244.2839011312244.2839011312

0.920.9501010101293.6858921834293.68589218340.920.94054228.96536123744228.9653612374284.8211540715284.8211540715

0.930.96317.4196685729317.41966857290.930.954649.55851808894649.5585180889334.66788166334.66788166

0.940.9701010101413.6897577562413.68975775620.940.965056.77806819515056.7780681951404.5233765176404.5233765176

0.950.98478.8936452652478.89364526520.950.975390.38392644025390.3839264402531.108489146531.108489146

0.960.9901010101556.7077810344556.70778103440.960.986285.91282119086285.9128211908670.0003804874670.0003804874

0.97110234102340.9718472.8890919618472.889091961996.5393053141996.5393053141

0.980.9815941.224205897415941.2242058974

0.990.9925506.980358264625506.9803582646

11196433.263043842196433.263043842

Parameters:N=1000 x 1000 mn=100max. speed: 20 m/s

random waypoint, s=99 (0 friends)




time (s)

rnxs(t)

walk graph

0.44818181820.44111111110.44484848480.438080808111111111

0.50080808080.50010101010.50060606060.50050505059.60631728559.606317285566.779602322366.779602322317.243158866417.243158866413.492529058413.4925290584

0.60010101010.60.60030303030.600303030319.781511782219.7815117822134.028450248134.02845024834.814385729934.814385729947.933966841547.9339668415

0.70010101010.70020202020.70141414140.700606060638.061277899138.0612778991204.5676810819204.567681081948.782396410948.7823964109115.5735222735115.5735222735

0.80090909090.80010101010.80.800202020272.290551245772.2905512457325.6468537583325.646853758367.055045248167.0550452481200.1324198877200.1324198877

0.90.90020202020.90010101010.9002020202120.3738735773120.3738735773595.1077930154595.1077930154159.6186800944159.6186800944419.9235600369419.9235600369

0.91040404040.910.91030303030.91128.3754443176128.3754443176620.5562691603620.5562691603187.1340434947187.1340434947470.9251861486470.9251861486

0.92010101010.920.920.92138.1345546764138.1345546764676.9220129227676.9220129227203.0408182166203.0408182166507.6000192657507.6000192657

0.93040404040.93020202020.93010101010.93149.7150872241149.7150872241749.9558331841749.9558331841229.45594818229.45594818559.2239996506559.2239996506

0.940.940.940.94169.3667553921169.3667553921814.1183926753814.1183926753258.0776625443258.0776625443615.5758669432615.5758669432

0.95010101010.950.95020202020.95181.8324054326181.8324054326894.9831652362894.9831652362293.6858921834293.6858921834702.2996717813702.2996717813

0.960.960.960.96221.4595575919221.4595575919892.5903063012892.5903063012317.4196685729317.4196685729762.6561611305762.6561611305

0.97010101010.970.970.97260.8146616574260.81466165741017.26732715561017.2673271556413.6897577562413.6897577562784.0629671197784.0629671197

0.980.98010101010.98010101010.98296.392171801296.3921718011175.06997062931175.0699706293478.8936452652478.89364526521032.37783912521032.3778391252

0.99010101010.990.990.99356.6871957798356.68719577981760.72786932941760.7278693294556.7077810344556.70778103441238.57840863621238.5784086362

11115456545640637.10435152840637.104351528102341023478021.876987889378021.8769878893

Parameters:N=1000 x 1000 mn=100restriction points: 20

random waypoint (5 friends; 20 m/s)

random waypoint (5 friends; 5 m/s)

restricted random waypoint (f =1; 5 friends; 20 m/s)

restricted random waypoint (f =1; 5 friends; 5 m/s)

time (s)

rnxs(t)

waypoint torus graphs

0.4481818182110.4481818182000.448181818200

0.500808080817.243158866417.24315886640.500808080822.513139666722.51313966670.500808080831.131017390731.1310173907

0.600101010134.814385729934.81438572990.600101010137.73537204637.7353720460.600101010176.86864622576.868646225

0.700101010148.782396410948.78239641090.700101010161.303283367461.30328336740.7001010101120.8096169089120.8096169089

0.800909090967.055045248167.05504524810.800909090988.071455539188.07145553910.8009090909170.1910596781170.1910596781

0.9159.6186800944159.61868009440.9144.6192999067144.61929990670.9232.7858202858232.7858202858

0.9104040404187.1340434947187.13404349470.9104040404144.2863958419144.28639584190.9104040404255.1733241632255.1733241632

0.9201010101203.0408182166203.04081821660.9201010101178.9349292414178.93492924140.9201010101252.5313627206252.5313627206

0.9304040404229.45594818229.455948180.9304040404209.6884186084209.68841860840.9304040404274.1116247656274.1116247656

0.94258.0776625443258.07766254430.94241.2116791258241.21167912580.94286.2344274809286.2344274809

0.9501010101293.6858921834293.68589218340.9501010101258.8056412442258.80564124420.9501010101327.9913067655327.9913067655

0.96317.4196685729317.41966857290.96316.3671912946316.36719129460.96383.8342507737383.8342507737

0.9701010101413.6897577562413.68975775620.9701010101369.7954788188369.79547881880.9701010101405.5089360171405.5089360171

0.98478.8936452652478.89364526520.98486.6167522727486.61675227270.98517.558973379517.558973379

0.9901010101556.7077810344556.70778103440.9901010101761.8453842464761.84538424640.9901010101712.6995164797712.6995164797

11023410234

Parameters:random waypointN=1000 x 1000 mn=1005 friendsmax. speed: 20 m/s

pause time: 5s

pause time: 100s

pause time: 200s

time (s)

rnxs(t)

waypoint bounded graph

waypoint bounded graph

0.10.10.44505050510.445050505165.149271957965.149271957936.602364699236.60236469921111

0.20.20.50030303030.5003030303114.9099377283114.909937728373.502250665373.502250665332.125615560332.125615560322.145205871122.1452058711

0.30.30.60070707070.6007070707209.6930315562209.693031556289.767388764489.767388764447.21328986247.21328986236.076543732236.0765437322

0.40.40.70090909090.7009090909273.3159656282273.315965628296.043090172996.043090172967.974754429367.974754429348.3588482548.35884825

0.50.50.80040404040.8004040404318.6226915384318.6226915384112.1101255758112.1101255758100.3974103758100.397410375874.79626324774.796263247

0.60.60.90.9320.0868171627320.0868171627160.2069447623160.2069447623172.5600446136172.5600446136100.6503290203100.6503290203

0.70.70.910.91422.2244994563422.2244994563271.7041918985271.7041918985177.9802343919177.9802343919112.3530048598112.3530048598

0.80.80.92010101010.9201010101470.2055457455470.2055457455330.0121501423330.0121501423186.9569774964186.9569774964109.9418400759109.9418400759

0.90.90.93010101010.9301010101665.1292021717665.1292021717444.7454060797444.7454060797198.8683202449198.8683202449113.4382496253113.4382496253

0.910.910.94010101010.9401010101643.330647274643.330647274459.2937740878459.2937740878222.8357190003222.8357190003119.5099897414119.5099897414

0.920.920.950.95689.9625720197689.9625720197505.2818458552505.2818458552232.2050503699232.2050503699123.3348309786123.3348309786

0.930.930.960.96708.563248374708.563248374503.2739277822503.2739277822260.7369553572260.7369553572143.5385707216143.5385707216

0.940.940.970.97640.5729046205640.5729046205530.8005615729530.8005615729284.0451835377284.0451835377152.1897155391152.1897155391

0.950.950.980.98759.4804781388759.4804781388636.3084609742636.3084609742314.9474134454314.9474134454162.1078749107162.1078749107

0.960.960.990.99661.887066167661.887066167713.059563257713.059563257383.098909888383.098909888233.1366803229233.1366803229

0.970.97111066.58554153551066.5855415355732.4205129816732.42051298161596159617651765

0.980.981525.71312459161525.7131245916801.4513423295801.4513423295

0.990.991619.53329398241619.53329398241083.729973791083.72997379

1123875.138324625623875.138324625620537.630712259220537.6307122592

tw - torus

tw,f - torus, bounded

tw - bounded

Parameters:N =100x100 n = 100

rectangular grid (0 friends)

torus-like grid (0 friends)

rectangular grid (5 friends)

torus-like grid (5 friends)

time (steps)

rnxs(t)

restricted_random_waypoint

0.15267.3778152745267.3778152740.10.10.10.10.14608.14169175954608.1416917595429.6534428397429.6534428397429.6534428397429.653442839762.932357211462.932357211434.876049487134.8760494871

0.211212.567763955211212.56776395520.20.20.20.20.29304.25364278459304.2536427845739.0033096476739.0033096476739.0033096476739.0033096476127.2223455263127.222345526374.637405672874.6374056728

0.318315.486994246118315.48699424610.30.30.30.30.315446.740138213915446.74013821391101.46757395331101.46757395331101.46757395331101.4675739533151.8192033276151.819203327675.177667987575.1776679875

0.424831.689804185424831.68980418540.40.40.40.40.418582.551839283218582.55183928321241.71708654521241.71708654521241.71708654521241.7170865452153.1716247744153.1716247744120.7017268031120.7017268031

0.534296.632035673834296.63203567380.50.50.50.50.516888.945362701316888.94536270131362.98555375671362.98555375671362.98555375671362.9855537567195.8047457899195.8047457899138.199128997138.199128997

0.643009.968969575443009.96896957540.60.60.60.60.614398.623754608414398.62375460841661.9628967541661.9628967541661.9628967541661.962896754276.0073014814276.0073014814163.1486256995163.1486256995

0.750762.973989236850762.97398923680.70.70.70.70.722594.621779542122594.62177954211856.04319877851856.04319877851856.04319877851856.0431987785395.4956988151395.4956988151202.9377025352202.9377025352

0.838450.968504519738450.96850451970.80.80.80.80.822949.000797440122949.00079744012336.95021217882336.95021217882336.95021217882336.9502121788273.8975942156273.8975942156224.4036281444224.4036281444

0.976523.253470537976523.25347053790.90.90.90.90.934851.638541739934851.63854173993688.17994720723688.17994720723688.17994720723688.1799472072427.9016011038427.9016011038480.7256749548480.7256749548

0.92114319.168229868114319.1682298680.910.920.910.920.9132720.727127620532720.72712762054150.68648601184150.68648601184150.68648601184150.6864860118366.0676389539366.0676389539560.7712653544560.7712653544

0.94103617.113825013103617.1138250130.920.940.920.940.9247294.778659611847294.77865961184260.28489682114260.28489682114260.28489682114260.2848968211554.1671654162554.1671654162604.9869238156604.9869238156

0.96101940.232056041101940.2320560410.930.960.930.960.9346103.629538688446103.62953868844482.21132140114482.21132140114482.21132140114482.2113214011599.7982504733599.7982504733664.6436538868664.6436538868

0.98152475.51645024152475.516450240.940.980.940.980.9460293.232381193960293.23238119394719.52967678444719.52967678444719.52967678444719.5296767844554.7002871833554.7002871833673.6774729849673.6774729849

1297257.737672863297257.7376728630.9510.9510.9589379.551584633389379.55158463335171.88568800325171.88568800325171.88568800325171.8856880032877.5746567407877.5746567407741.41603563741.41603563

0.960.960.9697062.075900537897062.07590053785111.28358586755111.28358586755111.28358586755111.2835858675726.0306161444726.0306161444

0.970.970.9781270.304808763881270.30480876385391.46722875795391.46722875795391.46722875795391.4672287579893.5123833068893.5123833068

0.980.980.9882335.256513341482335.25651334147407.74703582377407.74703582377407.74703582377407.7470358237977.0407319838977.0407319838

0.990.990.9993777.985874772593777.98587477258442.40345229668442.40345229668442.40345229668442.40345229661076.56259107891076.5625910789

111218224.438583001218224.43858300114656.27945661414656.27945661414656.27945661414656.2794566141264.93577172461264.9357717246

Parameters:n=100

s=50, N =333x333

s=100, N =333x333

s=50, N =100x100

s=100, N =100x100

s=50, N =33x33

s=100, N =33x33

time (steps)

r1xs(t)

random_waypoint

random_waypoint

0.10.26848484850.10.1

0.20.30030303030.20.2

0.30.40030303030.30.3

0.40.50040404040.40.4

0.50.60070707070.50.5

0.60.70030303030.60.6

0.70.80010101010.70.7

0.80.90.80.8

0.90.910.90.9

0.910.920.910.91

0.920.93020202020.920.92

0.930.94020202020.930.93

0.940.950.940.94

0.950.960.950.95

0.960.970.960.96

0.970.98010101010.970.97

0.980.990.980.98

0.9910.990.99

111

simulation area: 1000 x 1000 m torusnumber of nodes: 100speed: 20 m/spause time: 5 ssecurity range: 5 mconfidence intervals: 95%

tw,f100x99

tw100x99

random waypoint

random waypoint (5 friends)

restricted waypoint (20 points; =1)

restricted waypoint (20 points; =0.5)

t (s)

rnxs(t)

(Restricted) random waypoint convergence rnxs(t)

MGM-GM graphs

MGM-GM graphs

0.10.44818181820.11136.409933978436.409933978452.541338651552.54133865150.153.798747180853.79874718080.4448484848110.444848484811

0.20.50080808080.217.243158866417.243158866493.182974440493.1829744404113.3663018065113.36630180650.2138.8397455403138.83974554030.50060606069.60631728559.60631728550.500606060612.048402483612.0484024836

0.30.60010101010.334.814385729934.8143857299153.9278114273153.9278114273211.3007291284211.30072912840.3235.6913809818235.69138098180.600303030319.781511782219.78151178220.600303030327.32202592627.322025926

0.40.70010101010.448.782396410948.7823964109206.5050216398206.5050216398310.0044635057310.00446350570.4328.5862330409328.58623304090.701414141438.061277899138.06127789910.701414141447.055952684347.0559526843

0.50.80090909090.567.055045248167.0550452481302.4688351316302.4688351316432.6145015697432.61450156970.5441.5739791339441.57397913390.872.290551245772.29055124570.896.058834495396.0588344953

0.60.90.6159.6186800944159.6186800944436.2529034353436.2529034353572.2953013223572.29530132230.6589.6064563009589.60645630090.9001010101120.3738735773120.37387357730.9001010101156.3588539043156.3588539043

0.70.91040404040.7187.1340434947187.1340434947593.5375335967593.5375335967736.5937845751736.59378457510.7797.2210584997797.22105849970.9103030303128.3754443176128.37544431760.9103030303163.8077752307163.8077752307

0.80.92010101010.8203.0408182166203.0408182166845.5719489179845.57194891791165.78060495121165.78060495120.81211.71187077531211.71187077530.92138.1345546764138.13455467640.92168.9587769835168.9587769835

0.90.93040404040.9229.45594818229.455948181298.40320848661298.40320848661823.90202484841823.90202484840.91637.7257014191637.7257014190.9301010101149.7150872241149.71508722410.9301010101185.3047603067185.3047603067

0.910.940.91258.0776625443258.07766254431378.86289418651378.86289418652043.6352688622043.6352688620.911697.56555430551697.56555430550.94169.3667553921169.36675539210.94199.3489964629199.3489964629

0.920.95010101010.92293.6858921834293.68589218341435.42220783821435.42220783822334.96593187272334.96593187270.921689.87754443221689.87754443220.9502020202181.8324054326181.83240543260.9502020202217.1270289879217.1270289879

0.930.960.93317.4196685729317.41966857291620.40295521141620.40295521142637.83291777762637.83291777760.931691.39511426311691.39511426310.96221.4595575919221.45955759190.96239.8252145153239.8252145153

0.940.97010101010.94413.6897577562413.68975775621728.67225634471728.67225634473074.60807105713074.60807105710.941791.76399048551791.76399048550.97260.8146616574260.81466165740.97294.111390006294.111390006

0.950.980.95478.8936452652478.89364526521874.09808107921874.09808107923568.62689805443568.62689805440.951859.7230747221859.7230747220.9801010101296.392171801296.3921718010.9801010101394.7943042023394.7943042023

0.960.99010101010.96556.7077810344556.70778103442029.80805987682029.80805987684370.4838643344370.4838643340.962114.80500289462114.80500289460.99356.6871957798356.68719577980.99529.4640180544529.4640180544

0.9710.9710234102342377.05342516662377.05342516664923.84162272514923.84162272510.972436.35985480352436.359854803515456545611234312343

0.980.982717.6852635362717.6852635366303.67238159266303.67238159260.983096.15489154443096.1548915444

0.990.993310.16108286513310.161082865111521.184724360711521.18472436070.994910.76859206414910.7685920641

1172573.082269262672573.0822692626173539.265732265173539.2657322651192405.15947973192405.15947973

Parameters:N=1000 x 1000 mn=100 max. speed: 20 m/srestriction points: 20



restricted waypoint (=1; 0 friends)

restricted waypoint (=0.5; 0 friends)

restricted waypoint (=1; 5 friends)

restricted waypoint (=0.5; 5 friends)

time (s)

rnxs(t)

Gauss_Markov

new1000_100_0_100_1_20_5_5_0_0_1_20 restricted_bounded1000_100_0_100_1_20_5_5_0_0_1_20 restricted_torusN N_nodes N_friends N_comms step_time Max_speed Max_pause_time Se

c_power_range bidirectional fixed_coordinates(for two nodes only) restriction_pr

9900.1567.2583.078197152536.40993397849900.1obability N_of_points

19800.21272.15212.619817613893.182974440419800.2

29700.32159.65351.2240662837153.927811427329700.3

39600.43265.1471.1918706295206.505021639839600.4

49520.54648.8690.1568547878302.468835131649520.5

59400.66383995.4180290871436.252903435359400.6

69300.78765.851354.3015008716593.537533596769300.7

79200.812383.251929.3798533262845.571948917979200.8

89100.919225.252962.62546925061298.403208486689100.9

90100.91203603146.21398208271378.862894186590100.91

91080.9221573.353275.26793239081435.422207838291080.92

92080.9323145.353697.34689053481620.402955211492080.93

93060.9424864.353944.38986376451728.672256344793060.94

94060.9527053.154276.21456153871874.098081079294060.95

95040.9629724.64631.50507991342029.808059876895040.96

96040.9733596.755423.8305736912377.053425166696040.97

97020.9839033.856201.06568324312717.68526353697020.98

98020.9949019.557552.94462253323310.161082865198020.99

99001267240.9152669.4719385372573.082269262699001

avgstdevconfintavgstdevconfint

new1000_100_0_100_1_20_5_5_0_0_0.5_20 restricted_bounded1000_100_0_100_1_20_5_5_0_0_0.5_20 restricted_torus

9900.11223.2122.755040629753.79874718089900.1

19800.22839.25316.7969422699138.839745540319800.2

29700.34926.4537.7877100238235.691380981829700.3

39600.47511.2749.750105737328.586233040939600.4

49520.510677.751007.5593687614441.573979133949520.5

59400.614762.651345.3317835741589.606456300959400.6

69300.720451.41819.0554344726797.221058499769300.7

79200.828932.92764.81791348671211.711870775379200.8

89100.945287.653736.87298595471637.72570141989100.9

90100.9147955.43873.41229137151697.565554305590100.91

91080.9251083.353855.87021067611689.877544432291080.92

92080.9354721.553859.33291856451691.395114263192080.93

93060.9458844.74088.34913407661791.763990485593060.94

94060.9564013.054243.41445778351859.72307472294060.95

95040.9670604.954825.44645848282114.805002894695040.96

96040.9778992.85559.15274309432436.359854803596040.97

97020.9892240.57064.63699294633096.154891544497020.98

98020.99118568.9511205.12334639364910.768592064198020.99

99001619806.9439019.575863729192405.1594797399001

avgstdevconfint

new1000_100_5_100_1_20_5_5_0_0_1_20 restricted_boundednew1000_100_5_100_1_20_5_5_0_0_05_20 restricted_bounded

44040.44100144040.441001

49560.50107.3521.91916969239.606317285549560.50184.2527.491386210812.0484024836

59430.60306.3545.136372309519.781511782259430.60606.7562.341905311727.322025926

69440.70582.686.846143446838.061277899169440.701243.6107.369700714847.0559526843

79200.801023.45164.948628366572.290551245779200.802226.35219.181797890196.0588344953

89110.901875.15274.6625249858120.373873577389110.904142.15356.7710861249156.3588539043

90120.912006.8292.9200717279128.375444317690120.914414.65373.7676276427163.8077752307

91080.922154.35315.187876303138.134554676491080.924752.05385.520901884168.9587769835

92080.932342.35341.6117024681149.715087224192080.935152.85422.8182731449185.3047603067

93060.942572.95386.4518047162169.366755392193060.945599.25454.8636435356199.3489964629

94070.952830.8414.8952435952181.832405432694070.956143.7495.4285863881217.1270289879

95040.963141.35505.3143133369221.459557591995040.966789.7547.2200654216239.8252145153

96030.973547595.1126386085260.814661657496030.977706.95671.0872933257294.111390006

97030.984142.65676.2914565559296.39217180197030.988940.05900.8200635211394.7943042023

98010.995053.45813.8693464911356.687195779898010.9911154.451208.1020554224529.4640180544

99001.0012319545699001.004054312343

new1000_100_5_100_1_5_5_5_0_0_1_20 restricted_boundednew1000_100_5_100_1_5_5_5_0_0_05_20 restricted_bounded

43370.44100126980.27101

49550.50278.142857142930.786515291813.492529058429750.30178.7536.216999497915.8724985112

59430.60840.1428571429109.373105425847.933966841539600.40820.75129.537994832656.7714514903

69360.701646.5714285714263.7093457722115.573522273549560.501723.75212.763489893393.2459403976

79220.802871456.6512162836200.132419887759420.603000.05351.7939700569154.1775780263

89120.905282.5714285714958.1586258971419.923560036969320.704807.45454.1214160622199.0237071062

90090.915670.42857142861074.5313485644470.925186148679200.807659755.6282851132331.1624098278

91080.926168.42857142861158.213978092507.600019265789100.9013007.951173.8693316953514.4611502319

92070.936722.71428571431276.0067547216559.223999650690100.9113923.81239.4225565497543.1905722804

93060.9472641404.5873652666615.575866943291090.9214929.21323.9415076919580.2319325468

94050.957924.71428571431602.469002746702.299671781392070.9316140.151362.2754291027597.0321953779

95040.968850.42857142861740.1871410036762.656161130593060.9417595.31440.4905999072631.3108545534

96030.979829.71428571431789.0320207946784.062967119794050.9519264.151540.750065971675.2506686708

97020.9811563.71428571432355.62332262511032.377839125295060.9621272.61977.9648871344866.8648745461

98010.9914374.14285714292826.12051102871238.578408636296030.9724187.72524.72055983691106.4865638428

99001.00101476.95178026.05416578678021.876987889397020.9828372.43286.02249407681440.1355128252

98010.9936164.755134.07966307912250.0669005771

99001.00188705.1202505.0706746388750.0753057542

avgstdevconfint

new1000_100_5_100_1_20_60_5_0_0_1_20 restricted_bounded

27450.2772727273101

29720.300202020233.555.64264775482.4729524623

39630.4003030303101.814.88057723846.5215766998

49500.5200.526.456518448611.5948603006

59400.6339.7552.899980101523.1839983169

69360.700606060653883.799886948836.7262224721

79250.8005050505857.1138.023224590360.4901967913

89100.91491.7237.5415974652104.1052186647

90130.91040404041604.9255.7753743136112.0963719875

91080.921736291.6930614623127.8376935684

92070.931898.7308.2987443852135.115316815

93060.942075.5337.2000031217147.7816114453

94050.952294.25395.5516966679173.3548831624

95050.96010101012571.45433.028803588189.7796376158

96030.972978.25552.3269316933242.0633548477

97030.98010101013602.4752.8548752302329.9469324318

98020.99010101015176.951601.2825936532701.7797149428

9900120198.812779.08970730585600.5766674586

ModifiedGaussMarkov

new1000_100_0_100_1_20_5_5_0_0_waypoint_bounded1000_100_0_100_1_20_5_5_0_0_waypoint_torussimulation.exe N N_nodes N_friends N_comms step_time Max_speed Max_pause_time Se

c_power_range bidirectional fixed_coordinates(for two nodes only)

9900.11714.3119.885954578852.54133865159900.1

19800.24023.5258.6730307591113.366301806519800.2pause-rime 100

29700.36886.5482.1344538393211.300729128429700.3new1000_100_5_100_1_20_100_5_0_0_waypoint_bounded

39600.410391.75707.3512397075310.004463505739600.4

49520.514645.85987.1161225883432.614501569749520.51000

59400.620155.91305.832136387572.295301322359400.6360.851.369251503222.5131396667

69300.727787.651680.7194347722736.593784575169300.71193.286.102509285537.735372046

79200.839013.12660.01446177311165.780604951279200.82352.1139.878481095961.3032833674

89100.960367.24161.67994419261823.902024848489100.94078.1200.95663318588.0714555391

90100.9163732.554663.05524956832043.63526886290100.917311.85329.9844135075144.6192999067

91080.9267713.655327.79763203292334.965931872791080.927823.35329.2248112093144.2863958419

92080.9372493.356018.86296549182637.832917777692080.938412.75408.2839408007178.9349292414

93060.9478149.257015.47263572683074.608071057193060.949069.95478.4555718251209.6884186084

94060.9585100.28142.69779166073568.626898054494060.959819.15550.3836245843241.2116791258

95040.9694277.49972.33118710284370.48386433495040.9610700.75590.5285656445258.8056412442

96040.97105832.911234.95267317234923.841622725196040.9711812.3721.869364184316.3671912946

97020.98124413.4514383.37507597986303.672381592697020.9813325.65843.7791102191369.7954788188

98020.99159988.6526288.409545843611521.184724360798020.9915458.91110.3355064313486.6167522727

99001606736.329588507395972.410737292173539.2657322659900118873.81738.3371546273761.8453842464


pause-rime 200

new1000_100_5_100_1_20_5_5_0_0_waypoint_bounded1000_100_5_100_1_20_5_5_0_0_waypoint_torusnew1000_100_5_100_1_20_200_5_0_0_waypoint_bounded

44370.45100126580.271000

49580.50228.139.344497374917.243158866429730.30499.371.03305383331.1310173907

59410.60815.379.437562373234.814385729939630.401618.65175.394675247776.868646225

69310.701624.3111.309005641248.782396410949540.503110.15275.6567803017120.8096169089

79290.802950.25153.002536958767.055045248159470.605424.6388.3326571788170.1910596781

89100.905367.7364.2091793404159.618680094469330.709380.4531.1579604481232.7858202858

90130.915756.05426.9922315329187.134043494779210.8010027.45582.2405430748255.1733241632

91090.926216.9463.287440615203.040818216689100.9010733.4576.212259867252.5313627206

92110.936731.2523.560040291229.4559481890090.9111581.9625.452922205274.1116247656

93060.947340.9588.8675036391258.077662544391080.9212480.9653.1140707975286.2344274809

94060.958014.3670.116415652293.685892183492090.9313620.2748.3926354809327.9913067655

95040.968849.5724.2708493084317.419668572993080.9414986.55875.8120126939383.8342507737

96040.9710032.4943.934676598413.689757756294050.9516692.45925.2681247247405.5089360171

97020.9811703.651092.7133430136478.893645265295040.9619208.151180.9377752225517.558973379

98020.9914462.61270.2653846218556.707781034496030.9723376.31626.1987999141712.6995164797

99001.0048324184321023497030.98

98010.99

99001.00


1000_100_5_20_1_20_5_5_1_0_waypoint_bounded1000_100_5_20_1_20_5_5_1_0_waypoint_torus

8480.4210019910.28

9930.50232.557.238650909125.08546853510790.30

11880.59801.5591.982535527740.312358242214370.40

13870.691626.25142.998665801762.670738644917970.50

15840.792861.45155.102164971867.975230326221570.60

17820.895149.5341.2354488897149.550189953625160.70

18020.905488.25356.608715984156.287693403628750.80

18210.915890.7418.6087357954183.459884247432340.90

18410.926371427.2800141901187.260167410632700.91

18610.936927557.3936528258244.283901131233060.92

18810.947539.95649.8893407828284.821154071533420.93

19000.958266.3763.6268791277334.6678816633780.94

19200.969209.45923.0193289303404.523376517634150.95

19400.9710603.051211.854319671531.10848914634500.96

19600.9812537.61528.7702453796670.000380487434860.97

20001.0029325.3333333333880.6578980133996.539305314135220.98

35590.99

36001.00


new1000_100_0_20_1_20_5_5_1_0_waypoint_bounded1000_100_0_20_1_20_5_5_1_0_waypoint_torus

3600.101719.3142.595036535188.37964129413600.10

7200.204061.7224.3633214231139.0591871137200.20

10800.307000.8526.9300607186326.588434527410800.30

14400.4010434.2804.088275972498.369614581114400.40

18000.5014667.91036.9212388391642.678240180118000.50

21600.6020317.21241.5715668279769.519419353421600.60

25200.70278951629.99263802021010.260722677725200.70

28800.8039190.82796.96596729781733.544553219228800.80

32400.9060315.85282.93981289463274.337852053232400.90

32760.9163699.36033.7900204693739.710796466132760.91

33120.9268044.66823.17173233164228.965361237433120.92

33480.9372674.77501.77254683484649.558518088933480.93

33840.9477896.38158.79588133775056.778068195133840.94

34200.9584485.28697.04811735325390.383926440234200.95

34560.9693607.310141.92811002376285.912821190834560.96

34920.97104301.613670.47786046028472.88909196134920.97

35280.98124959.425720.1705593115941.224205897435280.98

35640.99156912.941153.921229263725506.980358264635640.99

36001.00499056.1316932.812922883196433.26304384236001.00


1000_100_5_100_1_5_5_5_0_0_waypoint_bounded

43670.441001

49510.50538.625152.374046346566.7796023223

59400.602013.25305.8187916616134.028450248

69320.704280.1875466.7713528413204.5676810819

79210.807807.125743.043190759325.6468537583

89120.90146211357.8844329814595.1077930154

90090.9115670.81251415.9513748125620.5562691603

91080.9216858.93751544.5636479278676.9220129227

92090.9318324.43751711.2082269068749.9558331841

93060.9419951.93751857.6108479711814.1183926753

94050.95220302042.1236658603894.9831652362

95040.9624530.8752036.6637711382892.5903063012

96030.9727812.81252321.14498236681017.2673271556

97030.9832430.18752681.21042861241175.0699706293

98010.99405174017.53260928481760.7278693294

99001.00119273.2461639.4134427840637.104351528

random_walks

0.10.50.9100m, 0.5100m, 0.9

0.1352043123

0.2242816951022320

0.3547237772165614

0.4891756563470969

0.513186818349341416

0.6182101108867491920

0.7243031515095562591

0.83391521074128253489

0.94874430634185784852

0.915098732091193885175

0.925354333698203195452

0.935712935774215835795

0.946089437854225226100

0.956535839774239696482

0.966930143288259726866

0.977500747111280727351

0.988188852712322838225

0.999330361497374189961

11625351247976809517831

random_walks

0.1134.086728497134.0867284970.189.188043762589.18804376250.158.016466735158.01646673510000

0.2195.6516140965195.65161409650.2122.0735860893122.07358608930.282.630702019582.63070201950000

0.3258.4883151032258.48831510320.3148.4828426596148.48284265960.396.176663576496.17666357640000

0.4305.3714939508305.37149395080.4180.6958628626180.69586286260.497.204677901897.20467790180000

0.5440.2590074734440.25900747340.5241.849551943241.8495519430.5139.134972357139.1349723570000

0.6621.1258332689621.12583326890.6309.594049137309.5940491370.6145.5918947741145.59189477410000

0.7923.174367433923.1743674330.7406.1646726067406.16467260670.7218.2011460535218.20114605350000

0.81202.70228607371202.70228607370.8555.4641893997555.46418939970.8278.404123845278.4041238450000

0.91232.05291651481232.05291651480.9977.0919602237977.09196022370.9459.628750438459.6287504380000

0.911288.07967904481288.07967904480.911046.95755505521046.95755505520.91473.7363593567473.73635935670000

0.921342.17919527641342.17919527640.921123.02729137281123.02729137280.92473.2378641143473.23786411430000

0.931485.9191481691485.9191481690.931172.68149210711172.68149210710.93547.2237624011547.22376240110000

0.941632.28346622761632.28346622760.941199.07601277171199.07601277170.94540.2790597501540.27905975010000

0.951478.74833155451478.74833155450.951546.56745121761546.56745121760.95554.7221123167554.72211231670000

0.963490.85785680453490.85785680450.964144.25414194234144.25414194230.961454.17413875661454.17413875660000

0.974668.82228657184668.82228657180.974084.58014646684084.58014646680.971856.58943168141856.58943168140000

0.987040.87185974397040.87185974390.985522.78775425795522.78775425790.982438.25602597182438.25602597180000

0.999511.19441922249511.19441922240.995234.45273127835234.45273127830.994169.49236925884169.49236925880000

183788.488255450483788.4882554504163654.166770403763654.1667704037137368.06362800437368.0636280040000

N=1000 x 1000 mn=100 s=99

GM (a=0.1; 0 friends; sr=5 m)







time (s)

rnxs(t)

broj_associjacija_rwaypoint

0.159.9791761590.186.552004695986.552004695959.9791761590.4364000.436400

0.286.71599868150.2154.3582950859154.358295085986.71599868150.500326.616630401426.61663040140.500365.996601313265.9966013132

0.3120.99650654050.3191.8265783973191.8265783973120.99650654050.600546.444626836346.44462683630.6005110.885038856110.885038856

0.4103.79410664770.4210.2672311376210.2672311376103.79410664770.700574.107098908874.10709890880.7005169.3573319551169.3573319551

0.5151.97200578020.5208.0096290432208.0096290432151.97200578020.8002110.7797704256110.77977042560.8002184.6169411856184.6169411856

0.6170.01238700730.6318.1850685636318.1850685636170.01238700730.9123.652771672123.6527716720.9262.3728078475262.3728078475

0.7254.94667498630.7406.3829160061406.3829160061254.94667498630.9101132.2802103128132.28021031280.9101276.3340579618276.3340579618

0.8309.64833035260.8645.7269086035645.7269086035309.64833035260.9203142.5534706409142.55347064090.9203276.5715615646276.5715615646

0.9505.35431422680.91034.26215063251034.2621506325505.35431422680.9305156.9539671236156.95396712360.9305274.2785457156274.2785457156

0.91505.16904688830.911076.80485095281076.8048509528505.16904688830.94160.9882900939160.98829009390.94283.507555507283.507555507

0.92563.40950087520.921054.57030924181054.5703092418563.40950087520.9501180.8319224316180.83192243160.9501308.9030581535308.9030581535

0.93610.4387855550.931106.76179711981106.7617971198610.4387855550.9601189.2162925343189.21629253430.9601288.5761257717288.5761257717

0.94541.37972470070.941063.5102717821063.510271782541.37972470070.97206.6475915696206.64759156960.97320.1652006407320.1652006407

0.95578.12463366040.951302.76346980271302.7634698027578.12463366040.9801242.1515989229242.15159892290.9801430.3199933346430.3199933346

0.961662.99876462130.963222.31572082083222.31572082081662.99876462130.9901331.4348734952331.43487349520.9901491.339627852491.339627852

0.972374.78348524180.973531.3020880883531.3020880882374.783485241816383.57869708576383.5786970857110034.932855625610034.9328556256

0.983296.37393774020.983710.82658764423710.82658764423296.3739377402

0.994143.72692018980.996150.49395104746150.49395104744143.7269201898

135547.6526838574159512.570433606359512.570433606335547.6526838574

N=1000 x 1000 mn=100 s=99ain=0.1aout=0.9b=0.25

MGM (B=20x20; 0 friends)

MGM (B= 80x80; 0 friends)



time (s)

rnxs(t)

Broj_associjacija_rwalk

0.159.9791761590.186.552004695986.552004695959.9791761590.4364000.436400

0.286.71599868150.2154.3582950859154.358295085986.71599868150.500326.616630401426.61663040140.500365.996601313265.9966013132

0.3120.99650654050.3191.8265783973191.8265783973120.99650654050.600546.444626836346.44462683630.6005110.885038856110.885038856

0.4103.79410664770.4210.2672311376210.2672311376103.79410664770.700574.107098908874.10709890880.7005169.3573319551169.3573319551

0.5151.97200578020.5208.0096290432208.0096290432151.97200578020.8002110.7797704256110.77977042560.8002184.6169411856184.6169411856

0.6170.01238700730.6318.1850685636318.1850685636170.01238700730.9123.652771672123.6527716720.9262.3728078475262.3728078475

0.7254.94667498630.7406.3829160061406.3829160061254.94667498630.9101132.2802103128132.28021031280.9101276.3340579618276.3340579618

0.8309.64833035260.8645.7269086035645.7269086035309.64833035260.9203142.5534706409142.55347064090.9203276.5715615646276.5715615646

0.9505.35431422680.91034.26215063251034.2621506325505.35431422680.9305156.9539671236156.95396712360.9305274.2785457156274.2785457156

0.91505.16904688830.911076.80485095281076.8048509528505.16904688830.94160.9882900939160.98829009390.94283.507555507283.507555507

0.92563.40950087520.921054.57030924181054.5703092418563.40950087520.9501180.8319224316180.83192243160.9501308.9030581535308.9030581535

0.93610.4387855550.931106.76179711981106.7617971198610.4387855550.9601189.2162925343189.21629253430.9601288.5761257717288.5761257717

0.94541.37972470070.941063.5102717821063.510271782541.37972470070.97206.6475915696206.64759156960.97320.1652006407320.1652006407

0.95578.12463366040.951302.76346980271302.7634698027578.12463366040.9801242.1515989229242.15159892290.9801430.3199933346430.3199933346

0.961662.99876462130.963222.31572082083222.31572082081662.99876462130.9901331.4348734952331.43487349520.9901491.339627852491.339627852

0.972374.78348524180.973531.3020880883531.3020880882374.783485241816383.57869708576383.5786970857110034.932855625610034.9328556256

0.983296.37393774020.983710.82658764423710.82658764423296.3739377402

0.994143.72692018980.996150.49395104746150.49395104744143.7269201898

135547.6526838574159512.570433606359512.570433606335547.6526838574

Parameters:N=1000 x 1000 mn=100 ain=0.1aout=0.9b=0.25


MGM (B= 80x80; 0 friends)



time (s)

rnxs(t)

No_of_enco_rw

GM 0f. alpha = 0.1GM 0f. alpha = 0.5

0.00100.0010

0.106375.2305.9517677846134.0867284970.104297.4203.504403159489.1880437625

0.2013877.95446.4271585541195.65161409650.209232.45278.5408360877122.0735860893

0.3022555.1589.8045082014258.48831510320.3014882.9338.8000341764148.4828426596

0.4032459.15696.7799830196305.37149395080.4021391.95412.3019428833180.6958628626

0.5044323.851004.558938304440.25900747340.5029056.2551.8390879119241.849551943

0.6058837.31417.2509750625621.12583326890.6038655.95706.4147786348309.594049137

0.7077408.82106.4488100767923.1743674330.7050845.5926.7643486317406.1646726067

0.80104340.52744.26033558661202.70228607370.8067829.651267.4278252056555.4641893997

0.90150222.052811.23099979551232.05291651480.9097394.052229.4750261229977.0919602237

0.91157227.952939.06980406361288.07967904480.91101873.152388.89052149391046.9575550552

0.92164750.83062.51112307341342.17919527640.92107091.152562.4622877841123.0272913728

0.93174032.23390.48909063011485.9191481690.93112805.252675.76052887671172.6814921071

0.94184295.053724.45519117231632.28346622760.94119074.22735.98610338131199.0760127717

0.95196075.753374.12711324221478.74833155450.95126927.73528.8730734361546.5674512176

0.962103343084.92753476273490.85785680450.96136653.83662.34439726954144.2541419423

0.97229175.54125.91374887534668.82228657180.97149134.83609.60952254724084.5801464668

0.98254011.256222.13231241177040.87185974390.98165082.754880.57684117685522.7877542579

0.99299667.458405.19630300829511.19441922240.99194775.54625.77051903115234.4527312783

1.00583881.474045.241919987483788.48825545041.00396559.3556252.216454366863654.1667704037


0100.4364100

0.12701.6132.378802564558.01646673510.50031007.1186.333571854481.6627380192

0.25634.8188.542219200582.63070201950.60053333.05260.1322487546114.0058201482

0.38980.8219.450653846696.17666357640.70056354.05256.3415638722112.3445107911

0.412848.35221.796320742197.20467790180.800210799.7329.1082208828144.2352988485

0.517505.25317.4705746829139.1349723570.918260.35538.4715478971235.9910804538

0.623076.75332.2036273131145.59189477410.910119456.5606.1734596284265.6621881672

0.730320.95497.8794479961218.20114605350.920320795.1690.1841020603302.4807765486

0.840673.1635.2473119726278.4041238450.930522249.15588.7693923502258.0346641925

0.958543.31048.7557590331459.6287504380.9423900.95653.7286154297286.5037584275

0.9161002.751080.9457299294473.73635935670.950125822.45680.4870140685298.230921043

0.9264074.551079.8082907334473.23786411430.960128266.2755.7428969668331.2126397337

0.9367517.31248.6252693093547.22376240110.9731515.8965.841852588423.2908186697

0.9471440.91232.7792264038540.27905975010.980135927.851204.5830147705527.9217597701

0.9576132.81265.7345942802554.72211231670.990143092.451220.4708528398534.8847796115

0.9682132.41285.07720022051454.1741387566196544.311020.683726520812470.8408675934

0.9789595.451640.69810157961856.5894316814

0.9899610.22154.7262764252438.2560259718

0.99116572.353684.64782684784169.4923692588

1234014.233022.762064656937368.063628004


0.427710000.44031000

0.5003764.6114.016342318949.96891649770.5006488.561.05519504626.7581109949

0.60042208.35185.448042092181.27464485780.61439.890.95840576339.8635221047

0.70024195.7262.4484109707115.02090372320.70012672.4142.104631577562.2789183095

0.87028.85294.1706048143128.92350420180.80034344.85159.868457439970.064110442

0.900411894.4333.4761729041146.14960188070.90037317.9231.7725518466101.5768709478

0.9112663.7390.8426928143171.29111041230.917739.5253.6633699673111.1707628451

0.9213484.2439.0913584354192.43661898150.928227.9244.5061402738107.1575061786

0.930114401.05393.7004572006172.54355709740.93028766.3284.0528305198124.4892782954

0.9415482.4458.7003838076201.03049010120.94019391.35307.4659202339134.7503224675

0.9516779.8559.4654967961245.19190954680.950110180.9382.397134431167.5897515277

0.9618377.65606.768947181265.9231671390.9611153.5392.2776272515171.9199862174

0.970120379.4656.6717036052287.79359920210.9712348.95400.1547694001175.3722304331

0.980123203.7700.6242404569307.05628206960.9813970.1460.7307582297201.9203240311

0.9928000.55933.3035538796409.03055125480.9917030.75444.9063621175194.9851083254

168025.912815.389974557914501.7036142928138491.555183.47771364895865.5458510322

tm_r_analy

MGM 0f 20x20MGM 0f 80x80

0.00000.0000

0.102744.6842105263136.857205644659.9791761590.104755.45197.489633305586.5520046959

0.205831.2631578947197.863825817886.71599868150.2010213.15352.2063203653154.3582950859

0.309232.052631579276.0832148474120.99650654050.3016401.35437.6994011756191.8265783973

0.4013168.5263157895236.8317190705103.79410664770.4023604.7479.7762746158210.2672311376

0.5017848.5789473684346.7614158643151.97200578020.5032193.95474.6250015594208.0096290432

0.6023588.6842105263387.9249716449170.01238700730.6042686.2726.0172971695318.1850685636

0.7030988.1052631579581.7233873717254.94667498630.7056111.95927.2623244912406.3829160061

0.8041578.2105263158706.5386345454309.64833035260.8075034.31473.3843640444645.7269086035

0.9059351.26315789471153.0898510864505.35431422680.90107676.152359.92284162441034.2621506325

0.9162043.47368421051152.6671182004505.16904688830.91112564.62456.99444979331076.8048509528

0.9265114.84210526321285.5570026326563.40950087520.92117902.252406.26088787691054.5703092418

0.9368634.78947368421392.8658537526610.4387855550.93124322.42525.34857208381106.7617971198

0.9472480.36842105261235.2906635249541.37972470070.941312152426.65960573491063.510271782

0.9577396.57894736841319.1331882797578.12463366040.95139861.22972.57447518591302.7634698027

0.9682949.47368421051469.61889876341662.99876462130.96150403.42847.61250690353222.3157208208

0.9790667.47368421052098.63456583942374.78348524180.97163805.33120.66875592583531.302088088

0.98101638.3157894742913.05895070663296.37393774020.98182373.453279.31745907073710.8265876442

0.99118671.6315789473661.87848288174143.72692018980.992146835435.29095720496150.4939510474

1.00231483.26315789531414.035477513235547.65268385741.00435344.952592.220802480259512.5704336063

MGM 5f 20x20MGM 5f 80x80

0.436410000.43641000

0.500346960.732372361326.61663040140.5003803.05150.587437443565.9966013132

0.60051405.65105.974810810546.44462683630.60052535.6253.0114205868110.885038856

0.70052673.9169.093527530374.10709890880.70054703.8386.4303028327169.3573319551

0.80024397.85252.7712248363110.77977042560.80027826.2421.248845071184.6169411856

0.97419.95282.1441354306123.6527716720.913181.85598.6679314155262.3728078475

0.91017852.4301.8297533379132.28021031280.910114040.35630.5239487918276.3340579618

0.92038362.75325.270717209142.55347064090.920314967.15631.0658715305276.5715615646

0.93058909.5358.1289829392156.95396712360.930516018.4625.8337933047274.2785457156

0.949568.5367.3342805732160.98829009390.9417242.5646.8920433809283.507555507

0.950110360.4412.6123961706180.83192243160.950118615.65704.8381131788308.9030581535

0.960111330.6431.7433935739189.21629253430.960120335.85658.4572299582288.5761257717

0.9712502.85471.5171789023206.64759156960.9722557.45730.5354543073320.1652006407

0.980114262.65552.5282822006242.15159892290.980125552.3981.8806391175430.3199933346

0.990117119.15756.2499778164331.43487349520.990130880.31121.1119057718491.339627852

140515.055641.27171622826383.5786970857170896.758868.032428038210034.9328556256

waypoint

1000_100_0_100_0_0_walk_bounded1000_100_0_100_0_0_walk_torus

9900.1386861.817405.52323288617628.15542665859900.1345074.1514040.53454626026153.4133940817

19800.2846664.5533344.811390702714613.717758297919800.2740753.923861.624835266110457.6105263021

29700.31381499.6543121.927354486718898.642675423929700.31174154.525509.132827902611179.6484028049

39600.41996303.757024.678648441824991.671095741239600.4169384034426.177769097115087.6380591809

49500.52733677.760450.200018905326492.942219947649500.52304380.551070.261763368222382.0846520172

59400.63619066.589698.998007957639311.538599852759400.6304918153859.11308316623604.3283642353

69300.74744656.9598041.147456978142967.574200627469300.7400665173167.367898969532066.3761166518

79200.86365755.8141338.03968896161942.897091974379200.8534050085719.986921923537567.6947289993

89100.99172221.5196249.46398277586008.412021222789100.9768651392310.413286111140456.019082213

90100.919581867.5218333.29795247195686.886818181590100.91805331191408.577848091140060.7801228068

91080.9210032911.45238464.514488115104509.60628526891080.928441852.5126049.3187052355242.4527342679

92080.9310571116.3274014.430863595120089.73472429792080.938883821149188.43464064665383.4160612036

93060.9411174982.4273831.076319633120009.37764793693060.949364060176330.50080967177278.7148446832

94060.9511886982.05302848.157160352132726.42152643994060.959963723.5199361.5150602587372.3014600551

95040.9612728822.8337453.66718387147892.65385086895040.9610696635226111.19824918999095.6342348819

96040.9713888370.75466328.29364978204373.32771978796040.9711704950244323.014190555107077.156004934

97020.9815564341.2537815.524771273235703.36604841897020.9813067745259492.789627036113725.471213198

98020.9918347475.25616456.951959212270168.80679026498020.9915385650393245.578152943172344.05141749

9900137584093.255662482.701615182481643.187093399001292707652618061.048557441147393.06182669


100_100_0_100_0_0_walk bounded100_100_0_100_0_0_walk torus

9900.12749.7894736842148.654176959465.14927195799900.12446.183.517347709436.6023646992

19800.26199.6842105263262.1954429284114.909937728319800.25333.55167.713563773773.5022506653

29700.310142.7368421053478.4665136437209.693031556229700.38530204.82649910889.7673887644

39600.414948.1052631579623.6379732164273.315965628239600.412327.05219.146064003996.0430901729

49500.520419.2105263158727.0164738274318.622691538449500.516806.5255.8069790415112.1101255758

59400.627271.1578947368730.3572385528320.086817162759400.622212.9365.5517675197160.2069447623

69300.735927.1052631579963.4096218199422.224499456369300.729260.5619.9603128215271.7041918985

79200.848021.57894736841072.8902457996470.205545745579200.838950.8753.0043405201330.0121501423

89100.968603.26315789471517.6567772612665.129202171789100.955461.31014.796640245444.7454060797

90100.9171806.26315789471467.9179829534643.33064727490100.9158037.951047.9923400181459.2937740878

91080.9275163.42105263161574.3202524613689.962572019791080.9260945.551152.9254997156505.2818458552

92080.9379424.10526315791616.7622959599708.56324837492080.9364173.31148.3439380255503.2739277822

93060.9484005.63157894741461.6255110331640.572904620593060.9467973.81211.1527610199530.8005615729

94060.9589440.10526315791732.9425487281759.480478138894060.9572501.91451.8951281542636.3084609742

95040.9696216.47368421051510.2590421081661.88706616795040.9677672.251627.0217504126713.059563257

96040.97104637.4736842112433.67870536271066.585541535596040.9784780.51671.1985456394732.4205129816

97020.98116618.7368421053481.2918394391525.713124591697020.9894727.21828.709455787801.4513423295

98020.99138040.8947368423695.36575989661619.533293982498020.991124552472.79796778341083.72997379

1289350.15789473754477.032985636523875.138324625699001226878.146861.683921829720537.6307122592

avgstdevconfint


44060.45101144060.451011

49530.50415733249530.503925122

59470.6013821084759470.6012828236

69390.7027071556869390.70243011048

79240.80476022910079240.80408817175

89100.90825539417389100.906858230101

90090.91877340617890090.917289256112

91090.92933242718791090.927753251110

92080.931000445419992080.938260259113

93070.941075950822393070.948868273120

94050.951168253023294050.959594281123

95040.961279859526195040.9610473328144

96030.971414164828496030.9711592347152

97020.981611271931597020.9813147370162

98010.991928087438398010.9915601532233

99001.00404343454159699001.003565624561765


100_one-node-s=100 bounded100_one-node-s=100 torus100_one-node-s=100 torus 4 directions33_one-node-s=100 bounded 4 directions33_one-node-s=50 bounded 4 directions

100.12629.2980.3597406323429.65344283970.192101.75810.8066727194355.34463616640.11518.25805.3582971834352.957134777143.2548.054656382121.0604818857118.3585.181091922237.3315507485

200.26231.851686.2173573759739.00330964760.2194884.951128.4932886958494.57416987320.23259.551186.3352004787519.9244543832336.778.645172502234.4671121506330.6193.734598708884.9063194687

300.310183.42513.26850304961101.46757395330.3298359.71670.5581197848732.13983954860.35326.11563.778787021685.3432590468579.5148.094742079464.9041501438537.5215.288423430494.3525203011

400.414055.752833.28217471871241.71708654520.439123782244.2548640332983.56853113930.48012.42277.1107825026997.9688545743854.7177.502290570877.7923318296805.25220.742973900296.7430370588

500.519527.253109.98593455951362.98555375670.54916516.32319.31333077611016.46370141020.511097.852788.80303082471222.22361234741183.35209.651157627991.88192653861119.3251.5853104238110.2600303862

600.625542.453792.17609344351661.9628967540.65922116.652418.92140545941060.11799811060.614552.42909.93648691771275.31168226331567.75266.9413251122116.98997277941474.6275.2085142502120.6131593798

700.734283.154235.0179180011856.04319877850.76928878.653150.22512604051380.61962107520.719140.353533.38584117721548.54522133232013.7316.5205738719138.71862404911903.95343.9957886829150.7599392389

800.845671.255332.32525437272336.95021217880.87939487.54052.01732084421775.83962868240.826414.15452.81715600682389.75711379432587.1360.2366035348157.87765503892630.85456.2875680279199.9730470385

900.966574.68415.48740434163688.17994720720.98954969.67214.05347331093161.63555753770.936690.157292.54380045673196.03755750363654.1470.6601075533206.27197062093650.9598.3722569561262.2432252625

910.9169192.69470.80954356744150.68648601180.919057208.257767.05323025273403.99357461160.9138070.958014.25721990773512.33640430323767.55488.3707042164214.03383447114090.95624.9045800845273.8713077981

920.9271894.49720.88520660544260.28489682110.929160483.759773.35954130844283.27862507780.9240583.459331.24553357674089.52102306624018.8596.4707254474261.4098581574485.05751.041135253329.152040931

930.9376332.210227.26479151634482.21132140110.939261656.810183.7413846524463.13282672510.9341978.359607.34497128994210.52463945614152.95578.5422219956253.55249425914889.4962.2920773368421.7350906091

940.9479807.8510768.76484279764719.52967678440.949364691.9511375.38350758944985.38264392940.9446138.459555.9227292764187.98827611514346.85596.882715712261.590417423557311095.9825200296480.3263980619

950.9584927.9511800.92606301465171.88568800320.959469216.3511018.08747505194828.79386270990.9549044.7510169.62744685844456.9511209444563.05614.6159669599269.36220989487136.251332.5718258513584.0142644361

960.9693668.511662.64749892625111.28358586750.969574199.613065.4623436235726.07764471010.9652180.5510256.18001358464494.88373561524959.4814.5391593443356.9807486324

970.97102798.1512301.95522018655391.46722875790.979685385.617729.49199379097770.13817710490.9755986.4510183.4563332944463.01178257825698.11262.4532466591553.2840256183

980.98109681.5516902.5922723027407.74703582370.989790783.9517788.24660000627795.8880073310.9861248.611040.6024120544838.665482431562051430.7566639995627.0448500432

990.99118963.419263.41472816998442.40345229660.999899874.7520786.91130413059110.08466372780.9969120.2512569.71421135995508.81555268517085.052021.5808424675885.9800468598

1001148732.633441.897338833114656.279456614199128565.0542503.767296156118627.7274641771193151.7528045.237317544112291.13382498438274.32430.01641969761064.9814324348

100_one-node-s=50 bounded100_one-node-s=50 torus

100x99 0 friends 4 directions bounded100_one-node-s=100 bounded 4 directions100_one-node-s=100 bounded 4 directions 2 friends

50.12442.951056.60461534463.06859807230.081632653141934.15743.0869662924325.6657555513

100.25878.61888.1413138461827.49870525960.183673469495028.81337.0322044698585.96856467230.11733.572.618324496231.82577970091734733210.78.80251160333.8577975607

150.39276.92198.4669036208963.50230936710.2857142857148403.71900.7898662897833.04134782230.24018.65139.054807445460.9422993276401913961598.3552.805776199223.1427124202

200.415073.13385.37307125511483.67699638840.3877551021912117.72187.6071065508958.74204974790.36641.2248.958166006109.108655439666412491091382.8581.007650710835.5024942189

250.519609.555521.98512622142420.07073776850.48979591842416802.63044.42358903521334.25097372930.49700.7309.1795765026135.501351181997013091362344.65101.843158569344.6338847827

300.626443.156011.87381485922634.7698456140.59183673472922039.254119.43248358831805.38503979390.513423.95309.4219525774135.6075751635134243091363532.3163.240893999371.5421178697

350.734998.856706.98733274332939.41099288370.6938775513428941.254577.71568953452006.2325223780.617802.2346.2196747123151.7345817598178023461525060.75178.575614236778.2627277355

400.844470.97698.7389732963374.05706120410.79591836733939246.855541.86247692582428.78009247570.723697.45371.1760080439162.671969427236973711636989.75210.412095659992.2154160034

450.965630.812006.3856720195261.93062223950.89795918374455188.658508.72625308873729.03965442510.831714.65477.1540935037209.1180314143317154772099802.55299.7469941906131.3674182008

460.9271827.512624.02981577095532.61996393120.91836734694559838.47503.26983738643288.38770095690.945643.451033.084521686452.760658246245643103345314493.85483.1509816327211.7462336183

470.9478773.8513220.58723624085794.06781713570.93877551024664241.559252.50543295394055.00877992690.9147525.451064.3950827137466.482856114247525106446615248497.3457973134217.9672677702

480.9685123.4512168.83394264565333.12536419520.95918367354770507.39338.10156576984092.52219427840.9249853.31081.740901948474.084852242849853108247416025.95484.3949535788212.2914180106

490.98107783.6520078.01504729678799.41100487660.97959183674884118.4518736.00183287728211.251804560.9352351.91267.3469553612555.428747300652352126755516929.65516.1822684226.2225584741

50113650745745.321907502820048.3906435113149110193.47368421127810.605222085912188.29312425890.9455404.551203.0036301734527.229577093155405120352717956.55588.540431469257.9343195671

0.9558858.451354.0061600963593.408097252458858135459319185.95510.5783588503223.7665834564

0.9663346.751488.1784299854652.210570775363347148865220744.55526.3563406747230.6814575898

333_one_node_s=50_bounded0.9769305.051794.265411189786.356558040969305179478622816.15530.2418787685232.3843374104

0.9877733.152518.73279072091103.8623581467777332519110425455.15611.7075561169268.0875668427

50.143185.812018.81477933665267.3778152740.9991657.42854.2889500761250.9235369747916572854125129763.6669.7459376902293.5235261404

100.279196.225584.224234867911212.56776395521181329.334661.658146779515190.8530512386181329346621519169450.411556.28621550795064.6695831586

150.3157492.841791.27708266418315.4869942461

200.4217077.856659.592472943224831.6898041854

250.5277875.478256.18029459434296.6320356738

300.6331804.298137.796231625343009.9689695754

350.7459421.4115828.1792993450762.9739892368

400.8688876.487735.318169480938450.9685045197

450.9852799.8174606.57693998876523.2534705379

460.92956565.6260847.229279515114319.168229868

470.941049766.4236427.866522329103617.113825013

480.961125502.4232601.649361736101940.232056041

490.981403166347910.298988834152475.51645024

5011824542.4678266.457449651297257.737672863

avgstdevconfint

333_one_node_s=100

100.131129.810514.6058271344608.1416917595

200.276067.421229.93738332749304.2536427845

300.3115908.235245.527314823915446.7401382139

400.4180545.642400.651048067718582.5518392832

500.5240664.838536.272363839216888.9453627013

600.633652432853.992641686614398.6237546084

700.7450327.451555.172934439722594.6217795421

800.8664456.452363.775606807122949.0007974401

900.9859068.479522.563802986434851.6385417399

910.91906595.274660.366615761732720.7271276205

920.92964328.8107914.64077084247294.7786596118

930.93975174.2105196.74181598946103.6295386884

940.941078547.4137573.80196570960293.2323811939

950.951148195.4203941.37524004389379.5515846333

960.961197720.2221470.93929046397062.0759005378

970.971251220185438.13920550481270.3048087638

980.981362745.6187868.08779380282335.2565133414

990.991540303213977.48218095393777.9858747725

10012000558.8497932.595616817218224.438583001

33_one node_s=50

50.1207.8143.595612746462.9323572114

100.2557.8290.2889939354127.2223455263

150.3966.4346.4127595802151.8192033276

200.41303.6349.498640913153.1716247744

250.51861.4446.776566082195.8047457899

300.62655.6629.7783737157276.0073014814

350.73495.2902.4204674097395.4956988151

400.84494.8624.9645589951273.8975942156

450.96141.2976.3624839167427.9016011038

460.926996.8835.2731289824366.0676389539

470.947614.81264.4683467766554.1671654162

480.9682511368.5868624242599.7982504733

490.9890241265.6847948838554.7002871833

50112460.42002.4018827398877.5746567407

33_one node_s=100

100.1308.879.578263363834.8760494871

200.2619.6170.303552517374.6374056728

300.3959.2171.536293535875.1776679875

400.41283275.4106025555120.7017268031

500.51700.4315.3352184581138.199128997

600.62419.2372.2636162721163.1486256995

700.73067.4463.0521568895202.9377025352

800.83785.8512.031932598224.4036281444

900.954241096.8935682189480.7256749548

910.9159281279.5372210295560.7712653544

920.926151.81380.4260936392604.9869238156

930.9366011516.5475594257664.6436538868

940.946799.21537.1604340471673.6774729849

950.957344.61691.7225836407741.41603563

960.967863.41656.6169744392726.0306161444

970.978436.62038.7677160481893.5123833068

980.989202.82229.3581363253977.0407319838

990.9910243.22456.44167445521076.5625910789

100111465.62886.26130140711264.9357717246

avgstdevconf

analy graphs

500_1500_5500_101000_11000_51000_10330x330500x5001000x10003330x3330

92483342547719101113899715551154469197

26031866548651126181805875858611112304

1320145954843291703842638601211134

123214886341396735184341136411

5808186298150016642360646334229111178

65302006130393098547204203173417481111

1927313927026719892439199503523123111

170233986675581190599240239122587965

135631753551512821282703984231121411

115447653714543151791253723111111

124784609178543164119245936111111

472217081508671595973176508012311

314224623533817950570740325761113194474

6395267792823283347107190429190122381247

17145293276641316308361590381210711

1517618321255051539383224421621111

12474050331114419012150211112258

5615156319957941398074503147124111

1199916257712908882726201187011

921063229178026889893753936791111206

2390582563112611223254295142111111

2582529952366568170888042987261111711

2744416097076614863371861121122111

23052482620421518749409954206365551111

194404006906349205177453338366111111

12613966296472449407726817711371121

2348160767930516847205118262421121111

151208120458118038224332911146508

1317444107908411230685986241156011

768736737450761236883342123111111

228283584838998069760100065251820111111

963049273435262163059170952111111

14475500012983461691159992232271178618

16364312148051646561393349521111931

121647547676089225504232319314611411

217728633586471596817356941668311265661

19641569668525181449347189851111

4102429871712351205593156429116511

492389823584033506184897384228111111

240221175781604436285358371896111111

26423328569911560782318528441111

13241352329438071501453060165632211

670947202143044343661840412654028010911

8547515758944118749421374711331513

55991633260226180826269854129211

159086290755092674378492489125711

111888959791293233165199441111

283594713845238715101606425149111111

11894643059323209505132528212211408

256538511926978013263525455732111111

1354727226318948150516326789111111

3118571528103997445337014115689011198518

13120883935285402518253457817711613

1152315239312436163495401661111

1224676676945986573259863112611

136834524372683114067890402125611228

4471464041645301115609597283111111

118276555896405102125171331111111

385825547702566015118534927295811427

26516978053238690032716431698593559511

547031758525521168881734334118711

111920719001481769482532382311864

38592281413548811175683400741121411

1115257927321976961086192166201111504

1534270701034193160373441123111111

30697989848294404763524783311411677541

1138131348181131049156172111112

140221591484610113688048030576861302

836664264238203688591702581001111560

3346134534758510113261032227881851111

1486327491125718364001232772825091001111

147597611023683183629137004111142

1531705125039022843612340711111230

904278911402356342608453748441111393

15065259766524372131816305648824814110

8504372341969360602330271739713311914

115963770311077802436271601111

2431271687494799898560923084311111419

166029523581805622030391114711

2091605676002812109674122671122111

366850466512621176694273911101812400

20142836288103913312251245052111111

171314421241692546179559594064131111

13045060200174010545922691481511999

579695267961899141217690614111211

14177810067114059597520330415111111

5444168053890639994101365176911111

413109229557726311512092097221142511

875642511473525771361240240257111052702

3256277698170016375729419832711337

31901769273852598934658154358901111235

1277945581111949627904913221111

1515119146711379132027731111343

657596487406251371214010251380341211

511077438536713188589567198383111111

11648064456177361157352064472611247

126962298852635711132465481145411

5967394795187576107117460311172526

791150287493412501458457462693211811

5902541550018511789829187990426174113

39552947712458313631198977239848111111

13744599165145571127304141511127811

18570468707351812182363257971158011

1807372914862249251187401909321113711

178257040129556739191103182598361111902

11372519161092492787415239912491111

4941419944789621978473091251288948

11835494163191562295162022341214973

51451780221298137722443624187177325111

14381183954750341222147228491111111

135891546024031625395335623248511165

479256188574610435209058289204841111

1625368407101544062701698901117411

6857530436108939371900824019906521911

34302363893030169978397739118209649

2520245788211293625273349871691424

1460745153212695064547862181282171

1747457174740022155142031279775601111

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peer-to-peer security in wireless ad hoc networks + commonsensenet

Documents

mobile networks

networks of vehicles

networks of cars

crisis networks

selfoperated networks

peer authentication

peer securitycooperation

peer securitypeer