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Technical Report Towards A Field Theory For Networks Jon Crowcroft Number 554

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Technical Report UCAM-CL-TR-554 ISSN 1476-2986 Number 554 Computer Laboratory Towards a field theory for networks Jon Crowcroft January 2003 15 JJ Thomson Avenue Cambridge CB3 0FD United Kingdom phone +44 1223 763500 http://www.cl.cam.ac.uk/ c 2003 Jon Crowcroft Technical reports published by the University of Cambridge Computer Laboratory are freely available via the Internet: http://www.cl.cam.ac.uk/TechReports/ Series editor: Markus Kuhn ISSN 1476-2986      !" # $&%&')(+*,%.-0/1*,%3254 6 798;:<>=@?A: BDCFEHGIAJKC5L;MONQPHRAETSUL;VWCYX1RZCFBDM[C5LQ\]M^LQCF_9\]RZ`aNcb@RZC5C5LQ\]M@GFRZ\YL EHM[C5LQ\YL;G5CYEHM^de.L;NQRAf1G5L0CYX^L BDM[C5LQ\]M^LQCb@f^CYGJgLQhNiIjM1GYC5\]RAEHM[CYGkIjM GYIjf^\]NiL;GQl_X1EHGPmL;RAV@GC5I+EHM1M1InZRZCYEmIjMolaBDCRAPHGYISpRZqAL;G CYX^LGYCYf1V^rIAJsBDM[C5LQ\]M^LQC!C5\]RZ`aNZt@h!X1RZChuLSpEmdjX[CvNQRAPCYX^LG5L;RZ\wN]XxJKIA\!CYX^Lzyw{@|~}Qw{€};| ‚„ƒ†…Z{ˆ‡At nALQ\YrpV1Em`‰NQf1PmCQl9Š‚CuCYX^LvG]RASULvCYEHSpLAt,C5\]RZ`aN!NiIjM,C5\]IjP9‹ŒNiIjM^dAL;G5CYEHIjMNiIjM[C5\YIjPK RAM1VUL;M^djETM^LQLQ\]EHM^d RZ\YLke.IACYXX^IACŽC5IAbEHNQGQl ‘X1RZC!EHJ“’•”RAGYX+Ni\YI>hvV1GY–0‹ŒRl—q€l˜Rl™wƒm…š™]›œjA|TwtžNQRAGYNQRAV^L;G;t€LQbEHV^L;SpEHNQGvRAM1V+G5I‰IjMxRZ\]LCYX^L M^IA\]S‰Ÿ WX@RZCaEmJvCYX1LFC5\YL;M1V¡NiIjM[CYEHMˆf^L;GUJgIA\aM^LQC~huIA\Yq¢PHEHM1q NQRZb@RANQEmC£rC5I e€L;NiIjSpLF”@RZC5C5LQ\;t hvEmCYXpSpIA\YLŽL;¤[f@RAP1NQRZb@RANQEmC£rpEHM¥CYX^LvRANQNiL;GYGuRAM1VUNiIA\YLAtˆIA\ LQnAL;MSUIA\YLNQRZb@RANQEHC~rpEHM¥CYX^L!RANQNiL;GYG CYX1RAM CYX1LaNiIA\YLc‹ŒRAGEHM0CYX^LpL;RZ\wPmr¢¦;§A¨Z©AGhvEHCYX¡¦Q©jªe@b@Gk«Š­¬­GknALQ\]GYf@G®e1bGPHEHM^qG“EHM¯CYX^L Š!°!±.Š!¬­²³_!5Ÿ´!IhµNiIjf1PHVFhuLNiIAb.L>Ÿ _X@EHGkEHGR[email protected]\RZe.Ijf^CCYX^L‰f1GYLaIAJŽ¶1L;PHV L;¤[f1RZCYEHIjM1G‹gLAl—d^l+dA\]R;nEmCYRZCYEmIjM1RAP·t3L;PHL;NiC5\]EHNQRAP¸t SpRZdjM^LQCYEHNZt¹G5C5\YIjM^d0RAM1Vºh¹L;RZq RZC5IjSaEHN»RAM1VºGYIxJgIA\YCYXkRAGzRcJŒf^CYf^\YL‰SUIˆV1L;P³JgIA\zSaRAM1RZdjEHM^d M^LQC~huIA\Yq¢C5\]RZ`‰NZl¼¯Lxe€L;PTEmLQnAL»CYX1RZC‰EHM½CYX1LJgf1CYf^\YLAtuIjM^L+NiIjf1PHV¾SUInALxJK\YIjS CYX1EHGUSUIV^L;P C5I+R»nALQ\YrcdAL;M^LQ\]RAP&b1\]L;GYNi\]Emb1CYEHnALC5L;NwX1M1EH¤ˆf^LUJgIA\kV^L;GYEmdjM1ETM^dM1LQC~huIA\YqcNiIjM[C5\YIjPsIjM V1E†¿.LQ\YL;M,C CYEHSUL;GYNQRAPHL;GQtŽEHM1NQPHf1V@EHM^dcC5\]RZ`aNFL;M^djETM^LQLQ\]EHM^d RAM@V¢CYX^LxGYLQCpIAJRAV1SpEHGYG]EmIjM¢RAM1V¾NiIjM1dAL;G5CYEmIjM NiIjM,C5\]IjPPHRhvGQl&¯L!RAPTG5IG5b.L;NQf1PHRZC5L!RZe€Ijf1C CYX^Lvf1GYLIAJ.CYX^L!GYRASpLvEHV^L;RkETMUhvEm\YL;PHL;GYGsM^LQC~huIA\YqGQl À Á Â0ÂÄŠƢǢÈÎÉ>Åx Ê Ë.̚ÍwÌpΈ̥̈́Ï5Ð!ÑÒ.ÑÓ+ÔgÕoÎ,ÏiÔgՀÖ̈́̚ΈׄшÕoΈØ.ÙKÌpΈׄ×wÚ.ÓxۏÏiÔgшÕ.דÔgÕ¯ÓÚ.ÜQË ÑˆÝ ÏiË.Ì¥Ð!Ñ̈́Þ0ΈØ9шڀÏܚшÕ.Ö̚×]ÏiÔKÑÕ ÜšÑÕ^τ̈́ÑÙsÎ[Õ.Òº×wÜQË.̚ҀÚ.ÙgÔKÕ.ÖxÑ[ݹτÍiÎ[ß+ÜpÔgÕ¯ÏiˀÌaà5Õ^τ̈́̚ՀÌ>ÏkÐkË.ÔgÜQË Ð­Ìpá1Ú.Ì>×wÏiÔKÑÕ ÔgÕ¯ÏiË.ÔK×ÛoΈÛ̚Í>â ã­äjå€æOç èéå€êAä,ë¸ìµí¯îšîZï¹ð¼ñ³êjë·òó ÊË.Ìôö́×]ςÔg×sτËoÎ[Ï ÏḯÎ[ß+Ü!ÔK×¹Êõ“ö¢ÎˆÕ€Ò‰ÏiË.Î[ςÎ[Û.Û.ÙgÔKÜZÎ[τÔgÑՀ×sÚ.×iÎˆÖˆÌ Ý·ÑÍwÓxׂÎpÓ+ÔT÷‰ÑˆÝ­øwÓ+ÔgÜ>̚ùUÎ[Õ.Ò̚ÙgÌ>Û.ËoΈÕ^τךúŽûŽÙgÌ>Û.ËoΈÕ^τ×!Î[̈́̓ÙKÑÕ.ÖUÙgÔTüÌ>Ò&ýˆÏiË1Ú.×Íwׄ̚̚Έ̈́ÜQË+ÓxΈÔgÕ.ÙTþ Ü>ÑÕ.ܚÌ>Õ^ÏiÍiÎ,Ïi̚×Uшս×wτÌZΈҀþº×wÏiÎ[ÏiÌØ9Ì>ËoÎZüÔKÑÚ.ÍшÝÊõ“ö¹ú&ÿºÔgÜ>̻ΈÍw̉üˆÌšÍwþº×„Ë€ÑÍwÏUÙKÔKüˆÌšÒ&ýØ.ڀÏzÕ@Ú Ó+̚ÍwÑÚ.ךú¢ÊˀÌ0Ø9Ì>ËoÎZü@ÔgÑÚ.ÍшÝÎٌÎ[̈́ÖÌxܚÑÙKÙg̚ÜÏiÔKÑÕ¼Ñ[ÝkÓxÔKܚÌcÔK×ÓxΈÔgՀÙKþ½ÏiΈވÌ>Õ Î[×Ý·ÑÙgÙKÑAÐkÔgÕ.Ö Ï5þ@Û.ÔKÜZΈÙsË1Ú.ÓxÎˆÕ ×„Ìš×wׄÔKÑÕÎ[̈́̈́ÔTü[ΈÙ3×]ÏQÎ[τÔg×wτÔgܚΈÙ&Ø̚ËoÎZü@ÔgÑڀ͚ú  ë 1ä,å€ä[ç ³ë£ç å  1 ê òä  í¯îZîZï³ðWñ êjë·ò9ó ÊˀÌ×w̚ܚшÕ.үΈ×wׄÚ.Ó+ۀÏiÔKÑÕ+Ôg׎ÏiËoÎ,ÏvτË.Ìà5Õ1τ̚ÍwÕ.Ì>Ï­Ôg×Ë.Ô Ì>ÍiΈÍwÜQË.ÔgܚΈقÔgբτË.ÌFׄÌ>Õ.ׄÌFÏiË.Î[ÏaΈܚÜ>̚×w׉Õ.ÌÏ5Эш̈́Þ1×Î[̻̈́üÌ>Íwþ¢ÓÚ.ÜQˡׄÙgÑAÐ!̚ÍUÏiË.ΈբÏiË.̾øwÜ>Ñ̈́Ì>ù ÑÍkÜ>Ñ̈́Ì>ךú à5Õ.Ò.̚Ì>Ò&ý‚×wÑÓxÌ+̈́Ì>ׄ̚Έ̈́ÜQËOÔK׉Ò.ÔK̈́Ì>Ü>ÏiÌ>ґÎ[ϽøwÓxΈÞ1ÔgÕ.Ö ÔTÏ×wÑù.â k̚Ü>̚Õ^ÏÐ!ÑÍwÞ¼ÑÕ¼à5Õ^Ïi̚ÍwÕ.Ì>ÏFÿºÌZΠׄÚ.Íw̚Ó+̚Õ^ÏΈÕ.Ò Û.ÍwÑjü@ÔKׄÔgшÕ.ÔgÕ.ÖFË.Έ×Ø9Ì>ÌšÕ ÓxÑ[ÏiÔKü[Î[τ̚үØ^þ0ÐkËoÎ,ÏkÑÕ.ÌpÓxÔKÖË^ϓܚΈÙgÙ3τË.ÌUׄ̚Έ̈́ÜQË Ý·Ñ͓ÏiË€Ì à5Õ^Ïi̚ÍwÕ.Ì>ÏûŽÍ„ÙgΈÕ.Ö ÓxÑ@Ò.Ì>ÙDú z×pÐkÔKτ˾τË.Ì+ö Ê ‰ý³ÔgÓ+Û.ÙgÔKܚÔTÏzÔKաτË.ÔgՀÞ@ÔKÕ.Ö Ôg×aÎ0ÏḯÎ[ß+ÜxÓxÎ[ÏiÍwÔT÷ºÏiËoÎ,Ï ËoΈ×zÎcÛ.̈́Ìݷ̚Íw̚Õ.Ü>̻ݷÑÍ×wË.ÑÍ]ÏUÙgÔTü̚Ò3ý3ΈՀҽÙgÑ@ÜZΈÙKÔ >ÌšÒ ÜZΈÙKÙgךýÑAüÌ>Í¥ÙgÑՀÖ̚Í>ý3ΈՀҽÙgÑՀÖ 5Ò.ÔK×wÏiΈÕ.ܚÌ !ÏiË.ÔK× ÜšÑڀÙgÒ Ø9ÌUÍwÌ •ÌšÕ€Ý·ÑÍwܚÌ>ÒØ^þ¯Û.ÍwÔgܚÔKÕ.Ö.ý.Ü>̈́̚Î[ÏiÔKÕ.ÖÎ+×w̚ÙTÝ •Ý·Ú.ÙTôoÙgÙKÔgÕ.ÖaÛ.̈́шÛ.Ë.̚×]þú        !#"$%'&#(*)+ -,. %/ 10# 324" 5 " 6  798;:< >=?@" 6)A ! :5 B %CD E - FG%*"/!#HG%/I 9 !#J (C 30B #K%/IL(M  /!#J8 !# / #J8 L  #%  :5/  #;8 #$  #%N 8O" :5 P-:Q%/ ' :9   /8R:4%''S  "6 #/!9 8O" :5 T 8Q 8U2A)V )W L@  X " H )Y:5 B %V F[Z  )V #IB\]P  H"S @8  @ " ^&BS:98(,9  798 $ %/&H:9% _ 5,. 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