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56 lines
2.0 KiB
56 lines
2.0 KiB
// Simple peer-to-peer file distribution protocol based on BitTorrent
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// gxn/dxp Jan 2006
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ctmc
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// N=4 clients, K=4 blocks to be downloaded
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// Actually there are N+1=5 clients, one of which has all blocks initially
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// Rate of block download for a single source
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const double mu=2;
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// Rate of download of block i:
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// A client can download from the single client which starts with all blocks
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// or from anyone that has subsequently downloaded it.
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// Total number of concurrent downloads for each block is 4.
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formula rate1=mu*(1+min(3,b11+b21+b31+b41));
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formula rate2=mu*(1+min(3,b12+b22+b32+b42));
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formula rate3=mu*(1+min(3,b13+b23+b33+b43));
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formula rate4=mu*(1+min(3,b14+b24+b34+b44));
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// client 1
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module client1
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// bij - has client i downloaded block j yet?
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b11 : [0..1];
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b12 : [0..1];
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b13 : [0..1];
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b14 : [0..1];
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// Downloading of each block (see rate computations above)
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[] b11=0 -> rate1 : (b11'=1);
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[] b12=0 -> rate2 : (b12'=1);
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[] b13=0 -> rate3 : (b13'=1);
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[] b14=0 -> rate4 : (b14'=1);
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endmodule
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// construct remaining clients through renaming
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module client2=client1[b11=b21,b12=b22,b13=b23,b14=b24,b21=b11,b22=b12,b23=b13,b24=b14] endmodule
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module client3=client1[b11=b31,b12=b32,b13=b33,b14=b34,b31=b11,b32=b12,b33=b13,b34=b14] endmodule
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module client4=client1[b11=b41,b12=b42,b13=b43,b14=b44,b41=b11,b42=b12,b43=b13,b44=b14] endmodule
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// labels
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label "done1" = b11+b12+b13+b14 = 4; // client 1 has received all blocks
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label "done2" = b21+b22+b23+b24 = 4; // client 2 has received all blocks
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label "done3" = b31+b32+b33+b34 = 4; // client 3 has received all blocks
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label "done4" = b41+b42+b43+b44 = 4; // client 4 has received all blocks
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label "done" = (b11+b12+b13+b14)+(b21+b22+b23+b24)+(b31+b32+b33+b34)+(b41+b42+b43+b44) = 16; // all clients have received all blocks
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// reward: fraction of blocks received
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rewards "frac_rec"
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true : ((b11+b12+b13+b14)/4)/4;
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true : ((b21+b22+b23+b24)/4)/4;
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true : ((b31+b32+b33+b34)/4)/4;
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true : ((b41+b42+b43+b44)/4)/4;
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endrewards
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