Consider distributing a file of F bits to N peers using a P2P architecture. Assu

Question

Consider distributing a file of F bits to N peers using a P2P architecture. Assume a fluid model. For simplicity assume that dmin is very large, so that peer download bandwidth is never a bottleneck.

a) Suppose that us<= (us+u1+u2+...+uN) / N. Specify a distribution scheme that has a distribution time of NF/us+u1+u2+...+uN.

b) Suppose that us>= (us+u1+u2+...+uN) / N. Specify a distribution scheme that has a distribution time of F/us.

Is this possible, or are the two questions wrong? I can do this if I switch around on the questions, like in a) if us>= (us+u1+u2+...+uN) / N, then I find it easy to calculate a scheme such that distribution time is NF/us+u1+u2+...+uN.

Thanks in advance!

Explanation / Answer

a. Consider a distribution scheme in which the server sends the file to each client, in parallel, at a rate of a rate of us/N. Note that this rate is less than each of the client’s download rate, since by assumption us/N = dmin. Thus each client can also receive at rate us/N. Since each client receives at rate us/N, the time for each client to receive the entire file is F/( us/N) = NF/ us. Since all the clients receive the file in NF/ us, the overall distribution time is also NF/ us. b. Consider a distribution scheme in which the server sends the file to each client, in parallel, at a rate of dmin. Note that the aggregate rate, N dmin, is less than the server’s link rate us, since by assumption us/N = dmin. Since each client receives at rate dmin, the time for each client to receive the entire file is F/ dmin. Since all the clients receive the file in this time, the overall distribution time is also F/ dmin. c. From Section 2.6 we know that DCS = max {NF/us, F/dmin} (Equation 1) Suppose that us/N = dmin. Then from Equation 1 we have DCS = NF/us . But from (a) we have DCS = NF/us . Combining these two gives: DCS = NF/us when us/N = dmin. (Equation 2) We can similarly show that: DCS =F/dmin when us/N = dmin (Equation 3). Combining Equation 2 and Equation 3 gives the desired result. (b) (4 points) Consider distributing a file of F bits to N peers using a P2P architecture. Assume a fluid model. For simplicity, assume that dmin is very large, so that peer download bandwidth is never a bottleneck.

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