# V r be the transmission rate let the channel be in

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Unformatted text preview: smission rate is rg In channel is in bad state, the transmission rate is rb Let a r.v. R be the transmission rate. Let the channel be in bad state with probability q , then pR (r ) = q, 1 − q, if r = rb ; if r = rg . We want to transmit a ﬁle over this wireless link. Let a r.v. X be the length of a ﬁle, measured in KB . X follows a Geometric distribution with parameter p : 1 pX (x ) = (1 − p )x −1 p , x = 1, 2 . . . ; E [X ] = . p Question: What is the PMF of the transmission time? Is the question well-deﬁned? M. Chen (IE@CUHK) ENGG2430C lecture 8 5 / 26 Transmission Time of a File over a Wireless Link * Additional assumption: X and R are independent Let a r.v. T = X be the transmission time; compute its PMF and R E [T ]. Its PMF is given by (divide and conquer) pT (t ) = pX |R (rb t |rb )pR (rb ) + pX |R (rg t |rg )pR (rg ) Compute the expected transmission time: E [T ] = E (T |R = rb )pR (rb ) + E (T |R = rg )pR (rg ) E [X ] E [X ] = ·q + · (1 − q ) rb rg 1 q 1−q = + p rb rg How will E [T ] change if X and R are correlated? (The same approach still works; only diﬀers in details.) M. Chen (IE@CUHK) ENGG2430C lecture 8 6 / 26 Transmission Time of a File over a Wireless Network * (From radio.weblogs.com) We want to transmit the ﬁle to a friend across a wireless network Transmission rates of links, denoted by Ri , i = 1, 2, . . . , are i.i.d. with the same PMF as R The number of links to traverse, denoted by N , is determined by routing and is uniformly distributed in {n1 , n1 + 1, . . . , n2 } Question: What is the expected end-to-end transmission time? Assume that Ri (i = 1, 2, . . . ), X , and N are independent. M. Chen (IE@CUHK) ENGG2430...
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## This document was uploaded on 03/31/2014.

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