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Assignment 4

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Submitted By RWalka1992
Words 497
Pages 2
Rosco Walka
Homework 4
CNT 4007
Spring 2016
1. System A consists of a single ring with 100 stations, one per repeater. System B consists of four 25 stations rings linked by a bridge. If the probability of a link failure is
Pl, a repeater failure is Pr, and a bridge failure is Pb, derive an expression for parts (a) to (e). 50 points
a) Probability of failure of system A. P[A fails] = 1 – (1 – Pl)100(1-Pr)100
b) Probability of complete failure of system B. P[B fails] = [1 – (1-Pl)25(1-Pr)25]3
c) Probability that a particular station will find the network unavailable, for systems A and B. System A: P[x in A; and A is unavailable] = 1 – (1-Pl)100(1-Pr)100; System B: P[x in B; and ‘s ring in unavailable] = 1 – (1-Pl)25(1-Pr)25
d) Probability that any two stations selected at random will be unable to communicate for systems A and B. System A: Pr[X and Y have no communication] = 1 – (1-Pl)100(1-Pr)100; System B: P1: Pr[X and Y on the same ring] = 1/3; P2 = Pr [X and Y not on same ring] = 2/3; P3 = Pr[X and Y on same ring, no communication] = 1 – (1-Pl)25(1-Pr)25; P4 = Pr[X and Y have no communication, X and Y are not on the same ring] = P[X’s ring doesn’t fail]* P[Y’s ring does not fail] * P[bridge does not fail] = [(1-Pl)25(1-Pr)25]2(10Pb) = 1 – (1-Pl)50(1-Pr)50(1-Pb); Pr[No communication between X and Y] = P1P3 + P2P4 = (1/3)( 1 – (1-Pl)25(1-Pr)25) + (1/3)( 1 – (1-Pl)50(1-Pr)50(1-Pb))
e) Compare values of parts (a) and (b) for 2 Pl = Pb = Pr = 10-2. P[A fails] = 1 – (1 – 10-2)100(1-10-2)100 = 1 – (0.99)100(0.99)100 = 1 – (0.366032)(0.366032) = 0.86602; P[B fails] = [1 – (1-10-2)25(1-10-2)25]3 = [1 – (0.99)25(0.99)25]3 = [1 – (0.777821)(0.777821)]3 = (0.394994)3 = 0.061627
2. We send a frame of 256 bits. If the probability that a bit changes in transmission is
0.001 and each bit is independent. 30 points
a. What is the probability that exactly 6 bits change? P[6 bits change] = 256C6 * 0.0016 * 0.999250 = 2.86978*10-7 = 0.0000003
b. What is the probability of no bits changing? P[no change] = 256C0 * 0.0010 * 0.999256 = 0.774043 = 0.77
3. If a Signal with a power level of 40 mW is inserted onto a transmission line and the measured power some distance away is 10 mW, calculate the loss of signal strength in decibels. 20 points 10log(40/10) = 10(0.60206) = 6.0206dB

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