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ENC3250 Solutions pg 10

ENC3250 Solutions pg 10 - T = Td S L/B =(Np N 1(P/B Circuit...

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-10- T = T d S + L/B = (N p + N – 1)(P/B) Circuit Switching vs. Virtual Circuit Packet Switching T V = End-to-End Delay, Virtual Circuit Packet Switching T V = S + T d T C = T V L/B = (N p + N – 1)(P/B) Datagram vs. Virtual Circuit Packet Switching T d = T V – S 3.2 From Problem 3.1, we have T d = (N p + N – 1)(P/B) + N × D For maximum efficiency, we assume that N p = L/(P – H) is an integer. Also, it is assumed that D = 0. Thus T d = (L/(P – H) + N – 1)(P/B) To minimize as a function of P, take the derivative: 0 = dT d /(dP) 0 = (1/B)(L/(P – H) + N – 1) - (P/B)L/(P – H) 2 0 = L(P – H) + (N – 1) (P – H) 2 - LP 0 = –LH + (N – 1)(P – H) 2 (P - H) 2 = LH/(N – 1) P = H + LH N 1 3.3 Each telephone makes 0.5 calls/hour at 6 minutes each. Thus a telephone occupies a circuit for 3 minutes per hour. Twenty telephones can share a circuit (although this 100% utilization implies long queuing delays).
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