-10-T=TdS + L/B =(Np+ N – 1)(P/B)Circuit Switching vs. Virtual Circuit Packet SwitchingTV=End-to-End Delay, Virtual Circuit Packet SwitchingTV=S + TdTC= TVL/B =(Np+ N – 1)(P/B)Datagram vs. Virtual Circuit Packet SwitchingTd= TV– S3.2From Problem 3.1, we haveTd= (Np+ N – 1)(P/B) + N ×DFor maximum efficiency, we assume that Np= L/(P – H) is an integer. Also, it isassumed that D = 0. ThusTd= (L/(P – H) + N – 1)(P/B)To minimize as a function of P, take the derivative:0=dTd/(dP)0=(1/B)(L/(P – H) + N – 1) - (P/B)L/(P – H)20=L(P – H) + (N – 1) (P – H)2- LP0=–LH + (N – 1)(P – H)2(P - H)2= LH/(N – 1)P = H + LHN−13.3Each telephone makes 0.5 calls/hour at 6 minutes each. Thus a telephone occupiesa circuit for 3 minutes per hour. Twenty telephones can share a circuit (althoughthis 100% utilization implies long queuing delays).
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