计算机网络课后习邈指导 陕西师范大学 时延为： d=nxL+- P13.(a)Suppose N packets arrive simultaneously to a link at which no packets are currently being transmitted or queued.Each packet is of lengthLand the link has transmission rate R.What is the average queuing delay for the Npackets? (b)Now se that Nsuch packets arrive to the link every LNR seconds.What is the average queuing delay ofa packet? 答：a由题意，第一个分组没有排队时延，第一个分组排队时延为0，第二个分组排队时 延为5第N个分组排队时延为-：，则平均排队时延为： R 2R b.由题意，N个分组的传输时间为秒，第1,2,3，，N个分组排队时延分别为： 0,告，业，则其平均排队时延为： N-1 R 2 P14.Consider the queuing delay in a router buffer.LetI denote traffic intensity,that/R b.Plot the total delay as a function of L/R. 答：a传输时延为LR,总时延为： daa=due+dramR-n+员FR-刀 b.令LRx,则 drotal=1 ax 当x=0时，总时延为0：当x逐渐增大是，总时廷doa也随之增大，当x接近1a时，趋近 于无穷大。 P15.Leta denote the rate of packets arriving at a link in packets/sec,and letdenote the link's transmission rate in packets/sec.Based on the formula for the total delay(ie.,the queuing delay plus the transmission delay)derived in the previous problem,derive a formula for the total delay 答：由题，a表示链路到达速率，单位为packets/sec:表示传输速率，单位为packets/ec, 共倒数μ即传输时延：由14题可知，总时延为：dot=祭流通强度I=片带入a和 以得到总时延为： 计算机网络课后习题指导 陕西师范大学 7 时延为： d￾￾￾￾￾ = ￾ × ￾ + (￾ − ￾) ￾ P13. (a) Suppose N packets arrive simultaneously to a link at which no packets are currently being transmitted or queued. Each packet is of length L and the link has transmission rate R. What is the average queuing delay for the N packets? (b) Now suppose that N such packets arrive to the link every LN/R seconds. What is the average queuing delay of a packet? 答：a. 由题意，第一个分组没有排队时延，第一个分组排队时延为 0，第二个分组排队时 延为￾ ￾ ，第 N 个分组排队时延为(￾￾￾)×￾ ￾ ，则平均排队时延为： ￾0 + L ￾ + 2L ￾ + ⋯ + (￾ − 1) × ￾ ￾ ￾ × 1 ￾ = (￾ − 1)￾ 2￾ b. 由题意， N 个分组的传输时间为￾￾ ￾ 秒，第 1，2，3，···，N 个分组排队时延分别为： 0, ￾ ￾ , ￾￾ ￾ ···, (￾￾￾)￾ ￾ ，则其平均排队时延为： 1 ￾ ￾ (￾ − 1) × ￾ ￾ ￾ ￾￾￾ = 1 ￾ × ￾ ￾ × ￾ ￾ ￾￾￾ ￾￾￾ = ￾ ￾ × ￾ − 1 2 P14. Consider the queuing delay in a router buffer. Let I denote traffic intensity; that is, I = La/R. Suppose that the queuing delay takes the form IL/R (1 – I) for I < 1. a. Provide a formula for the total delay, that is, the queuing delay plus the transmission delay. b. Plot the total delay as a function of L/R. 答：a. 传输时延为 L/R，总时延为： ￾￾￾￾￾￾ = ￾￾￾￾￾￾ + ￾￾￾￾￾￾ = ￾￾ ￾(1 −￾) + ￾ ￾ = L ￾(1 − ￾) b. 令 L/R=x，则 ￾￾￾￾￾￾ = ￾ 1− ￾￾ 当 x=0 时，总时延为 0；当 x 逐渐增大是，总时延￾￾￾￾￾￾也随之增大，当 x 接近 1/a 时，￾￾￾￾￾￾趋近 于无穷大。 P15. Let a denote the rate of packets arriving at a link in packets/sec, and let μ denote the link’s transmission rate in packets/sec. Based on the formula for the total delay (i.e., the queuing delay plus the transmission delay) derived in the previous problem, derive a formula for the total delay in terms of a and μ. 答：由题，a 表示链路到达速率，单位为 packets/sec；μ 表示传输速率，单位为 packets/sec， 其倒数 1/μ 即传输时延；由 14 题可知，总时延为：￾￾￾￾￾￾ = ￾/￾ ￾￾￾ ，流通强度I = ￾￾ ￾ ，带入 a 和 μ 得到总时延为：