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**ECE358: Computer Networks Fall 2014**

Solutions to Homework #1

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R 11. Suppose there is exactly one packet switch between a sending host and a receiving host. The transmission rates between the sending host and the switch and between the switch and the receiving host are π
1 and π
2 , respectively. Assuming that the switch uses store-and-forward packet switching, what is the total end-to-end delay to send a packet of length πΏ? (Ignore queuing, propagation delay, and processing delay.) A B Switch R1 R2 Store and forward Packet L t1 t2 t3 π π‘ππππ 1 = πΏ π
1 π π‘ππππ 2 = πΏ π
2 Transmitting 1st bit Transmitting last bit No processing delay No propagation delay Time π πππβπ‘πβπππ = π π‘ππππ 1 + π π‘ππππ 2 = πΏ π
1 + πΏ π
2

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**R 13. Suppose users share a 2Mbps (Megabits per second) link**

R 13. Suppose users share a 2Mbps (Megabits per second) link. Also suppose each user transmits continuously at 1Mbps when transmitting, but each user transmits only 20 percent of the time. a) When circuit switching is used, how many users can be supported? b) Suppose packet switching is used, why will there be essentially no queuing delay before the link if two or fewer users transmit at the same time? Circuit switching Only two users ο 1Mbps+1Mbps= 2Mbps X 2Mbps 1Mbps (20%) Since each user requires 1Mbps when transmitting, if two or fewer users transmit simultaneously, a maximum of 2Mbps will be required. Since the available bandwidth of the shared link is 2Mbps, there will be no queuing delay before the link. Whereas, if three users transmit simultaneously, the bandwidth required will be 3Mbps which is more than the available bandwidth of the shared link. In this case, there will be queuing delay before the link.

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**π ππππ = π π = 2500 ππ 2.5 β 10 5 ππ/π ππ =10 ππ ππ **

R 18. How long does it take a packet of length 1,000 bytes to propagate over a link of distance 2,500 Km, propagation speed 2.5 X 108 m/s, and transmission rate 2Mbps? More generally, how long does it take a packet of length L to propagate over a link of distance d, propagation speed s, and transmission rate R bps? Does this delay depend on packet length? Does this delay depend on transmission rate? A B d=2500km S =2.5β π/π ππ Packet L=1000 Bytes R=2Mbps π ππππ = π π = 2500 ππ 2.5 β ππ/π ππ =10 ππ ππ Depending on packet length ο No Depending on transmission rate ο No

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**R 19. Suppose Host A wants to send a large file to Host B**

R 19. Suppose Host A wants to send a large file to Host B. The path from Host A to Host B has three links, of rates R1= 500kbps, R2=2Mbps, and R3=1Mbps. a) Assuming no other traffic in the network, what is the throughput for the file transfer? b) Suppose the file is 4 million bytes. Dividing the file size by the throughput, roughly how long will it take to transfer the file to Host B? c) Repeat (a) and (b), but now with R_2 reduced to 100kbps. Throughput=min(R1 , R2 , R3)= R1 = 500Kbps d= 4β 10 6 β8 πππ‘π 500 β πππ‘/π ππ =64 π ππ R2=100Kbps ο throughput = min(R1 , R2 , R3)= R2 = 100Kbps d= 4β 10 6 β8 πππ‘π 100 β πππ‘/π ππ =320 π ππ A B R1=500Kbps X R2=2Mbps R3=1Mbps

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P 6. This elementary problem begins to explore propagation delay and transmission delay, two central concepts in data networking. Consider two hosts, A and B, connected by a single link of rate π
bps. Suppose that the two hosts are separated by π meters, and suppose the propagation speed along the link ia π meter/sec. π»ππ π‘ π΄ is to send a packet of size πΏ bits to π»ππ π‘ π΅. a) Express the propagation delay , π ππππ , in terms of π and π . b) Determine the transmission time of the packet , π π‘ππππ , in terms of πΏ and π
. c) Ignoring processing and queuing delays, obtain an expression for the end-to-end delay. d) Suppose π»ππ π‘ π΄ begins to transmit the packet at time π‘=0. At time π‘= π π‘ππππ , where is the last bit of the packet? e) Suppose π ππππ is greater than π π‘ππππ . At time π‘= π π‘ππππ , where is the first bit of the packet? f) Suppose π ππππ is less than π π‘ππππ . At time π‘= π π‘ππππ , where is the first bit of the packet? g) Suppose π =2.5Γ 10 8 π/π , πΏ=120 bits, and π
=56 kbps. Find the distance π so that π πππ equals π π‘ππππ . π ππππ = π π π ππ A B m meters S π/π ππ Packet L bits R bps

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**π πππβπ‘πβπππ = π ππππ + π π‘ππππ **

Continue P6. π π‘ππππ = πΏ π
π ππ π πππβπ‘πβπππ = π ππππ + π π‘ππππ At π‘=π π‘ππππ ο the last bit is just leaving host A. The first bit is still in the link, and has not reached Host B yet. The first bit has aready reached host B. π ππππ = π π , π π‘ππππ = πΏ π
m= πΏπ π
=536 ππ

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P 7. In this problem, we consider sending real-time voice from Host A to Host B over a packet-switching network (VoIP). Host A converts analog voice to a digital 64 kbps bit streaming on the fly. Host A then groups the bits into 56-byte packets. There is one link between Hosts A and B; its transmission rate is 2Mbps and its propagation delay is 10 msec. as soon as Host A gathers a packet, it sends it to Host B. As soon as Host B receives an entire packet, it converts the packet's bits to an analog signal. How much time elapses from the time a bit created (from the original analog signal at Host A) until the bit is decoded ( as part of analog signal at host B)? A B Packet L = 56 bytes Encode rate= 64Kbps R=2M bps π ππππ =10 ππ ππ time π ππππ π π‘ππππ π ππππ Generating the packet π ππππ = 56β8 πππ‘π 64β 10 3 πππ =7ππ ππ, π π‘ππππ = 56β8 πππ‘π 2β 10 6 πππ =0.224ππ ππ Delay till decodeing = =17.224msec

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P 10. Consider a packet of length πΏ which begins at end system π΄ and travels over three links to a destination end system. These three links are connected by two packet switches. Let π π , π π and π
π denote the length, propagation speed, and the transmission rate of link π, for π=1, 2, 3. The packet switch delays each packet by π ππππ . Assuming no queuing delays, in terms of π π , π π , π
π , (π=1, 2, 3), and πΏ, what is the total end-to-end delay for the packet? Suppose now the packet is 1,500 bytes, the propagation speed on all three links is 2.5 x 108 m/s, the transmission rates of all three links are 2Mbps, the packet switch processing delay is 3msec, the length of the first link is 5,000 km, the length of the second link is 4,000 km, the length of the last link is 1,000 km . for these values, what is the end-to-end delay? A B Packet L R1 time π ππππ 2 π π‘ππππ 1 π ππππ 1 R2 R3 d1 d2 d3 s1 s2 s3 π π‘ππππ 2 π ππππ 2 π ππππ 3 π π‘ππππ 3 π ππππ 3 π πππβπ‘πβπππ = π π‘ππππ 1 + π π‘ππππ 2 + π π‘ππππ 3 + π ππππ 1 + π ππππ 2 + π ππππ 3 + π ππππ 2 + π ππππ 3 = πΏ π
1 + πΏ π
2 + πΏ π
3 + π1 π 1 + π2 π 2 + π3 π 3 +2β π ππππ =64ππ ππ

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**P 11. In the above problem. Suppose π
1 = π
2 = π
3 =π
and π ππππ =0**

P 11. In the above problem. Suppose π
1 = π
2 = π
3 =π
and π ππππ =0. Further suppose the packet switch does not store-andβ forward packets but instead immediately transmits each bit it receives before waiting for the entire packet to arrive. What is the end-to-end delay? A B Packet L R time π π‘ππππ 1 π ππππ 1 d1 d2 d3 s1 s2 s3 π ππππ 2 π ππππ 3 π πππβπ‘πβπππ = π π‘ππππ 1 + π ππππ 1 + π ππππ 2 + π ππππ 3 = πΏ π
+ π1 π 1 + π2 π 2 + π3 π 3

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Β© JΓΆrg Liebeherr, 1998-2003 CS757 Three Network Technologies Telephone Network βThe largest worldwide computer network, specialized for voice βSwitching.

Β© JΓΆrg Liebeherr, 1998-2003 CS757 Three Network Technologies Telephone Network βThe largest worldwide computer network, specialized for voice βSwitching.

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