ECE358: Computer NetworksFall 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 and , 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 ? (Ignore queuing, propagation delay, and processing delay.)

A BSwitchR1 R2

Store and

forward

PacketL

t1

t2

t3

𝑑𝑡𝑟𝑎𝑛𝑠 1=𝐿𝑅1

𝑑𝑡𝑟𝑎𝑛𝑠 2=𝐿𝑅2

Transmitting 1st bit

Transmitting last bit

No processing

delay

No propagation

delayTime

+

3

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?

X2Mbps

1Mbps (20%)

1Mbps (20%)

a. Circuit switchingOnly two users 1Mbps+1Mbps= 2Mbps

b. 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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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?

• Depending on packet length No• Depending on transmission rate No

A B

d=2500km

S Packet

L=1000 Bytes

R=2Mbps

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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.

a. Throughput=min(R1 , R2 , R3)= R1 = 500Kbpsb. R2=100Kbps throughput = min(R1 , R2 , R3)= R2 = 100Kbps

A B

R1=500Kbps

XX

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 bps. Suppose that the two hosts are separated by meters, and suppose the propagation speed along the link ia meter/sec. is to send a packet of size bits to .a) Express the propagation delay , , in terms of and .b) Determine the transmission time of the packet , , in terms of and .c) Ignoring processing and queuing delays, obtain an expression for the end-to-end delay.d) Suppose begins to transmit the packet at time . At time , where is the last bit of the packet?e) Suppose is greater than . At time , where is the first bit of the packet? f) Suppose is less than . At time , where is the first bit of the packet?g) Suppose , bits, and kbps. Find the distance so that equals .

A B

m meters

S PacketL bits

R bps

7

Continue P6.b. c. + d. At the last bit is just leaving host A.e. The first bit is still in the link, and has not reached Host B yet.f. The first bit has aready reached host B.g. ,

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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)?

Delay till decodeing =7+0.224+10=17.224msec

A BPacketL = 56 bytesEncode rate= 64Kbps

R=2M bps𝑑𝑝𝑟𝑜𝑝=10𝑚𝑠𝑒𝑐

time

𝑑𝑝𝑟𝑜𝑐

𝑑𝑡𝑟𝑎𝑛𝑠

𝑑𝑝𝑟𝑜𝑝

Generating the packet

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P 10. Consider a packet of length which begins at end system and travels over three links to a destination end system. These three links are connected by two packet switches. Let , and denote the length, propagation speed, and the transmission rate of link , for . The packet switch delays each packet by . Assuming no queuing delays, in terms of , , , (, and , 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 BPacket

L

R1

time

𝑑𝑝𝑟𝑜𝑐 2

𝑑𝑡𝑟𝑎𝑛𝑠 1

𝑑𝑝𝑟𝑜𝑝1

R2 R3d1 d2 d3

s1 s2 s3

𝑑𝑡𝑟𝑎𝑛𝑠 2

𝑑𝑝𝑟𝑜𝑝2 𝑑𝑝𝑟𝑜𝑐 3

𝑑𝑡𝑟𝑎𝑛𝑠 3

𝑑𝑝𝑟𝑜𝑝3

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P 11. In the above problem. Suppose and . Further suppose the packet switch does not store-and– 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 BPacket

L

R

time

𝑑𝑡𝑟𝑎𝑛𝑠 1

𝑑𝑝𝑟𝑜𝑝1

R Rd1 d2 d3

s1 s2 s3

𝑑𝑝𝑟𝑜𝑝2 𝑑𝑝𝑟𝑜𝑝3