# Introduction to Packet-Switched Networks

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## 1.8 Exercises

1. We transmit data directly between two servers 6,000 km apart through a geostationary satellite situated 10,000 km from Earth exactly between the two servers. The data enters this network at 100Mb/s.

1. Find the propagation delay if data travels at the speed of light (2.3 × 108 m/s).
2. Find the number of bits in transit during the propagation delay.
3. Determine how long it takes to send 10 bytes of data and to receive 2.5 bytes of acknowledgment back.
2. We would like to analyze a variation of Exercise 1 where servers are placed in substantially closer proximity to each other still using satellite for communication. We transmit data directly between two servers 60 m apart through a geostationary satellite situated 10,000 km from Earth exactly between the two servers. The data enters this network at 100Mb/s.

1. Find the propagation delay if data travels at the speed of light (2.3 × 108 m/s).
2. Find the number of bits in transit during the propagation delay.
3. Determine how long it takes to send 10 bytes of data and to receive 2.5 bytes of acknowledgment back.
3. Stored on a flash memory device is a 200 megabyte (MB) message to be transmitted by an e-mail from one server to another, passing three nodes of a connectionless network. This network forces packets to be of size 10KB, excluding a packet header of 40 bytes. Nodes are 400 miles apart, and servers are 50 miles away from their corresponding nodes. All transmission links are of type 100Mb/s. The processing time at each node is 0.2 seconds.

1. Find the propagation delays per packet between a server and a node and between nodes.
2. Find the total time required to send this message.
4. Equation (1.2) gives the total delay time for connection-oriented networks. Let tp be the packet propagation delay between each two nodes, tf1 be the data packet transfer time to the next node, and tr1 be the data packet processing time. Also, let tf2 be the control-packet transfer time to the next node, and tr2 be the control-packet processing time. Give an expression for D in terms of all these variables.
5. Suppose that a 200MB message stored on a flash memory device attached to a server is to be uploaded to a destination server through a connection-oriented packet-switched network with three serially connected nodes. This network forces packets to be of size 10KB, including a packet header of 40 bytes. Nodes are 400 miles apart from each other and each server is 50 miles away from its corresponding node. All transmission links are of type 100Mb/s. The processing time at each node is 0.2 seconds. For this purpose, the signaling packet is 500 bits long.

1. Find the total connection request/accept process time.
2. Find the total connection release process time.
3. Find the total time required to send this message.
6. We want to deliver a 12KB message by uploading it to the destination’s Web site through a 10-node path of a virtual-circuit packet-switched network. For this purpose, the signaling packet is 500 bits long. The network forces packets to be of size 10KB including a packet header of 40 bytes. Nodes are 500 miles apart. All transmission links are of type 1Gb/s. The processing time at each node is 100 ms per packet and the propagation speed is 2.3 × 108 m/s.

1. Find the total connection request/accept process time.
2. Find the total connection release process time.
3. Find the total time required to send this message.
7. Consider five serial connected nodes A, B, C, D, E and that 100 bytes of data are supposed to be transmitted from node A to E using a protocol that requires packet headers to be 20 bytes long.

1. Ignore tp, tr, and all control signals; and sketch and calculate total tf in terms of byte-time to transmit the data for cases in which the data is converted into 1 packet, 2 packets, 5 packets, and 10 packets.
2. Put all the results obtained from part (a) together in one plot and estimate where the plot approximately shows the minimum delay (no mathematical work is needed, just indicate the location of the lowest delay transmission on the plot).
8. To analyze the transmission of a 10,000-bit-long packet, we want the percentage of link utilization used by the data portion of a packet to be 72 percent. We also want the ratio of the packet header, h, to packet data, d, to be 0.04. The transmission link speed is s = 100 Mb/s.

1. Find the link utilization, ρ.
2. Find the link capacity rate, μ, in terms of packets per second.
3. Find the average delay per packet.
4. Find the optimum average delay per packet.
9. Consider a digital link with a maximum capacity of s = 100 Mb/s facing a situation resulting in 80 percent utilization. Equal-sized packets arrive at 8,000 packets per second. The link utilization dedicated to headers of packets is 0.8 percent.

1. Find the total size of each packet.
2. Find the header and data sizes for each packet.
3. If the header size is not negotiable, what would the optimum size of packets be?
4. Find the delay for each optimally sized packet.
10. Develop a signaling delay chart, similar to Figures 1.7 and 1.8, for circuit-switched networks. From the mentioned steps, get an idea that would result in the establishment of a telephone call over circuit-switched networks.
11. In practice, the optimum size of a packet estimated in Equation (1.7) depends on several other contributing factors.

1. Derive the optimization analysis, this time also including the header size, h. In this case, you have two variables: d and h.
2. What other factors might also contribute to the optimization of the packet size?
12. Specify the class of address and the subnet ID for the following cases:

13. Specify the class of address and the subnet ID for the following cases:

14. Apply CIDR aggregation on the following IP addresses: 150.97.28.0/24, 150.97.29.0/24, and 150.97.30.0/24.
15. Apply CIDR aggregation on the following IP addresses: 141.33.11.0/22, 141.33.12.0/22, and 141.33.13.0/22.
16. Use the subnet mask 255.255.254.0 on the following IP addresses, and then convert them to CIDR forms:

1. 191.168.6.0
2. 173.168.28.45
3. 139.189.91.190
17. A certain organization owns a subnet with prefix 143.117.30.128/26.

1. Give an example of one of the organization’s IP addresses.
2. Assume the organization needs to be downsized, and it wants to partition its block of addresses and create three new subnets, with each new block having the same number of IP addresses. Give the CIDR form of addresses for each of the three new subnets.
18. A packet with the destination IP address 180.19.18.3 arrives at a router. The router uses CIDR protocols, and its table contains three entries referring to the following connected networks: 180.19.0.0/18, 180.19.3.0/22, and 180.19.16.0/20, respectively.

1. From the information in the table, identify the exact network ID of each network in binary form.
2. Find the right entry that is a match with the packet.
19. Part of a networking infrastructure consists of three routers R1, R2, and R3 and six networks N1 through N6, as shown in Figure 1.17. All address entries of each router are also given as seen in the figure. A packet with the destination IP address 195.25.17.3 arrives at router R1.

1. Find the exact network ID field of each network in binary form.
2. Find the destination network for the packet (proof needed).
3. Specify how many hosts can be addressed in network N1.
20. Consider an estimated population of 620 million people.

1. What is the maximum number of IP addresses that can be assigned per person using IPv4?
2. Design an appropriate CIDR to deliver the addressing in part (a).
21. A router with four output links L1, L2, L3, and L4 is set up based on the following routing table:

 Mask Result Link 192.5.150.16 L3 192.5.150.18 L2 129.95.38.0 L1 129.95.38.15 L3 129.95.39.0 L2 Unidentified L4

The router has a masking pattern of 255.255.255.240 and examines each packet using the mask in order to find the right output link. For a packet addressed to each of the following destinations, specify which output link is found:

1. 192.5.150.18
2. 129.95.39.10
3. 129.95.38.15
4. 129.95.38.149
22. A router with four output links L1, L2, L3, and L4 is set up based on the following routing table:

1. 129.95.39.10
2. 129.95.38.16
3. 129.95.38.149
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