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Communication Networks: Fundamental Concepts and Key Architectures

Indra Widjaja, Alberto Leon-Garcia, Alberto Leon-Garcia

Chapter 7

Packet-Switching Networks - all with Video Answers

Educators

Chapter Questions

Problem 1

Explain how a network that operates internally with virtual circuits can provide connectionless service. Comment on the delay performance of the service. Can you identify inefficiencies in this approach?

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Problem 2

Is it possible for a network to offer best-effort virtual-circuit service? What features would such a service have, and how does it compare to best-effort datagram service?

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Problem 3

Suppose a service provider uses connectionless operation to run its network internally. Explain how the provider can offer customers reliable connection-oriented network service.

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Problem 4

Where is complexity concentrated in a connection-oriented network? Where is it concentrated in a connectionless network?

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Problem 5

Comment on the following argument: Because they are so numerous, end systems should be simple and dirt cheap. Complexity should reside inside the network.

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Problem 6

In this problem you compare your telephone demand behavior and your Web demand behavior.
a. Arrival rate: Estimate the number of calls you make in the busiest hour of the day; express this quantity in calls/minute. Service time: Estimate the average duration of a call in minutes. Find the load that is given by the product of arrival rate and service time. Multiply the load by $64 \mathrm{kbps}$ to estimate your demand in bits/hour.
b. Arrival rate: Estimate the number of Web pages you request in the busiest hour of the day. Service time: Estimate the average length of a Web page. Estimate your demand in bits/hour.
c. Compare the number of call requests/hour to the number of Web requests/hour. Comment on the connection setup capacity required if each Web page request requires a connection setup. Comment on the amount of state information required to keep track of these connections.

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Problem 7

Apply the end-to-end argument to the question of how to control the delay jitter that is incurred in traversing a multihop network.

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Problem 8

Compare the operation of the layer 3 entities in the end systems and in the routers inside the network.

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04:00

Problem 9

In Figure 7.6 trace the transmission of IP packets from when a Web page request is made to when the Web page is received. Identify the components of the end-to-end delay.
a. Assume that the browser is on a computer that is in the same departmental LAN as the server.
b. Assume that the Web server is in the central organization servers.
c. Assume that the server is located in a remote network.

Samriddhi Singh
Samriddhi Singh
Numerade Educator

Problem 10

In Figure 7.6 trace the transmission of IP packets between two personal computers running an IP telephony application. Identify the components of the end-to-end delay.
a. Assume that the two PCs are in the same departmental LAN.
b. Assume that the $\mathrm{PCs}$ are in different domains.

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Problem 11

In Figure 7.6 suppose that a workstation becomes faulty and begins sending LAN frames with the broadcast address. What stations are affected by this broadcast storm? Explain why the use of broadcast packets is discouraged in IP.

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Problem 12

Explain why the distance in hops from your ISP to a NAP is very important. What happens if a NAP becomes congested?

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Problem 13

Consider the operation of a switch in a connectionless network. What is the source of the load on the processor? What can be done if the processor becomes the system bottleneck?

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Problem 14

Consider the operation of a switch in a connection-oriented network. What is the source of the load on the processor? What can be done if the processor becomes overloaded?

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Problem 15

Suppose that a computer that is used as a switch can process 20,000 packets/second. Give a range of possible bit rates that traverse the $\mathrm{I} / \mathrm{O}$ bus and main memory.

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Problem 16

A 64-kilobyte message is to be transmitted from over two hops in a network. The network limits packets to a maximum size of 2 kilobytes, and each packet has a 32 -byte header. The transmission lines in the network are error free and have a speed of $50 \mathrm{Mbps}$. Each hop is $1000 \mathrm{~km}$ long. How long does it take to get the message from the source to the destination?

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Problem 17

An audio-visual real-time application uses packet switching to transmit $32 \mathrm{kilobit} / \mathrm{second}$ speech and $64 \mathrm{kilobit} / \mathrm{second}$ video over the following network connection.
(GRAPH CANT COPY)
Two choices of packet length are being considered: In option 1 a packet contains 10 milliseconds of speech and audio information; in option 2 a packet contains 100 milliseconds of speech and audio information. Each packet has a 40 byte header.
a. For each option find out what percentage of each packet is header overhead.
b. Draw a time diagram and identify all the components of the end-to-end delay in the preceding connection. Keep in mind that a packet cannot be sent until it has been filled and that a packet cannot be relayed until it is completely received. Assume that bit errors are negligible.
c. Evaluate all the delay components for which you have been given sufficient information. Consider both choices of packet length. Assume that the signal propagates at a speed of $1 \mathrm{~km} / 5$ microseconds. Consider two cases of backbone network speed: $45 \mathrm{Mbps}$ and $1.5 \mathrm{Mbps}$. Summarize your result for the four possible cases in a table with four entries.
d. Which of the preceding components would involve queueing delays?

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Problem 18

Suppose that a site has two communication lines connecting it to a central site. One line has a speed of $64 \mathrm{kbps}$, and the other line has a speed of $384 \mathrm{kbps}$. Suppose each line is modeled by an $\mathrm{M} / \mathrm{M} / 1$ queueing system with average packet delay given by $E[D]=E[X] /(1-\rho)$ where $E[X]$ is the average time required to transmit a packet, $\lambda$ is the arrival rate in packets/second, and $\rho=\lambda E[X]$ is the load. Assume packets have an average length of 8000 bits. Suppose that a fraction $\alpha$ of the packets are routed to the first line and the remaining $1-\alpha$ are routed to the second line.
a. Find the value of $\alpha$ that minimizes the total average delay.
b. Compare the average delay in part (a) to the average delay in a single multiplexer that combines the two transmission lines into a single transmission line.

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Problem 19

A message of size $m$ bits is to be transmitted over an $L$-hop path in a store-and-forward packet network as a series of $N$ consecutive packets, each containing $k$ data bits and $h$ header bits. Assume that $m \gg k+h$. The bit rate of each link is $R$ bits/second. Propagation and queueing delays are negligible.
a. What is the total number of bits that must be transmitted?
b. What is the total delay experienced by the message (i.e., the time between the first transmitted bit at the sender and the last received bit at the receiver)?
c. What value of $k$ minimizes the total delay?

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Problem 20

Suppose that a datagram network has a routing algorithm that generates routing tables so that there are two disjoint paths between every source and destination that is attached to the network. Identify the benefits of this arrangement. What problems are introduced with this approach?

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02:53

Problem 21

Suppose that a datagram packet network uses headers of length $H$ bytes and that a virtual-circuit packet network uses headers of length $h$ bytes. Use Figure 7.19 to determine the length $M$ of a message for which virtual-circuit switching delivers the packet in less time than datagram switching does. Assume packets in both networks are the same length.

Samriddhi Singh
Samriddhi Singh
Numerade Educator

Problem 22

Suppose a routing algorithm identifies paths that are "best" in the following sense: (1) minimum number of hops, (2) minimum delay, or (3) maximum available bandwidth. Identify the conditions under which the paths produced by the different criteria are the same? are different?

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Problem 23

Suppose that the virtual circuit identifiers are unique to a switch, not to an input port. What is traded off in this scenario?

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Problem 24

Consider the virtual-circuit packet network in Figure 7.24. Suppose that node 4 in the network fails. Reroute the affected calls and show the new set of routing tables.

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Problem 25

Consider the datagram packet network in Figure 7.26. Reconstruct the routing tables (using minimum-hop routing) that result after node 4 fails. Repeat if node 3 fails instead.

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Problem 26

Consider the following six-node network. Assume all links have the same bit rate $R$.
(GRAPH CANT COPY)
b. Explain why the routing tables in part (a) lead to inefficient use of network bandwidth.
c. Can VC routing improve efficiency in the use of network bandwidth? Explain why or why not.
d. Suggest an approach in which the routing tables in datagram routing are modified to improve efficiency. Give the modified routing tables.

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Problem 27

Consider the following six-node unidirectional network. Assume all links have the same bit rate $R=1$.
(GRAPH CANT COPY)
a. If flows $\mathrm{a}$ and $\mathrm{b}$ are equal, find the maximum flow that can be handled by the network.
b. If flow a is three times larger than flow b, find the maximum flow that can be handled by the network.
c. Repeat (a) and (b) if the flows are constrained to use only one path.

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Problem 28

Consider the network in Figure 7.30.
a. Use the Bellman-Ford algorithm to find the set of shortest paths from all nodes to destination node 2 .
b. Now continue the algorithm after the link between node 2 and 4 goes down.

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Problem 29

Consider the network in Figure 7.28.
a. Use the Dijkstra algorithm to find the set of shortest paths from node 4 to other nodes.
b. Find the set of associated routing table entries.

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Problem 30

Suppose that a block of user information that is $L$ bytes long is segmented into multiple cells. Assume that each data unit can hold up to $P$ bytes of user information, that each cell has a header that is $H$ bytes long, and that the cells are fixed in length and padded if necessary. Define the efficiency as the ratio of the $L$ user bytes to the total number of bytes produced by the segmentation process.
a. Find an expression for the efficiency as a function of $L, H$, and $P$. Use the ceiling function $c(x)$, which is defined as the smallest integer larger or equal to $x$.
b. Plot the efficiency for the following ATM parameters: $H=5, P=48$, and $L=24 k$ for $k=0,1,2,3,4,5$, and 6 .

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Problem 31

Consider a videoconferencing application in which the encoder produces a digital stream at a bit rate of $144 \mathrm{kpbs}$. The packetization delay is defined as the delay incurred by the first byte in the packet from the instant it is produced to the instant when the packet is filled. Let $P$ and $H$ be defined as they are in problem 30 .
a. Find an expression for the packetization delay for this video application as a function of $P$.
b. Find an expression for the efficiency as a function of $P$ and $H$. Let $H=5$ and plot the packetization delay and the efficiency versus $P$.

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Problem 32

Suppose an ATM switch has 16 ports each operating at SONET OC-3 transmission rate, $155 \mathrm{Mbps}$. What is the maximum possible throughput of the switch?

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Problem 33

Refer to the virtual circuit packet network in Figure 7.24. How many VCIs does each connection in the example consume? What is the effect of the length of routes on VCI consumption?

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Problem 34

Generalize the hierarchical network in Figure 7.27 so that the $2^K$ nodes are interconnected in a full mesh at the top of the hierarchy and so that each node connects to two $2^L$ nodes in the next lower level in the hierarchy. Suppose there are four levels in the hierarchy.
a. How many nodes are in the hierarchy?
b. What does a routing table look like at level $j$ in the hierarchy, $j=1,2,3$, and 4 ?
c. What is the maximum number of hops between nodes in the network?

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01:15

Problem 35

Assuming that the earth is a perfect sphere with radius $6400 \mathrm{~km}$, how many bits of addressing are required to have a distinct address for every $1 \mathrm{~cm} \times 1 \mathrm{~cm}$ square on the surface of the earth?

Ethan Somes
Ethan Somes
Numerade Educator
03:38

Problem 36

Suppose that $64 \mathrm{kbps}$ PCM coded speech is packetized into a constant bit rate ATM cell stream. Assume that each cell holds 48 bytes of speech and has a 5 byte header.
a. What is the interval between production of full cells?
b. How long does it take to transmit the cell at $155 \mathrm{Mbps}$ ?
c. How many cells could be transmitted in this system between consecutive voice cells?

James Chok
James Chok
Numerade Educator
06:36

Problem 37

Suppose that $64 \mathrm{kbps}$ PCM coded speech is packetized into a constant bit rate ATM cell stream. Assume that each cell holds 48 bytes of speech and has a 5 byte header. Assume that packets with silence are discarded. Assume that the duration of a period of speech activity has an exponential distribution with mean $300 \mathrm{~ms}$ and that the silence periods have a duration that also has an exponential distribution but with mean $600 \mathrm{~ms}$. Recall that if $T$ has an exponential distribution with mean $1 / \mu$, then $P[T>t]=e^{-\mu t}$.
a. What is the peak cell rate of this system?
b. What is the distribution of the burst of packets produced during an active period?
c. What is the average rate at which cells are produced?

Rosina Dapaah
Rosina Dapaah
Numerade Educator
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Problem 38

Suppose that a data source produces information according to an on/off process. When the source is on, it produces information at a constant rate of $1 \mathrm{Mbps}$; when it is off, it produces no information. Suppose that the information is packetized into an ATM cell stream. Assume that each cell holds 48 bytes of speech and has a 5 byte header. Assume that the duration of an on period has a Pareto distribution with parameter 1. Assume that the off period is also Pareto but with parameters 1 and $\alpha$. If $T$ has a Pareto distribution with parameters 1 and $\alpha$, then $\mathrm{P}[T>t]=t^{-\alpha}$ for $t>1$. If $\alpha>1$, then $\mathrm{E}[T]=\alpha /(\alpha-1)$, and if $0<\alpha<1$, then $\mathrm{E}[T]$ is infinite.
a. What is the peak cell rate of this system?
b. What is the distribution of the burst packets produced during an on period?
c. What is the average rate at which cells are producd?

Victor Salazar
Victor Salazar
Numerade Educator
04:29

Problem 39

An IP packet consists of 20 bytes of header and 1500 bytes of payload. Now suppose that the packet is mapped into ATM cells that have 5 bytes of header and 48 bytes of payload. How much of the resulting cell stream is header overhead?

Aparna Shakti
Aparna Shakti
Numerade Educator

Problem 40

Suppose that virtual paths are set up between every pair of nodes in an ATM network. Explain why connection setup can be greatly simplified in this case.

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Problem 41

Suppose that the ATM network concept is generalized so that packets can be variable in length. What features of ATM networking are retained? What features are lost?

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Problem 42

Explain where priority queueing and fair queueing may be carried out in the generic switch/router in Figure 7.10.

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01:00

Problem 43

Consider the head-of-line priority system in Figure 7.43. Explain the impact on the delay and loss performance of the low-priority traffic under the following conditions:
a. The high-priority traffic consists of uniformly spaced, fixed-length packets.
b. The high-priority traffic consists of uniformly spaced, variable-length packets.
c. The high-priority traffic consists of highly bursty, variable-length packets.

Kratika Bhadauria
Kratika Bhadauria
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Problem 44

Consider the head-of-line priority system in Figure 7.43. Suppose that each priority class is divided into several subclasses with different "drop" priorities. Each priority subclass has a threshold that if exceeded by the queue length results in discarding of arriving packets from the corresponding subclass. Explain the range of delay and loss behaviors that are experienced by the different subclasses.

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Problem 45

Incorporate some form of weighted fair queueing in the head-of-line priority system in Figure 7.43 so that the low-priority traffic is guaranteed to receive $r$ bps out of the total bit rate $R$ of the transmission link. Explain why this feature may be desirable. How does it affect the performance of the high-priority traffic?

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Problem 46

Consider a packet-by-packet fair-queueing system with three logical queues and with a service rate of one unit/second. Show the sequence of transmissions for this system for the following packet arrival pattern. Queue 1: arrival at time $t=0$, length 2; arrival at $t=4$, length 1. Queue 2: arrival at time $t=1$, length 3; arrival at $t=2$, length 1 . Queue 3 : arrival at time $t=3$, length 5 .

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02:03

Problem 47

Repeat problem 46 if queues 1,2 , and 3 have weights, 2,3 , and 5 , respectively.

Arun Bana
Arun Bana
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Problem 48

Suppose that in a packet-by-packet weighted fair-queueing system, a packet with finish tag $F$ enters service at time $t$. Is it possible for a packet to arrive at the system after time $t$ and have a finish tag less than $F$ ? If yes, give an example. If no, explain why.

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Problem 49

Deficit round-robin is a scheduling scheme that operates as follows. The scheduler visits the queues in round-robin fashion. A deficit counter is maintained for each queue. When the scheduler visits a queue, the scheduler adds a quantum of service to the deficit counter, and compares the resulting value to the length of the packet at the head of the line. If the counter is larger, the packet is served and the counter is reduced by the packet length. If not, the deficit is saved for the next visit. Suppose that a system has four queues and that these contain packets of length $16,10,12$, and 8 and that the quantum is 4 units. Show the deficit counter at each queue as a function of time and indicate when the packets are transmitted.

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Problem 50

Suppose that ATM cells arrive at a leaky bucket policer at times $t=$ $1,2,3,5,6,8,11,12,13,15$, and 19 . Assuming the same parameters as the example in Figure 7.55 , plot the bucket content and identify any nonconforming cells. Repeat if $L$ is reduced to 4 .

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Problem 51

Explain the difference between the leaky bucket traffic shaper and the token bucket traffic shaper.

Adam Conner
Adam Conner
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Problem 52

Which of the parameters in the upper bound for the end-to-end delay (equation 11) are controllable by the application? What happens as the bit rate of the transmission links becomes very large?

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Problem 53

Supose that a TCP source (with an unlimited amount of information to transmit) begins transmitting onto a link that has $1 \mathrm{Mbps}$ in available bandwidth. Sketch the congestion window versus the time trajectory. Now suppose that another TCP source (also with an unlimited amount of information to transmit) begins transmitting over the same link. Sketch the congestion window versus the time for the initial source.

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Problem 54

Suppose that TCP is operating in a $100 \mathrm{Mbps}$ link that has no congestion.
a. Explain the behavior of slow start if the link has RTT $=20 \mathrm{~ms}$, receive window of 20 kbytes, and maximum segment size of 1 kbyte.
b. What happens if the speed of the link is 1 Mbps? $100 \mathrm{kbps}$ ?

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Problem 55

Random early detection (RED) is a buffer management mechanism that is intended to avoid congestion in a router by keeping average queue length small. The RED algorithm continuously compares a short-time average queue length with two thresholds: $\min _{t h}$ and $\max _{t h}$ - When the average queue length is below $\min _{t h}$, RED does not drop any packets. When the average queue length is between $\min _{t h}$ and $m a x_{t h}$ RED drops an arriving packet with a certain probability that is an increasing function of the average queue length. The random packet drop is used to notify the sending TCP to reduce its rate before the queue becomes full. When the average queue length exceeds $\max _{t h}$, RED drops each arriving packet.
a. What impact does RED have on the tendency of TCP receivers to synchronize during congestion?
b. What is the effect of RED on network throughput?
c. Discuss the faimess of the RED algorithm with respect to flows that respond to packet drops and nonadaptive flows, for example, UDP.
d. Discuss the implementation complexity of the RED algorithm.

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