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Problems
1 TCP over Long Fat Networks (LFNs)
The goal of this problem is to familiarize yourself with the basics of ns while examining
the inter-action between Teri. LFNs and routers. LFNs (pronounced "elephants") are
networks with "fat pipes," where the bandwidth-delay products are large. Two about-to-
disappear .tom's AlphaWidgets.com and BetaGadgets.com have decided to connect their
networks to divert each others' dwindling set of customers to each other in the hope that
this will save them. They hope to stick a single router between their two networks, and
they have given Ben Bitdiddle, who is taking 6.829, the task of configuring the router. Ben
decides to perform a few simulations studies in ns in order to understand better the
details of configuring the router.
1. Ben begins his study by examining the dynamics of a simple TCP connection from
AlphaW-idgets to BetaGadgets over his router. Download Ben's script from ht tp :
//nms lcs . mit . edu/6.829/ps/ps2/LFN .t cl and examine it.
(a) What is the round-trip time (RTT) and bandwidth of the links that Ben is simulating?
How fast is his router? What kind of queueing discipline does his router use?
(b) (b) Run the script and plot the evolution of the sender's TCP window over time.
Identify where TCP slow-start ends and where congestion-avoidance begins.
Computer Network Assignment Help

2. Ben looks at a map of BetaGadgets' network and notices that some of BetaGadgets'
traffic travels over satellite links. He estimates that the average RTT for a connection
between AlphaWidgets and BetaGadgets over satellite is 500 ms.
(a) Reconfigure Ben's script so that the RTT for the connection is 500ms and repeat parts
(a) and (b) above.' (Note: You will need to increase the length of the simulation in
order to see TCP enter the steady state.)
(b) Without looking at the simulation results, tell us how big the average congestion
window would need be to allow a single TCP of fully utilizing the bottleneck link.
(c) From your plot in 2-(a), what is the maximum value of TCP's congestion window size in
the steady state? What is peculiar about the evolution of TCP's congestion window over
time in this case (use part (a))?

3. Ben figures that the problem with his satellite simulation has something to do with the
size of the queue at the router; packets seem to be getting dropped as the T CP
connection bursts traffic in slow start.
(a) Plot the evolution of the queue over time as well along with the evolution of the
sender's congestion window.

To understand how the queue evolves over time. Ben sets up the timing diagram shown
in Figure 1. In this figure, time proceeds vertically downwards, and the arrows indicate
the progress of packets back-and-forth across the network.
(b) Fill in the picture with the appropriate arrival and departure times for each packet.
For the purposes of this exercise, you may assume that the packet takes 125ms to
propagate through each leg of its trip, that packets take Oms to process at the endpoints,
and that the processing time for acknowledgments is negligible.
(c) During slow-start, how is the maximum queue length related to the current
congestion window size cwnd?
(d) Assume you don't have control over the router to increase its maximum queue
length. Can you change the behavior of the TCP sender so that it can achieve a large
maximum cwnd and fully utilize the link? How?2
2 Fun with RED and active queue management (AQM)
This problem is to help you understand different queue management schemes. This
problem uses the file AQM.tcl in http ://nms . les . mit . edu/6.829/ps/ps2/. You will also
find the files in http : //nms . 1 cs . mit . edu/ 6.829/p s/ps2 /s cr ipt s/ useful in data
processing and trace analysis. (But feel free to write any code you want to!)

Ben just learned about several queue management schemes, including RED and RED
with ECN, and Weighted Fair Queueing (WFQ) from 6.829. Ben wants to compare these
schemes. Help Ben set up the simulation topology shown in Figure 2 in the file AQM .t cl.
Let BW (ni, n2 ) be the bandwidth of the duplex link between n and n2. Set BW(S;,R0) =
100Mbps, BC& = 100Mbps, Vi = 0,1, 2. Set BW(Ro,R1)= I.5Mbps.
1. Fair Queueing.
(a) Ben first configures the Ro-R1 link to use fair queueing. Let So be a CBR source sending
1000-byte packets at a rate of 200 packets every second, and SI and S2 be long-running
TCP sources. Plot the goodput each source sees over time. Does it match your
intuition? Now set bo = BIV(RI,D0) = 56K bps (see create-netl). What goodput does
each source see in this case? Why?
(b) Now make So a TCP source too. What goodput does each source see for the cases
where Lb = 100Mbps and Lb = 56Kbps? Why?
(c) Based on this study, can you tell what the pros and cons of deploying fair queueing are?
2. RED.
(a) Next, Ben sets a RED queue with parameters mint hr esh_ = 6, maxthr esh_ = 18,
maxp_ = 0.1, q_weight_ = 0.002, gentle_ = true on the Ro-R1 link.

The buffer size on this link is set to be 54 packets (see opt (glen)). All sources are long
running TCPs. What are the goodput and loss rates of each connection?
3. RED & ECN.
(a) Ben hears the hype that ECN is likely to be deployed in the next few years. So, he
makes all the TCP sources ECN-capable. What does he see this time? Does the
goodput of each source increase? What about the loss rate?
(b) Ben wants to see how ECN-capable flows interact with non-ECN flows. So, he sets up
So to be ECN-capable and Si! S2 to be not. What does he see this time? Is there any
benefit of deploying ECN in this network?
(c) Ben becomes concerned about the possibility that an ECN-capable receiver might
cheat to get higher throughput than it deserves. The form of cheating is simple: When the
receiver gets a packet with ECN set on it, it does not echo it to the sender but instead
suppresses this information. Ben sets up Do to be a cheating receiver; the others are
honest ECN-capable connections. What are the goodput and loss rate of each source
now? What happens when the number of cheating receivers varies?
4. Overall, how do you compare the fairness provided by the following queuing
disciplines: FQ, RED, RED & ECN, and DropTail?

3 How useful is traceback?
Suppose we had the ability to traceback IP packets deployed on network paths? Would
this mitigate all attacks? Consider two cases: (i) Traceback is deployed on certain paths.
and (ii) traceback is universally deployed.
Clearly describe what types of attacks can be handled (and how) using traceback, and
what cannot. You might also speculate on additional helpful mechanisms that may be used
in conjunction with traceback.
4 Buffering in a fast router
Louis Reasoner has been recruited by a hot new startup to design the packet queueing
component of a high-speed router. The link speed of the router is 40 Gigabits/s, and he
expects the average Internet round-trip time of connections through the router to be
100 ms. Computer Network Assignment Help

Louis remembers from his 6.829 days that he needs to put in some amount of buffering
in the router to ensure high link utilization in the presence of the TCP sources in the
network growing and shrinking their congestion windows. Louis hires you as a consultant
to help design his router's buffers.
Assume for the purposes of these questions that you're dealing with exactly one TCP
connection with RTT 100 ms (it turns out that this assumption does not change the
results too much, for a drop-tail gateway, if the connections all end up getting
synchronized). Also assume that the source is a long-running TCP connection
implementing additive-increase (increase window size by 1/W on each acknowledgment,
with every packet being acknowledged by the receiver, such that the window increases
by 1 every RTT) and multiplicative-decrease (factor-of-two window reduction on
congestion). Assume that no TCP timeouts occur. Don't worry about the effects during
slow start (that was dealt with in Problem 1); this problem is about the effects on router
buffering during TCP's AIMD congestion-avoidance phase.
You should (be able to) answer this question without running any simulation.
1. Show that if the amount of buffering in the router is equal to the product of
bandwidth and round-trip delay (the bandwidth-delay product), the TCP connection can
achieve a 100% link utilization (or very close to it). How much memory does this
correspond to for the router under consideration?

2. Louis is shocked at how much memory is needed and thinks he may not be able to
provide this much buffering in his router. He asks you what the average link utilization is
likely to be when the amount of buffering in the router is very small compared to the
bandwidth-delay product. Explain your answer.
3. Louis decides that this utilization will not do. He asks you how the average link
utilization, U, varies as a function of r, the ratio of the amount of router buffering, B, to
the "pipe-size," P (the bandwidth-delay product). Calculate U(r) for 0 < r < 1. (We know,
from part 1, that U(1) = 1, and the answer to part 2 is U(0).)
4. Sketch U versus r, for 0 < r < 1. From this curve, what can you conclude about the gain
in link utilization as you add more memory?
Hint: A good way to think about this problem is in terms of the TCP congestion window
vs. time plots and look at how P, B, and the (time-varying) TCP congestion window size
relate to each other. Think about the "steady-state" of a TCP connection and about how
much data a TCP can send in one round-trip time. Don't worry about the TCP receiver
flow control window limitation (i.e., assume that the receiver has a very large buffer).
5 Rate guarantees in a high-speed switch
Lem A. Prover has been asked to design a scheme for providing rate guarantees to
queues in a crossbar-based CIOQ packet switch.

She thinks about the problem a little and thinks that if she simply implemented
weighted fair queueing on the queues, she might be able to solve the problem.
Recall that weighted fair queueing is a relative rate sharing scheme, while what Lem is
looking for is an absolute rate guarantee scheme.
Formally, consider an N x N switch with N egress links in all and Q queues per egress
link. The switch has speedup 2. Normalize all rates such that every ingress and egress
link has rate 1. The switch is configured so that on a given egress link, queue i is
guaranteed a rate ye (with 0 < 9. < 1 and EiQi gi < 1).
The service model required for guaranteed service is as follows: If queue i has an arrival
rate of ai and a guaranteed rate of ye, then the queue's service rate is at least
min(ai.gi).
Assume that in each time-slot the switch does a maximal matching; with speedup 2,
this means that if the arrival rates on the ingress-egress pairs form a doubly
substochastic matrix,3 the switch can support 100% throughput, i.e., no queue grows
unbounded at an ingress and all packets that arrive get transmitted to the appropriate
egress.
1. Assume that the arrival rates on the ingress-egress pairs form a doubly substochastic
matrix. Prove that there is a choice of weights in a weighted fair queueing system that
will allow Lem to implement the rate guarantee service model described above.

2. Give an example of arrival rates that are not doubly substochastic, where the
weighted fair queueing approach of the previous part cannot meet the rate guarantee
service model.
3. Lem wants to see if she can prove the result we mentioned in lecture 6, that if the
arrival rates to ingress-egress pairs form a doubly substochastic matrix, then a maximal
matching scheduling scheme in each time-slot running on a switch of speedup 2
provides 100% through-put.
She decides to consider a simplified version of this problem. Suppose that in each time-
slot at most one packet arrives on an ingress link and at most one packet arrives for any
given egress link. (I.e., the arrival rates are doubly substochastic even when measured
over a single time-slot duration.) Let qii be the current queue length of packets at
ingress i destined for egress j. Prove that if the switch does a maximal matching in each
time-slot and has speedup S > 2, then each qii has a finite upper-bound.
Hint: Look at the sum of all the queue lengths, Ei jqij and consider the increment and
decre-ment in this quantity in each time-slot. If you show that the sum of all queue
lengths is bounded, then you're done because each queue length is > 0.
6 XCP with lying participants
After reading the XCP paper in 6.829, Alyssa P. Hacker and Cy D. Fect get into an
argument about how fragile XCP is in the presence of senders who lie about the
information they are given. Computer Network Assignment Help

Consider a version of XCP where the sender reports to the network its RTT and its
throughput; i.e., the fields in the congestion header are: (i) RTT (ii) throughput (instead
of cwnd), and (iii) feedback. This change will make it easier for you to reason about this
problem.

# AQM.tcl is a simulation script to experiment
with queue management
# schemes. This has been used in the
Computer Networks
# course 6.829 at MIT.
#
# Xiaowei Yang
# Updated by Todd Nightingale 9.25.02
# To be run using NS:
# % ns AQM.tcl
#
# Options can be set using -OPTION VAULE
# % ns AQM.tcl -test "RED" -qlen 100
# Generic Testing Class
Class TestSuite
# Specific Testing Classes
Solution

Class Test/FQCBR -superclass TestSuite
Class Test/FQTCP -superclass TestSuite
Class Test/RED -superclass TestSuite
Class Test/ECN -superclass TestSuite
Class Test/REDECN -superclass TestSuite
Class Test/ECNCHEAT -superclass TestSuite
Class Test/ECNCHEATALL -superclass TestSuite
Class Test/DropTail -superclass TestSuite
Class Test/Pareto -superclass TestSuite
Class Test/ParetoDropTail -superclass TestSuite
# set defaults for all user specifiable
parameters
# (there are the parameters students will
change from the command line)
proc default-options {} {
global opt
set opt(test) "RED"
set opt(outdir) "out"
set opt(qtrace) "on"
set opt(traceall) "on" Computer Network Assignment Help

set opt(pipe) "on"
set opt(cwndtrace) "on"
set opt(namtrace) "off"
set opt(autonam) "off"
set opt(stoptime) 200
set opt(startuptime) 20
set opt(nconn) 3
set opt(delay) 2ms
set opt(bw) 100Mb
set opt(qlen) 54
set opt(bndelay) 40ms
set opt(bnbw) 1.5Mb
set opt(maxwin) 120
set opt(pktsize) 1000
{
print $1, $7 > cwndfile;
}
{
print $3, $11 > Qfile;
}

#
# LFN.tcl is a simulation script to study the
relation between the
# optimal buffer size and link utilization. This
has been used in the
# Computer Networks course 6.829 at MIT.
#
# Xiaowei Yang
Class TestSuite
Class Test/LFN -superclass TestSuite
proc default-options {} {
global opt
set opt(test) "LFN"
set opt(outdir) "out"
set opt(qtrace) "on"
set opt(cwndtrace) "on"
set opt(traceall) "on"
set opt(namtrace) "off"

}
proc usage {} {
global opt
puts "Options:"
puts "t-test <LFN>. The test to run. Default:
$opt(test)."
puts "t-outdir <value>. Data file output
set opt(bw) 100Mb
set opt(qlen) 10
set opt(bndelay) 16ms
set opt(bnbw) 1.5Mb
set opt(maxwin) 400
set opt(maxseg) 1000
set opt(autonam) "off"
set opt(stoptime) 200
set opt(startuptime) 5
set opt(nconn) 1
#set opt(filesize) 5000
set opt(delay) 2ms

or off. Default: $opt(qtrace)."
puts "t-cwndtrace <on/off>. Congestion
window tracing on or off. Default:
$opt(cwndtrace)."
puts "t-traceall <on/off>. Trace all on or off.
Default: $opt(traceall)."
puts "t-namtrace <on/off>. Nam tracing on
or off. Default: $opt(namtrace)."
puts "t-autonam <on/off>. Execute nam at
the end of simulation. Default:
$opt(autonam)."
directory. Default: $opt(outdir)."
puts "t-qtrace <on/off>. Queue tracing on
puts "t-stoptime <value>. The simulation stop
time. Default: $opt(stoptime)."
puts "t-startuptime <value>. Each
connection randoms starts between time 0
and value. Default: $opt(startuptime)."
puts "t-nconn <value>. Number of
connections. Default: $opt(nconn)."
puts "t-filesize <value>. Length of transfer
file size, in packets. Default: $opt(filesize)."

puts "t-delay <value>. Non-bottleneck Link
Delay. Default: $opt(delay)."
puts "t-bw <value>. Non-bottleneck link
bandwidth. Default: $opt(bw)."
puts "t-qlen <value>. Bottleneck max queue
length. Default: $opt(qlen)."
puts "t-bndelay <value>. Bottleneck
propagation delay. Default: $opt(bndelay)."
puts "t-bnbw <value>. Bottleneck
bandwidth. Default: $opt(bnbw)."
puts "t-maxwin <value>. Maximum TCP
window size. Default: $opt(maxwin)."
puts "t-maxseg <value>. Maximum TCP
segment size. Default: $opt(maxseg)."
}
TestSuite instproc init {} {
global opt
$self instvar ns_ qmon S_ D_ R_ allf namf
# set up topology
remove-packet-header AODV ARP

Trace set show_tcphdr_ 1
Agent/TCP/FullTcp set segsize_
$opt(maxseg);
Agent/TCP/FullTcp set window_
$opt(maxwin);
set ns_ [new Simulator]
#set allf [open "| awk -f script/xplot3.awk >
$opt(outdir)/all.xpl" w]
if {$opt(traceall) == "on"} {
set allf [open "$opt(outdir)/all.out"
w]
$ns_ trace-all $allf
}
if {$opt(namtrace) == "on" } {
set namf [open nam.out w]
$ns_ namtrace-all $namf
}
}
TestSuite instproc finish {} {

global opt
$self instvar ns_ allf qf cwndf namf
if {$opt(traceall) == "on"} {
flush $allf
close $allf
}
if {$opt(qtrace) == "on"} {
flush $qf
close $qf
}
if {$opt(namtrace) == "on"} {
flush $namf
close $namf
}
if {$opt(cwndtrace) == "on"} {
flush $cwndf
close $cwndf
}

if {$opt(autonam) == "on"} {
exec nam $opt(outdir)/nam.out &
}
#exec awk -f script/xplot3.awk
$opt(outdir)/all.out > $opt(outdir)/all-
$opt(qlen).xpl &
exit 0
}
Test/LFN instproc init {} {
global opt
$self instvar testName_
$self set testName_ $opt(test)
$self next
$self create-topology
}
Test/LFN instproc create-topology {} {
global opt
$self instvar ns_ S_ D_ R_ qf
for {set i 0} {$i < $opt(nconn)} {incr i} {

set S_($i) [$ns_ node]
}
set D_($i) [$ns_ node]
}
set R_(0) [$ns_ node]
set R_(1) [$ns_ node]
$ns_ duplex-link $S_($i) $R_(0)
$opt(bw) $opt(delay) DropTail
$ns_ duplex-link $R_(1) $D_($i) $opt(bw)
$opt(delay) DropTail
}
# set up bottleneck link
$ns_ duplex-link $R_(0) $R_(1) $opt(bnbw)
$opt(bndelay) DropTail
$ns_ queue-limit $R_(0) $R_(1) $opt(qlen)

if {$opt(qtrace) == "on"} {
#set qf [open "| awk -f
script/queue.awk > $opt(outdir)/queue-
$opt(qlen).xpl" w]
set qf [open $opt(outdir)/queue-
$opt(qlen).out w]
set bnk [$ns_ link $R_(0) $R_(1)]
$ns_ monitor-queue $R_(0) $R_(1)
$qf
$bnk start-tracing
}
}
Test/LFN instproc run {} {
global opt
$self instvar ns_ R_ S_ D_ cwndf qf
#set cwndf [open "| awk -f
script/cwnd.awk > $opt(outdir)/cwnd-
$opt(qlen).xpl" w]
set cwndf [open $opt(outdir)/cwnd-
$opt(qlen).out w]
} Computer Network Assignment Help

set rng [new RNG]
set tcp [new Agent/TCP/FullTcp]
set tcpsink [new Agent/TCP/FullTcp]
$ns_ attach-agent $S_($i) $tcp
$ns_ attach-agent $D_($i) $tcpsink
$tcpsink listen
$ns_ connect $tcp $tcpsink
set ftp [new Application/FTP]
$ftp attach-agent $tcp
$tcp attach $cwndf
$tcp tracevar cwnd_
#$tcp tracevar ssthresh_
}
set starttime [$rng uniform 0
$opt(startuptime)]
#$ns_ at $starttime "$ftp produce
$opt(filesize)"
$ns_ at $starttime "$ftp start"

}
$ns_ at $opt(stoptime) "$self finish"
$ns_ run
}
proc runtest {arg} {
global opt
default-options
set b [llength $arg]
for {set i 0} {$i < $b} {incr i} {
set tmp [lindex $arg $i]
if {[string range $tmp 0 0] != "-"} continue
set name [string range $tmp 1 end]
if {$name == "help"} {
usage
} elseif {[info exists opt($name)]} {
set val [lindex $arg [incr i]]
global opt($name)
set opt($name) $val
puts "-$name set to $opt($name)"
} else { Computer Network Assignment Help

puts "Invalid option: $name"
usage
}
}
set t [new Test/$opt(test)]
$t run
}
global argv arg0
runtest $argv
BEGIN {
nconn = 2;
for (i = 0; i < nconn; i++) {
loss[i] = 0;
total[i] = 0;
}
startup = 2;
}

{
if (($1 == "+") && ($4 == (2 * nconn))) {
total[$8]++;
}
if ($1 == "d") {
loss[$8]++;
}
}
END {
for (i = 0; i < nconn; i++) {
printf "%d %6.5fn", i, loss[i] * 1.0 /
total[i];
}
}
{
if ($1 == "Q" && NF>2)
print $2, $3 > Qfile
else if ($1 == "a" && NF>2)
print $2, $3 > afile
}

#
# Helper script. Works with AQM.tcl. Assume
FullTCP show_hdr
# formate. $8 is the flow id.
# Compute goodput of TCP, throughput of
other sources
# Compute loss rate
# Compute link utilization
# Works only for dumpbell topologies, where
nodes i < nconn are
# sources, 2*nconn > i >= nconn are
destinations, 2*nconn is the router
# connecting all sources, and 2*nconn+1 is the
router connecting all
# destinations.
# This has been used in the Computer
Networks course 6.829 at MIT.
#
# Xiaowei Yang
BEGIN {
nconn = 2;

for (i = 0; i < nconn; i++) {
# src[i] = i;
dst[i] = nconn + i;
bytes[i] = 0;
start[i] = 0;
virgin[i] = 1;
loss[i] = 0;
total[i] = 0;
prevT[i] = 0;
prevB[i] = 0;
prevL[i] = 0;
prevP[i] = 0;
}
prefix = "";
interval = 1.0;
loss_interval = 100;
startuptime = 25;
bw = 1500000;
totalB = 0;
prevtotalB = 0;
prevtotalT = 0;
}

{
if (NR == 1) {
split(FILENAME, a, "-");
if (a[1] == "") {
a[1] = prefix;
}
}
# compute tcp throughput. only count data
bytes, no header.
tcpput = (($1 == "+") && ($5 == "ack") &&
($3 >= nconn) && ($3 < 2*nconn));
nontcpput = (($1 == "r") && (($5 == "cbr") ||
($5 == "pareto")) && ($3 == (2 * nconn + 1)));
if (tcpput || nontcpput) {
fid = $8;
if (virgin[fid]) {
start[fid] = prevT[fid] = $2;
virgin[fid] = 0;
} else {
if (tcpput) {
bytes[fid] = $13;

} else {
bytes[fid] += $6;
}
printf "%f %6.5fn", $2, bytes[fid]
* 8.0 / ($2 - start[fid]) > a[1]"-tput-"fid".dat";
if (($2 - prevT[fid]) > interval) {
printf "%f %6.5fn", $2,
(bytes[fid] - prevB[fid]) * 8.0 / ($2 - prevT[fid])
> a[1]"-stput-"fid".dat";
prevT[fid] = $2;
prevB[fid] = bytes[fid];
}
}
}
if (($1 == "+") && ($4 == (2 * nconn))) {
fid = $8;
total[fid]++;
printf "%f %6.5fn", $2, loss[fid] * 1.0
/ total[fid] > a[1]"-loss-"fid".dat";
if ((total[fid] - prevP[fid]) >
loss_interval ) {

printf "%f %6.5fn", $2, (loss[fid] - prevL[fid]) /
(total[fid] - prevP[fid]) > a[1]"-sloss-"fid".dat";
prevP[fid] = total[fid];
prevL[fid] = loss[fid];
}
}
if ($1 == "d") {
fid = $8;
loss[fid]++;
}
if (($1 == "-") && ($3 == 2*nconn) && ($4 ==
(2*nconn + 1))) {
totalB += $6;
if ($2 - prevtotalT > interval) {
printf "%f %6.5fn", $2, (totalB -
prevtotalB) * 8.0 / ($2 - prevtotalT) / bw >
a[1]"-linkutil.dat";
prevtotalB = totalB;
prevtotalT = $2;
}
}
} Computer Network Assignment Help

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