MEASUREMENTS ON DELAY AND HOPCOUNT OF THE

INTERNET

Aiguo Fei Guangyu Pei Roy Liu and Lixia Zhang

Department of Computer Science

University of California

Los Angeles CA

fafei p ei royliu lixiagcsuclaedu

only exp osed the unexp ected b ehavior of the current

Abstract

Internet proto cols but also help us b etter understand

the dynamics of large scale systems

To nd out how big the Internet is we measured the

roundtrip delays and hopcounts from a UCLA host

Endtoend b ehaviors in the Internet including de

computer to a randomly selected set of three thousand

lay and hopcount numb er of hops along a path from

Internet hosts around the world Our results show that

one host to another had also b een the sub ject of a

over of these hosts in continental US are within

numb er of studies In K systematic measurements

hops from UCLA and the roundtrip delays to of

were taken to see how the network delay varied with

these hosts are less than ms There seems no strong

dierent packet sizes dierent paths dierent times

correlation b etween the delay and hopcount although

during the day and dierent days in a week In B

the average delay increases with hopcount Measure

the author rep orted analysis of endtoend packet de

ments to international hosts show that the delay and

lay and loss b ehavior from observing the round trip

hopcount strongly dep end on the countries the hosts

delays of small UDP packets sent at regular time in

lo cate Physical distances and link sp eeds are the most

tervals In that study compression of prob e packets

imp ortant factors that determine the roundtrip delay

and rapid uctuations of queueing delays over small

intervals were observed and analysized by applying

some queueing mo del During spring Rautman

Intro duction

a UCLA graduate student used traceroute to measure

the delays and routes from UCLA to three sp ecic sites

The Internet has exp erienced exp onential growth in re

at USC MIT and UCLUniversity College London

cent years By estimateH there are ab out mil

R Rautmans main interest was to nd out how

lion hosts connected to the Internet at the time this

the network delay may vary with time and day as in

pap er is b eing written and this numb er is increasing

K He rep orted that the variance in delay from

everyday To design network proto cols and technolo

daytoday is not large although weekend days tend

gies that can scale with such rapid growth it is imp or

to have less delay Network delay varies with dierent

tant to know how big the Internet size is and how

time of the day however there is no denite correla

fast this size grows Although a numb er of measure

tion b etween the time and the delay Furthermore the

ment studies have b een conducted over the last few

three destinations exhibited dierent delay variation

years most of them fo cus on the trac characteristics

patterns Some endtoend delay and hopcount mea

congestion control issues and routing proto col stabil

surements are also rep orted in some research of cho os

ity During fall we conducted a massive measure

ing replicated Internet servers CC GS Along

ment eort aiming sp ecically at nding out how big

with the examination of dierent approaches for lo

the Internet was

cating nearby replicated Internet servers the authors

Internet measurement has a history as long as in GS discussed an optimized approach for hop

the Internet itself Measurement exp eriments on the count probing and presented some statistics of Inter

ARPANET packet delays was conducted as early net hopcount For example they rep orted an average

as K More measurement studies CPB hops among Internet site pairs In CC

CPB H PF were p erformed on the NSFNET the authors showed that empirical distributions of hop

after it replaced ARPANET in MERIT More re count and roundtrip time to Internet servers are

cently measurement studies showing the Internet rout dramatically dierent They were interested in how

ing instability and dynamics have also b een rep orted in go o d delay or hopcount is as a distance metric in se

GR LMF P These measurement studies not lecting replicated Internet server

The main ob jective of our study is to answer a sim

are received or timed out the average is taken as the

ple but fundamental question how big is the Internet

roundtrip delay One may take half of the roundtrip

Our denition of big is not measured by the p opula

delay as oneway delay but since routes may b e asym

tion that is how many hosts connected to the Internet

metricP it can only b e an approximation In this

but rather by the size that is how long is the path in

pap er we rep ort the roundtrip delay only We ran our

terms of hopcount and the delay from one host to an

program on a Sun Ultra Sparc machine with Solaris

other For example how long and how many hops do es

to collect all the data

it take to reach all the hosts out there in the Internet

What dierence can one exp ect if one is to access two

Some details in the measurement are worth men

hosts that are lo cated say in New York and Australia

tioning Sometimes a prob e packet receives no reply

given the source is here at UCLA

This can b e caused by a numb er of dierent reasons

We measured the roundtrip delays and hopcounts

the prob e packet or the reply may have got lost or

from a host at Computer Science Department of UCLA

a router may b e congured not to send back time

to hosts in four continents We examined the de

exceeded ICMP message or it only generates ICMP

lay and hopcount distributions of hosts chosen from

messages at a limited rate P Without receiving a

dierent US domains dierent geographical lo cations

reply within the timeout p erio d a second packet with

within continental USA and dierent countriesareas

the same TTL will b e sent The timer we used is sec

One of our goals was to understand how geographical

onds our measurements show that delays to all hosts

distance aects the delay and hopcount how dierent

reached except those in China are far less than sec

the delay and hopcount would b e for hosts in dier

onds If no reply is received for three consecutive pack

ent countries We to ok b oth the delay and hopcount

ets with the same TTL then that no de in the route is

measurement at the same time to see how the delay is

treated as unknown and TTL for next prob e packet is

related to the hopcount

increased by If no reply is received for consecu

The rest of this pap er is organized as follows We

tive TTL values our program will rep ort a failure It

rst describ e how we did our measurements and how

is p ossible that our measurement returns a failure but

we picked out those hosts in the next section then we

the destination is reachable but that p ossibility should

present our measurement results and analysis in sec

b e small based on all our observation If network or

tion Two measurementrelated issues Internet di

hostunreachable messages are received for consecu

ameter and Internet mapping are discussed in section

tive prob e packets with the same TTL it is treats this

followed by a brief summary in section

as a failure to o Sometimes such error message can

b e generated b ecause of administrative conguration

of the intermediate or destination router not b ecause

Measurement Metho d

a network or destination really cant b e reached but

one cant tell Another detail worth mentioning is that

To collect hopcount and delay data we wrote a small

the delay we measured is only for the packet size we

program based on the traceroute J S utility orig

used packets of dierent sizes may exp erience dierent

inally written by Van JacobsonJ Here is a short

delays

description of how it works For any destination it

sends a byte UDP packet to it with TTL Time To

Live starting from until the destination is reached We need a set of hosts randomly selected from the

For example if the destination is n hops away for global Internet as the destinations for our measure

any TTLn the UDP packets cannot reach the des ment We found a list of DNS servers from the Inter

tination and the intermediate no de which receives a NIC ftp siteNIC and randomly picked a set of IP ad

packet with TTL sends an ICMPInternet Control dresses from that list as our study sub jects In order

Message Proto col timeexceeded error message back to study the eect of physical lo cation on hopcount

to the source In this way the intermediate no des can and delay we also handpicked a numb er of hosts We

b e tracked out At the same time the UDP packet divided the continental US into four regions and picked

uses a p ort numb er which in general will not b e in a numb er of web servers of universities from each re

use so when the destination receives it it will send gion We used web servers of universities b ecause we

back a p ortunreachable message thus the program know for sure the geographical lo cations of those uni

knows destination is reached When it is known that versities and the web server names are easy to gure

the destination is reached our program sends a num out Hopcount and delay to hosts in China is one

b er of packets we used in our measurements to of our interests unfortunately the list from the Inter

the destination one by one in a stopandwait fashion NIC contained only few sites in China We visited the

with a timeout of seconds The time from sending homepage of CERNETChina Education and Research

a prob e packet to receiving the reply is the roundtrip NetworkCERNET and found a list of Chinese uni

time RTT After all the packets are sent and replies versities connected to CERNET

jor US domains com edu net gov org mil statis

Measurement Results and

tics of delay and hop count are shown in table a and

Analysis

b Std in tables stands for standard deviation and

avg stands for average

Our rst measurement is delay and hopcount to US

hosts We picked out a total of hosts from six ma

Table a Measurements of US Domains Delays

domain of of delay of median avg delay delay std avg delay delay std

hosts success hosts  delay of low of low of low of low

com ms ms ms ms ms ms

edu ms ms ms ms ms ms

net ms ms ms ms ms ms

gov ms ms ms ms ms ms

org ms ms ms ms ms ms

mil ms ms ms ms ms ms

total ms ms ms ms ms ms

detailed dierence exhibited in our measurement may Table b Measurements of US Domains Hop Count

domain avgerage std median hop count of

partly b e due to our rather limited sample sizeAnother

low 

concern is that net and mil domains may have hosts

outside continental US thus we also made graphs of

com

distributions without results from these two domains

edu

not shown here The resulting graphs lo ok very sim

net

ilar to the graphs including all domains indicating

gov

that few hosts we picked are outside of continental

org

US We can also see that the dierence in hop count

mil

among domains is far less signicant than that in delay

total

e put all the hopcounts and delays together and

W Total Distribution for US Hosts

generated the distribution graphs of delay hopcount 180

200

delay vs hopcount as shown in Fig In this and and 160

160 140

all other gures the height of a bar represents numb er

120

hosts for a given hopcount or delay range eg from of 120 100

80

to ms it can b e seen as a plot of p df proba ms 80

60

bility density function In the plot of average delay vs 40 40

Number of Hosts 20

hopcount the length of the error bar is twice as much

0 0

the standard deviation thus it is signicance

as 0 60 120 180 240 300 360 420 4 8 12 16 20 24

el of delay for hosts of a given hopcount

lev Delay (msec) Hop Count

e can see from the ab ove tables that there is

W 250

some dierence among dierent domains Since we

take sample hosts from dierent domains ac

didnt 200

cording to their real p ercentages eg there are more

150

hosts in com domain than that in edu domain but

we to ok ab out same numb er of com and edu hosts

100

in our measurement strictly we couldnt simply add

Delay (msec)

all together as in Fig But it should b e close

them 50

to the distribution with samples taken according to

statistical p ercentages if we do this way b ecause their 0

5 10 15 20 25

shap es of distributions for dierent domains lo ok

basic Hop Count

similar despite minor dierence in average or median

Fig Distribution of delay hopcount and delay vs Distribution graphs for dierent domains are shown

hopcount for hosts in US in Fig This similarity suggests that the Internet in

US is homogeneous with resp ect to domains Some

Table US Regional Measurements

region of of average hop count average delay std median median

hosts success hop count std delay hop count delay

West ms ms ms

Mountain ms ms ms

Centraleast ms ms ms

East ms ms ms

y is long eg ab out ms to MIT it is ab out

US Domains la

Although the delay to a given host uctuates Hop Count Distribution Delay Distribution to

30 30

our large sample space should minimize the eect of

single event So we b elieve the time of conducting 20 20 a

gov our measurements should not aect the validity To

10 10

examine how delay may vary with timeofday we ran

0 0

picked a subset of hosts from com domain 5 10 15 20 25 0 100 200 300 400 500 domly

60 70

did one measurement during the day which lasted from

50 60

to pm and did another measurement at mid 40 50 no on 40

30

t which lasted from am to am The dif net 30 nigh 20

20

b etween the mean delays from these two mea 10 10 ference

0 0

surements is ab out The mean and standard de

5 10 15 20 25 0 100 200 300 400 500

on hop count remained ab out the same only

60 90 viation 80 50

70

dierence on mean This result agrees with 40 60 a Number of Hosts 50

30

ations in PR that though there is certain edu 40 observ

20 30

variation of routing the route change do esnt 20 dynamic 10 10

0 0

happ en very often a dominant route exists and the

5 10 15 20 25 0 100 200 300 400 500

ariation of hopcount is minimal For international 60 50 v

50 40

measurement b ecause of time zone dierence the ef 40

30

of timeofday should b e even less 30 com fect 20

20

results for US regional measurements are

10 10 The

wn in Table and Fig We call the four regions 0 0 sho

5 10 15 20 25 0 100 200 300 400 500

est Mountain Area CentralEast and East Using

Hop Count Delay(msec) W

standard state name abbreviations West contains WA

Fig Distribution of hopcount and delay for four ma

OR and CA Mountain area contains MT ID WY

jor US domains

NV UT CO AZ and NM CentralEast contains ND

From Fig one can see in general that average

SD NE KS OK TX MN IA MO AR LA WI IL

delay increases with the increase of hopcount though

MI IN OH KY TN MS and AL East contains ME

the relation is not linear At the same time the stan

VT NH NY PA WV VA NC SC GA and FL They

dard deviation of delay is comparable with the mean

are going from west coast to east coast with increasing

delay This means there is no strong correlation b e

distance to our measurement starting p oint A numb er

tween hop count and delay In other words one cant

of hosts from each region were picked as describ ed in

accurately predict the delay to a host given the hop

the previous section

count as suggested in CC Our observation shows

The distributions of hop count and delay are shown

that delay is not simply determined by numb er of hops

in Fig From the table ab ove and that gure it is

it dep ends on a lot of other factors including physical

clear that b oth hopcount and delay increase with the

distance distance to the backb one link capacities and

increase of physical distance It suggests that at least

trac conditions along the route This also demon

inside the US physical distance is an imp ortant fac

strates the great heterogeneity of the Internet

tor on hopcount and round trip delay At the same

As p ointed out by RautmanR delay varies with time one also observes that the physical distance has

timeofday and dayofweek The results we show here a bigger eect on delay than on hopcount This can

were obtained during weekdays most measurements b e attributed to the fact that most widearea trac is

last from afterno on to night some were done at mid routed through the backb one a few hops on the back

night Because our measurements have a large sample b one can route trac from west coast to east coast

space it takes a long time to nish more than one hour while propagation delay is what one can never b eat

8

for US hosts longer for international hosts we Taking a signal propagation sp eed  ms of

were unable to do measurements at some sp ecic time light sp eed for signal in b er the roundtrip delay is

and compare However according to RautmanR ms for a distance mil esfrom Los Angeles to

the variation is not very large esp ecially when the de New York

Table International Measurements

countryarea of of average hop count average delay std median median

hosts success hop count std delay hop count delay

Canada ms ms ms

Australia ms ms ms

Germany ms ms ms

France ms ms ms

UK ms ms ms

Italy ms ms ms

China ms ms ms

Japan ms ms ms

Taiwan ms ms ms

South Korea ms ms ms

were only two links b etween China and the US US Regional there

Hop Count Distribution Delay Distribution

the time of our measurement one is Kbps and

6 6 at

the other Mbps while links inside China were of very

4 4

w sp eed to o West lo 2 2

0 0 5 10 15 20 25 0 50 100 150 Distribution for Hosts in Canada and Australia

15 8 20 25

6 20 10 15

Mountain 4 15 5 10 ca 2 10

5 0 0 5 5 10 15 20 25 0 50 100 150 15 15 0 0 10 15 20 25 0 100 200 300 400 500 600

10 10 Number of Hosts Central East 40 20 5 5 30 15 0 0 5 10 15 20 25 0 50 100 150 20 au 10 15 15

10 5 10 10 East Coast 0 0 10 15 20 25 0 100 200 300 400 500 600 5 5

Hop Count Delay ( msec )

Measurements of Canada and Australia 0 0 Fig 5 10 15 20 25 0 50 100 150

Hop Count Delay(msec)

The data for the four Europ ean countries shows a

Fig Measurements of US regional

very interesting phenomenon Almost all hosts with

We did our measurements to countries and ar hop count are UK hosts and these hosts have a

eas outside of USA including Canada Australia four longer delay than other hosts with hopcount over

in Asia and four in Europ e The results are shown in At the same time most hosts with hopcount or

table Fig to Fig are in France and the delay is even shorter than

All these show that hopcount and delay to an in hosts in other countries with hop count less than

ternational host heavily dep end on the sp ecic country This suggests that there is a link to UK with few hops

the host is in and vary over a wide range from country but pretty slow while there is a link to France with a

to country While network condition inside that coun numb er of no des but pretty fast Examining the tra

try plays an imp ortant role physical distance and the ceout data we identied a common path of hops

connection b etween US and that country are also im from UCLA to mcinet then to demonnet shared by

p ortant factors As seen from the dierence b etween UK hosts and all of them have a total hop count of

Canada and Australia in Fig hop counts to these and a roundtrip delay around ms While the

two countries lo ok similar but there is a dramatic dif delay up to MCIs last hop is ab out ms the delay

ference in delay due to the dierence in physical dis up to erminrouterrouterdemonnet is ab out ms

tances Comparing the results of China and Japan It is clear that demonnet was the ISP shared by those

hosts and intro duced the long delay We also iden Fig these two countries have similar physical dis

tied a common path of hops shared by UK tance from US the hop counts are close to o but the

hosts which has a delay ab out ms up to the last delays to these two countries are dramatically dierent

We found out from CERNET homepageCERNET hop JANETgwTeleglob enet which should b e in Eu

rop e b ecause there is a ms gap b etween it and the Fig were generated by putting measurements of four

hop b efore it We also found of France hosts Europ ean countries together As stated ab ove b ecause

shared the same path as long as hops from UCLA of the dierence among those countries the result is

very meaningful The main purp ose of having them

European Countries not

is to show the delayhopcount anomaly observed Hop Count Distribution Delay Distribution here

60 30

and compare the distributions with those from US 50 25 40 20 Total Distribution of European Countries 30 UK 15 20 10 80 120 10 5 100 0 0 10 20 30 100 200 300 400 500 60 80 40 20

30 15 40 60

20 France10 40 20 10 5 20 Number of Hosts 0 0 0 0 10 20 30 100 200 300 400 500 200 300 400 500 600 700 800 900 8 12 16 20 24 28 30 15 Delay (msec) Hop Count

20 10 Number of Hosts Germany 650 10 5 600 550 0 0 500 10 20 30 100 200 300 400 500 450 15 50 400 40 350 10 30 Italy 300 250 20 5 10 200 Delay (msec) 0 0 150 10 20 30 100 200 300 400 500 100 Hop Count Delay(msec) 50

0

Measurements of four Europ ean countries Fig 10 15 20 25 Hop Count Asian Countries/Area

Hop Count Distribution Delay Distribution Fig Measurements of four Europ ean countries put to 50 70

60 delay distribution hopcount distribution and 40 gether

50

y vs hopcount 30 40 dela Japan 20 30 20 10 10

0 0 Discussions 5 10 15 20 25 30 0 1000 2000 3000 4000 5000 10 20

8

15

One limitation of our measurements is that the start 6

Korean10

p oint is only at UCLA So if one do es measurement 4 ing

5

a dierent place delay and hopcount could b e

2 from

0 0

t However we b elieve the statistics should still 5 10 15 20 25 30 0 1000 2000 3000 4000 5000 dieren

50 20

b e similar Consider the delay it has three parts delay 40

15

from source to the backb one delay on the backb one

Number of Hosts 30

China 10

y in the destination site The rst part dep ends 20 dela

5

the top ology at the source site how the site is con 10 on

0 0

to the backb one The third part most likely 5 10 15 20 25 30 0 1000 2000 3000 4000 5000 nected

25 40

do es not dep end on the lo cation of the source The 20

30

second part dep ends on the relative lo cations of source 15

Taiwan20

destination With a large sample space the sec 10 and

10

and third parts would yield similar statistics re 5 ond

0 0

sp ectively with measurements from dierent starting

5 10 15 20 25 30 0 1000 2000 3000 4000 5000

t and the main dierence b etween measurements

Hop Count Delay(msec) p oin

from dierent sources is the dierence of the rst part

Fig Measurements of Asian CountriesArea

The same holds for hopcount measurement

to MCI backb one to Sprintlink backb one and then to Our measurement may help answer whats the

p ennsaukenhssieurogatenet and the Internet diameterP which is interesting to some

delay up to is ab out ms Hopcount p eople and would b e an imp ortant parameter to con

and delay distributions and delay vs hopcount in sider in large scale simulations and top ology mo deling

of the Internet Intuitively one may think the di p eering information and commercial ISPs may b e hesi

ameter of the Internet is the numb er of hops of the tant to provide such information ab out their networks

longest route needed to connect two farapart hosts Also their database only has top ology information of

In our measurement the longest route recorded has a dierent backb ones but do esnt have any information

hopcount of In measurement of P the longest ab out interconnections and subnetworks During our

route is hops Such a diameter gives us the impres measurement we collected thousands of routes at the

sion of how big the Internet is in size However since same time One interesting future research problem

one can hardly claim a long route he or she observed is to discover top ology and interconnection informa

is indeed the longest one the ab ove intuitive deni tion of dierent ISPs networks and other subnetworks

tion may not b e easily measurable A sound denition from the routes collected If we can succeed in dis

should also b e a description of an executable empiri covering the Internet top ology one will b e able to dis

cal metho d to measure such a metric An alternative cover information which ISPs are unwilling to pro

metric to represent how big the Internet is would b e vide to public by sending prob e packets and collecting

the average hopcount b ecause of some go o d prop er routes A new research pro ject the Internet Distance

ties of hopcount distribution As shown in the previ Map ServiceIDMaps F aims at discovering such

ous section and in CC hopcount is pretty much top ology information and more to meet applications

evenly distributed with the mean at the center So needs Our measurement pro ject could b e considered

average hopcount should give us a fairly go o d impres an early exp erimental step in that direction As shown

sion on how deep verticallyGR the Internet is in the last section we successfully identied the com

However the Internet is so highly heterogeneous and mon route shared by most UK hosts and that by most

our measurement shows that routes to dierent coun France hosts and we also identied a slow path to some

tries are really countrysp ecic one has to b e careful at hosts in UK

cho osing sample hosts when doing such measurement

Another interesting problem is how the diameter

Summary

or average hopcount grows with the growth of the In

ternet The growth trend concerns the scalability of

With the rapid growth in recent years the Internet has

network proto cols Some p eople b elieve that it grows

b ecome the biggest lab mankind has ever made In

as the logarithm of the size numb er of no des of the

this pap er we rep orted our measurement exp eriment

Internet When Internet size grows exp onentially we

conducted in this lab We measured hopcount and

exp ect its diameter to grow linearly There is evi

roundtrip delay from our host computer at UCLA to

dence that average hopcount do es increase with the

more than hosts worldwide and examined the

growth of the Internet In P the author rep orts

relation b etween delay and hop count Our results

that the mean hopcount of routes measured during

show that in the continental US more than of

Novemb er and Decemb er is while that mea

hosts can b e reached within hops and the round

sured during Novemb er and Decemb er is To

trip delays to more than of hosts are less than

carefully study how the mean hopcount or Internet

ms for our measurement packets We also observed

diameter increases with the growth of the Internet

no strong correlation b etween hopcount and delay al

systematic measurements have to b e carried out from

though the average roundtrip delay do es increase with

time to time on a regular basis

the hopcount We also observed that the hopcount

People had b een enthusiastic ab out information and delay to hosts in dierent countries demonstrate

country sp ecic patterns

sup erhighway after the widespread use of Inter

net In comparison with the widelyavailable freeway Our measurement on the network roundtrip delay

maps some p eople including ourselves have b een in may provide useful information to a numb er of appli

terested in maps of the Internet There are maps cations that need an estimate of delay of the underly

which have geographical lo cations of switching sys ing network Delay and hopcount knowledge together

tems NAPsnetwork access p oint subnetworks and may help researchers in cho osing parameters for large

their interconnections and there are logical maps scale simulation and mo deling of the Internet Mean

which show top ology and interconnections only Maps while it is still an op en research problem if we can dis

for NFSNET backb ones can b e found at Merit home cover Internet top ology from routes collected through

pageMERIT and maps for the new vBNS can b e traceroute We are condent that active probing utiliz

found at vBNS homepageVBNS There is an on ing the ICMP proto col is an eective way to do a lot of

going research eort to visualize backb ones of dierent Internet measurements but we also want to p oint out

ISPsInternet Service ProviderMAPNET They have that it shouldnt b e abused since it generates network

a database of backb one top ologies of a numb er of ISPs trac which can b e signicant sometimes We realize

and provide a Java applet to visualize the maps How that no measurement results can hold forever or every

ever an ISP needs to provide its backb one top ology or where b ecause of rapid change and great heterogeneity

of the Internet Our measurement is b est viewed as

H C Huitema How many hosts in the Internet

a snapshot of the Internet at the time We exp ect

See ftpftpb ellcorecompubhuitemastatssize

that systematic approaches to Internet size measure

to dayhtml

ment will b e develop ed so on which will lead to p eri

J V Jacobson Traceroute program Avail

o dic snapshots giving us an accurate picture of b oth

able from ftpftpeelblgovtraceroutetarZ

the Internet size and its growth rate and patterns

K L Kleinro ck Queueing Systems Vol

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