Dataword
Codeword
0000
0000000
0001
0001011
0010
0010110
0011
0011101
0100
0100111
0101
0101100
0110
0110001
Belman-Ford
Equation
0111
0111010
Dataword
1000
1001
1010
1011
1100
1101
1110
1111
COE371 – Computer Networks – Formula Sheet
ARQ Protocols
Nodal delay
• COMPUTER NETWORKS AND THE INTERNET
Utilization of Stop-and-Wait ARQ:
U sw =
t n = t pc + t q + t t r + t pr
A
B
Propagation
!
668
PART IV
NETWORK LAYER
Total
packets,
linksat each node along the path. The most
packetdelay
suffers for
fromM
several
types ofNdelays
important of these delays areTthe
nodal
queuing delay, transmisD 1 +processing
d 2 + · · · + ddelay,
tot =
N
sion delay, and propagation delay; together, these delays accumulate to give a total
Transfer all the packets through 1st link:
nodal delay. The performance of many Internet applications—such as search, Web
D 1 = tinstant
t t r [2] + . . .and
+ t tvoice-over-IP—are
browsing, email, maps,
greatly affected
t r [1] +messaging,
r [M ] + t pr [M ]
by network
In order
to acquire
a deep remaining
understanding
packet
switching and
Transfer
the delays.
M -th and
last packet
through
(N of
− 1)
links.
computer
For
i = 2, 3,networks,
. . . , N : we must understand the nature and importance of these delays.
d i = t pc [M ] + t q [M ] + t t r [M ] + t pr [M ]
Types of Delay
Sender
Dataword
Avg. response time without web caching:
Ttot = TLAN + Tacc + TInt
Avg. response time with web caching where 0 ≤ η ≤ 1:
¡
¢¡
¢
Ttot = ηTLAN + 1 − η TLAN + Tacc + TInt
a3 a2 a1 a0
RTTa [k] = (1 − α) RTTa [k − 1] + αRTTi [k]
¯
¯
∆i [k] = ¯RTTa [k] − RTTi [k]¯
¡
¢
∆a [k] = 1 − β × ∆a [k − 1] + β × ∆i [k]
CIDR
a3 a2 a1 a0 r2 r1 r0
Block assignment
Fraction
m bits
q bits
site
The reasonDefines
that classful
addressing
has become obsolete is
address
depletion. Since the
Defines subnet
Defines
interface
addresses were not distributed properly, the Internet was faced with the problem of the
addresses being rapidly used up, resulting in no more addresses available for organizations and individuals that needed to be connected to the Internet. Ton:understand
the prob48 bits
Decision
logic
Checker
Shared
Unreliable
transmission
b 3 b 2 b 1 b 0 q 2 q 1 q0
Codeword
Codeword
Multiple Access
In the encoder, the dataword has k bits (4 here); the codeword has n bits (7 here).
ALOHA
The size Throughput:
of the dataword is augmented by adding n − k (3 here) 0s to the right-hand side
of the word. The n-bit result is(fed into
the generator. The generator uses a divisor of size
Ge −2G for pure ALOHA
n − k + 1 (4 here), predefined
S ≈ and agreed upon. The generator divides the augmented
dataword by the divisor (modulo-2
division).
The quotient
of the division is discarded;
Ge −G
for slotted
ALOHA
the remainder (r2r1r0) is appended to the dataword to create the codeword.
The decoder
receives the codeword (possibly corrupted in transition). A copy of all
CSMA/CD
efficiency:
n bits is fed to the checker, which is a replica of the generator. The remainder produced
1
ηe ≈
1 + 5t pr /t t r
ATM
AAL5: Number of bytes in data, padding, and trailer must be divisible by 48:
D + X + 8 = 0 mod [48]
Multimedia Networks
Sampling frequency:
f s ≥ 2 f max
Network Security
SKC property:
K e = K d = K s → K s [K s (m)] = m
Class D is not divided into prefix and
suffix. It is used for multicast addresses. All
128 bits
PKC property:
addresses that start with 1111 in binary belong to class E. As in Class D, Class E is not
dividedGlobal
into prefix
and suffixSubnet
and isidentifier
used as reserve. Interface identifier
routing prefix
n bits
Divisor
d3 d2 d1 d0
Generator
TO[k]
= RTTaspace
4 ×IPv6
∆a [k]
[k] +of
Like the address space of IPv4,
the address
is divided into several blocks
of varying size and each block is allocated for a special purpose. Most of the blocks are
TCP Throughput
still unassigned and have been set aside for future use. Table 22.1 shows only the

assigned blocks. In this
table,
the+last
column shows the fraction each block occupies in
Wmin
Wmax

without loss

the whole address space.
2RTT
Ra ≈
1.22 MSS
assigned
Table 22.1 Prefixes for

with probability of loss ℓ
pIPv6 addresses
RTT ℓ 18 INTRODUCTION TO NETWORK LAYER
CHAPTER
531
Address Depletion
Accept
Syndrome s2 s1 s0
TimeoutAddress
value: Space Allocation
22.1.3
Block prefix
Dataword
Decoder
000
Let’s explore these delays in the context of Figure 1.16. As part of its end-to-end 0000
Internet
Protocol
0000
0000::/8
Special addresses
1/256
For
arrival
rate λ,
transmission
time t t ra i.e.
transmission
ratethe
µ: upstream node
route
between
source
and destination,
packet
is sent from
001
2000::/3
Global unicast
1/8
IP Routers
18.18 Occupation
of the address space
in classful addressing
= λ/µ
λtto
= λL/R b the nodal delay at router A.Figure
through router A to router B.ρOur
goal=is
t r characterize
1111 110
FC00::/7
Unique local unicast
1/128
Required
buffering for
N TCP flows going
through
router port:
Note that router A has an outbound link leading to router B. This link is preceded by 1111
1110
10
FE80::/10
Link
local addresses
1/1024
Packet
Error
Rate,
P
(
e
a queue (also known as a buffer). When the packet arrives at router A from the 1111 1111
FF00::/8
Multicast
1/256
RTTspace:
· R b 4,294,967,296
whenaddresses
N small
Address
addresses
For
bit error
raterouter
p b and
packet size
L bits:header to determine the appropriate
upstream
node,
A examines
the of
packet’s
B≈
p
¡ the ¢packet
RTT · R b / N when N large
L
outbound link for the packet and then directs
to this link. In this example, Global Unicast Addresses
Pe = 1 − 1 − pb
the outbound link for the packet is the one that
leads to router B. A packet can be
A
B
C
D
E
IP
Addressing
space that is used for unicast (one-to-one) communication
transmitted Delay
on a linkModel
only if there is no other packet currently being transmitted on The block in the address
HTTP1.0
50%
25%
12.5% 6.25%6.25%
between
two
hosts
in
the
Internet
is
called
the
global
unicast
address
block.
CIDR
for
IPv4
classful
addresses:
the link and
if there
are no other packets preceding it in the queue; if the link is
HTTP1.0
response
time:
which
three leftmost bits are the same for all
bits
8 bits means
8 bitsthat the
8 bits
currently busy or if there are other packets already queued for the link, the newly the block is 82000::/3,
bits, which isFirst
more
than
addresses in this block (001). The size of this block Class
is 2125Prefixes
= N (2RT T + t t r )
byte
totqueue.
arriving packet will then join Tthe
enough
expansion for
many years to come.
n =address
8 bits in this
Class Afor0 Internet
A An
0 toblock
127 is
Prefix
Suffix
HTTP1.1 Delay Models
divided
parts: global routing
prefix (n bits), Bsubnet
(m128
bits),
and
n = identifier
16 bits
Class Binto
10 threePrefix
to 191
Suffix
Processing
Delay
without
pipelining:
interface
(q bits),
also
the to
recomn = 24
bitsshows 192
Class C identifier
110
C figure
223
Prefixas shown in Figure
Suffix22.1. The
mended length for each
part.
Ttot the
= RT
T + N header
t t rdetermine
(RT T +
)
D Not applicable 224 to 239
Multicast addresses
The time required to examine
packet’s
and
where to direct the Class D 1110
E Not applicable 240 to 255
Reserved for future use
packet
is part of the processing delay. The processing delay can also include other Class E 1111
with
pipelining:
factors, such as the time needed to check for bit-level errors in the packet that occurred Figure 22.1 Global unicast address
2RT
T + N tnode
tot ≈the
tr
in transmitting the packet’s bitsTfrom
upstream
to router A. Processing delays IPv6 global unicast addresses with typical n = 48, m = 16, q = 64:
Web Caching
Receiver
Encoder
a3 a2 a1 a0
EWMA algorithm with α = 1/8 and β = 1/4:
Total delay for 1 packet, N links
Traffic Intensity, ρ
Figure 10.5 CRC encoder and decoder
CRC Technique
Timers
The nodal delay at router A
¡
¢
¡
¢
Ttot = N t t r + t pr + (N − 1) t pc + t q
Link Layer
Transmission Control Protocol
Nodal
Queueing Transmission
processing (waiting for
transmission)
Figure 1.16
d x (y) = min[c (x, a) + d a (y); c (x, b) + d b (y); c(x, c) + d c (y)]
Figure 10.5 shows one possible design for the encoder and decoder.
tt r
t t r + RT T
Utilization of pipelined ARQ with window size w:
w · tt r
U pl =
t t r + RT T
Utilization in terms of bandwidth-delay product a p = RT T /t t r :
w
U pl =
1 + ap
Sum of processing, queuing, transmission, and link propagation
Codeword
1000101
1001110
1010011
1011000
1100010
1101001
1110100
1111111
Discard
Network Delay
Remainder
PTER 1
Table 10.3 A CRC code with C(7, 4)
£
¤
£
¤
K A+ K A− (m) = K A− K A+ (m) = m
RSA algorithm:
C = P e mod n ↔ P = C d mod n