MODELING NETWORKS AS GRAPHS
By
Sudheer kovi
TOPICS COVERED ARE:
1)Network Protocols.
a) Stop-and-Wait
b) Alternating Bit Protocol
c) Sliding Window Protocol
d) Transmission Control Protocol
2)Modeling Networks as Graphs.
Network?
It is a process of inter connection, it can be both
connection oriented or wireless.
The Need for Networks?
Transferring data from one end to the other, either
in the form of signals or packets of data.
NETWORK PROTOCOLS
The job of a network is to enable efficient and
reliable communication between hosts, and these
protocols are mainly designed for solving the
problems like Error control, Flow control,
Bandwidth limitation.
1. Error control : while transmitting the data the
messages can be lost, corrupted or reordered.
2. Flow control : Incompatibility between the
sending and receiving hosts, the receiving host
may not be able to process messages as fast as the
sending host can send them.
3. Bandwidth limitation : Limitation on the speed in
which data is being transferred, if its more or less
than the required bandwidth data could be lost.
 To solve these problems acknowledgement is one of the finest
solution, protocol stack is the best way to explain this.
Application layer:
(World Wide Web and Email)
HTTP,SMPT
Transport layer:
(Transmits messages between client and server)
TCP,UDP
Network layer:
(Relays messages through a series of switches from source
to destination)
IP
Link layer:
Transmits messages from one node to the next node
Physical layer:
Transmits bits across a physical network
ETHERNET
WIRES,CABLES
RADIO FREQUENCY
STOP-AND-WAIT
 Automatic Repeat request (ARQ), is an error control method, and it is a
part of stop and wait flow control protocol.
 If error is detected by receiver, it discards the frame and send a
negative ACK (NAK), causing sender to re-send the frame.
 In case a frame never got to receiver, sender has a timer, where each
time a frame is sent, timer is set.
 If no ACK or NAK is received during timeout period, it re-sends the
frame.
STOP-AND-WAIT
 Suppose timeout and sender retransmits a frame but receiver
actually received the previous transmission receiver has duplicated
copies.
A
B
Frame 0
ACK
Frame 1
ACK
Frame 2
Timeout
Frame 2
ACK
Frame 3
Timeout
ACK
Frame 3
ACK
B receive the Duplicate
Frame
ALTERNATING BIT PROTOCOL
 The Alternating Bit Protocol doesn’t add arbitrary subscripts.
 It add a single control bit to each data message and to each ACK.
 In this if the sender sends the data D0 to receiver it sends the ACK1
indicating that the sender next data message should be D1.
 To avoid receiving and accepting two copies of same frame, frames
and ACKs are alternatively labeled 0 or 1: ACK1 for D0, ACK0 for
D1
 The Alternating Bit Protocol does not solve all error control
problems.
ALTERNATING BIT PROTOCOL
SENDER
RECEIVER
D0
D0
ACK 1
D0
ACK 1
D1
ACK1
D0
ACK1
SLIDING WINDOW PROTOCOL
 The sliding window protocol can solve wasted bandwidth problems
by using more sophisticated ARQ technique.
 In sliding window protocol sequence number is assigned to the
messages that sender sends to receiver.
 The sliding window protocol begins by choosing a window size W.
 Data messages are initially entered into a FIFO queue, and the
sequence number is assigned, that is maintained by the sender.
 Sliding window protocol is used sending messages on the internet.
 The message that have been send are shown in the sender’s queue
with dark shade.
SLIDING WINDOW PROTOCOL
 Same in the receiver side the received messages are seen with the
dark shade.
 In this it will not wait for the ACK of message ‘n’ before sending
the message n+1
 The Sliding window protocol cannot be modeled as a finite state
machine because of the need to store the message sequence number.
SENDER
0
1
2
3
4
5
6
7
RECEIVER
8
9 10 11 12 13 14
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14
0
0
1
2
3
4
5
6
7
8
1
9 10 11 12 13 14
2
A3
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14
3
4
0
1
2
3
4
5
6
7
8
5
9 10 11 12 13 14
6
A4
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14
TRANSMISSION CONTROL PROTOCOL
 In the internet protocol stack, the transport layer sits immediately
below the application layer.
 Transmission Control Protocol is the most widely used Internet
protocol Web, HTTP, SMPT, FTP, and Telnet.
 TCP is a two way, reliable, byte stream oriented end-to-end protocol.
 TCP connection is established by a three step handshake procedure:
one host initiates the connection, and the other acknowledges it, and
the originator then confirms the acknowledgement.
 In TCP ones connection is open then data can be transmitted between
the two hosts until the connection is closed.
TRANSMISSION CONTROL PROTOCOL
 In this a connection progress through a series of states during its
lifetime.
 The states are : LISTEN, SYN-SEND, SYN-RECEIVED,
ESTABLISHED, FIN-WAIT-1, FIN-WAIT-2, CLOSED-WAIT,
CLOSING, LAST-ACK,TIME-WAIT, and CLOSED.
 CLOSED represents the state when there is no Transmission Control
Block.
 The transition in the below diagram has a label of the form <event> /
<action>.
CLOSED
rcv SYN
sen SYN, ACK
SYN
RCVD
rcv ACK of SYN
x
CLOSE
snd FIN
LISTEN
SEND
SND SYN
CLOSE
Delete TCB
SYN
SENT
Rcv SYN, ACK
sen ACK
ESTEB
CLOSE
snd FIN
rcv FIN
snd ACK
FIN
WAIT-1
rcv FIN
rcv ACK of FIN
snd ACK
x
Active OPEN
Create TCB
snd SYN
CLOSE
Delete TCB
Passive OPEN
create TCB
CLOSED
WAIT
CLOSE
sen FIN
LAST
ACK
CLOSING
FIN
WAIT-2 rcv ACK of FIN
x
rcv FIN
TIME WAIT
snd ACK
Timeout = 2MSL
Delete TCB
CLOSED
rcv ACK of FIN
x
MODELING NETWORKS AS GRAPHS
 In this we generally model a network to a graph, in which processors
correspond to vertices and links to edges by doing so we can solve
many problems associated to it.
 Let g be a undirected graph with vertices V an edges U .
 Edges corresponds to laying cables between two vertices.
 One of the efficient technique to find the minimum spanning tree,
we use kruskal’s algorithm.
 Consider spanning tree T where T(G)-subset of edges of G. Where T
has no cycles, G is connected to every other vertex using just the
edges in T.
MODELING NETWORKS AS GRAPHS
In this we have 2ways to determine efficient path.
1.
Shortest Path
2.
Eulerian Circuit
MODELING NETWORKS AS GRAPHS
Shortest-Path :
 Given a weighted graph and two vertices u and v, we want to find a
path of minimum total weight between u and v. Length of a path is
the sum of the weights of its edges.
 G is an unweighted, undirected graph.
 Where u and v are Vertices in G.
 k ≥ 0, there exists a path from u to v whose length is at most k.
MODELING NETWORKS AS GRAPHS
Example:
 Shortest path between ‘S’ and ‘T’
23
2
s
3
9
18
14
30
15
6
2
6
11
5
5
19
4
6
16
20
7
44
t
MODELING NETWORKS AS GRAPHS
EULERIAN CIRCUIT:
 The shortest way to traverse all the links in a network is via an Eulerian
Circuit.
 We check the network to verify that all links are working properly.
 It describe the network as a graph G.
 Where vertices corresponds to network nodes.
 Edges corresponds to network links.
 Where vertex cover C of a graph G with vertices v, and edges E is a
subset of v.
 In this every edge E touches at least one vertices in C.
REFERENCES
1.
Automata, Computability and Complexity : theory and application
by Rich, Elaine.
2.
http://en.wikipedia.org/wiki/Sliding_window_protocol
3. users.ecs.soton.ac.uk/sqc/EL336/CNL-5.pdf
THANK YOU