This document provides an overview of how telephone systems work through a 10 step mathematical problem and solution. It begins with introductions to telephones and their history. It then presents a telephone system state with lines and links, current calls in progress, and upcoming calls. The 10 step mathematical solution walks through changing system states as calls are processed, completed, or blocked based on available lines and links. It demonstrates how the telephone network dynamically routes calls over time.

1. Welcome To Our
Presentation

3. o Introduction
o About Telephone
o Short History
o How Telephone System works?
o Mathematical Problem
o Mathematical Solution
o Part - 1
o Mathematical Solution
o Part - 2
o Ending…
Contents
Telephone System

4. Introduction
In other words we can say :-
A telephone converts sound, typically &most efficiently the human voice, into
electronic signals that are transmitted via cables & other communication channels
to another telephone which reproduces the sound to the receiving user.
What is Telephone?
Device that coverts sound & electrical waves into audible relays & is
used for communication. The telephone consists of 2 essential parts,
a microphone & a speaker. This allows the user to speak into the
device & also hear transmissions from the other user.

5. History of the Telephone System.

6. How do telephone systems work?
Your voice generates sound energy when the vocal chords in your throat vibrate. The sound energy travels
through the air into the microphone & makes the diaphragm inside vibrate. The diaphragm converts the energy
from your voice into electricity & this electrical energy flows down the phone line.
About Telephone System.

7. Alexander Graham Bell
United Kingdom
Born: March 3, 1847
Died: August 2, 1922
Education:
University College London
(1868-1870)
He made the 1st call on March
10, 1876

8. Mabel Hubbard was Bell's girlfriend who he later marries on 1877.

9. How Telephone System works?

11. State : Problem
1
2
3
4
5
6
7
8
Lines
1
1
0
1
0
1
0
0
Links
max
4
in use
2
clock
1000
Call In Progress
From To End
1 4 1023
2 6 1055
Processed Completed Blocked Busy
100 60 20 20
Next Call
From To Length
3 6 30
Arrival time
1035
Next call to Arrive
From To Length Arrival Time
3 6 30 1035
3 7 25 1062
1 8 20 1075
Problem

12. System state : 1
1
2
3
4
5
6
7
8
Lines
0
1
0
0
0
1
0
0
Links
max
4
in use
1
clock
1023
Call In Progress
From To End
2 6 1055
Processed Completed Blocked Busy
101 61 20 20
Next Call
From To Length
3 6 30
Arrival time
1035
Next call to Arrive
From To Length Arrival Time
3 6 30 1035
3 7 25 1062
1 8 20 1075
System state : 2
1
2
3
4
5
6
7
8
Lines
0
1
0
0
0
1
0
0
Links
max
4
in use
1
clock
1035
Call In Progress
From To End
2 6 1055
Processed Completed Blocked Busy
102 61 20 21
Next Call
From To Length
3 7 25
Arrival time
1062

13. System state : 3
1
2
3
4
5
6
7
8
Lines
0
0
0
0
0
0
0
0
Links
max
4
in use
0
clock
1055
Call In Progress
From To End
Processed Completed Blocked Busy
103 62 20 21
Next Call
From To Length
3 7 25
Arrival time
1062
Next call to Arrive
From To Length Arrival Time
1 8 20 1075
System state : 4
1
2
3
4
5
6
7
8
Lines
0
0
1
0
0
1
0
0
Links
max
4
in use
1
clock
1055
Call In Progress
From To End
3 6 1085
Processed Completed Blocked Busy
103 62 20 21
Next Call
From To Length
3 7 25
Arrival time
1062

14. System state : 5
1
2
3
4
5
6
7
8
Lines
0
0
1
0
0
1
0
0
Links
max
4
in use
1
clock
1062
Call In Progress
From To End
3 6 1085
Processed Completed Blocked Busy
104 62 20 22
Next Call
From To Length
1 8 20
Arrival time
1075
Next call to Arrive
From To Length Arrival Time
1 8 20 1075
System state : 6
1
2
3
4
5
6
7
8
Lines
1
0
1
0
0
1
0
1
Links
max
4
in use
2
clock
1075
Call In Progress
From To End
3 6 1085
1 8 1095
Processed Completed Blocked Busy
104 62 20 22
Next Call
From To Length
Arrival time

15. System state : 7
1
2
3
4
5
6
7
8
Lines
1
0
0
0
0
0
0
1
Links
max
4
in use
1
clock
1085
Call In Progress
From To End
1 8 1095
Processed Completed Blocked Busy
105 63 20 22
Next Call
From To Length
Arrival time
Next call to Arrive
From To Length Arrival Time
System state : 8
1
2
3
4
5
6
7
8
Lines
1
0
1
0
0
0
1
1
Links
max
4
in use
2
clock
1085
Call In Progress
From To End
1 8 1095
3 7 1110
Processed Completed Blocked Busy
105 63 20 22
Next Call
From To Length
Arrival time

16. System state : 9
1
2
3
4
5
6
7
8
Lines
0
0
1
0
0
0
1
0
Links
max
4
in use
1
clock
1095
Call In Progress
From To End
3 7 1110
Processed Completed Blocked Busy
106 64 20 22
Next Call
From To Length
Arrival time
Next call to Arrive
From To Length Arrival Time
System state : 10
1
2
3
4
5
6
7
8
Lines
0
0
0
0
0
0
0
0
Links
max
4
in use
0
clock
1110
Call In Progress
From To End
Processed Completed Blocked Busy
107 65 20 22
Next Call
From To Length
Arrival time

17. Thank You