1. Tele traffic
A telephone network is composed of a variety of common equipment, such as:
Digital receivers
Call processors
Inter-stage switching links &
Inter-office trunks
The amount of common equipment designed into a network is determined under an assumption that not all users of the network need service at one time.

2. Tele traffic
The exact amount of common equipment required is unpredictable, because of the random nature of the service requests.
Network conceivably could be designed with enough common equipment to instantly service all requests except for occurrences of very rare or unpredicted peaks
The goal of traffic analysis is to provide a method for determining the cost-effectiveness of various sizes and configuration of networks.

3. Trunk & busy hour
The term trunk is used to describe any entity that will carry one call. It may be an international circuit with a length of thousands of km or a few meters of wire between switches in the same telephone exchange.
The arrangement of trunks and switches within an exchange is called its trunking.

4. Busy hour
The busy hour is based upon customer demand at the busiest hour during a week, month or year
A period of one hour time is chosen which corresponds to the peak traffic load and this is called the busy hour. Or , It is the period of one hour where the volume of the traffic is greatest.
Average daily peak hour;
Time consistent busy hour; 1 hr same for each day
Fixed daily mean hour;

9. Traffic variation Traffic fluctuates over several time scales:
Trends (> year)
- the overall traffic growth, no. of users, change in the usages
- traffic prediction give the basis for network planning
(ii) Seasonal variation
- Changes related to different seasons (e.g. vacation periods)
(iii) Weekly variation ( days)
- different activities on different days
(iv) Daily profile
- Random fluctuation

10. Off-peak
Since the amount of equipment provided must be sufficient to cope with the busy hour, much of it is idle during most of the day.
It is for this reason, the telecommunication operator offer their customers cheaper calls at off-peaks periods.
It cost them noting to carry such calls.

11. Techniques of traffic analysis
On the basis of system’s treatment of overload traffic, the traffic analysis are two types:
Loss System: Overload traffic is rejected without being serviced. Conventional ckt switching system operates as a loss system. The measure of performance for a loss system is the probability of rejection ( blocking probability). The blocking probability analysis are called congestion theory and uses Erlang B formula
Delay ( waiting) system: Overload traffic is held on a queue until the facilities become available to service it. Packet switching posses the basic characteristics of a delay system. A delay system is measured in terms of service delays. Delay analysis are termed as queuing theory. It uses Erland C formula

12. Full availability
Full availability means that every call that arrives can be connected to any outgoing trunk which is free.
If the incoming calls are connected to the outgoing trunks by switches, each switched must have sufficient outlets to provide access to every outgoing trunk.
In many practical cases, the above condition is not satisfied, the switches have insufficient outlets and so can provide only limited availability.

13. Grade of service (GOS)
GOS is the a measure of the ability of a user to access a trunked system during the busiest hour.
The GOS is a benchmark used to define the desired performance of a particular trunked system by specifying a desired likelihood of a user obtaining channel access given a specific number of channels available in the system.
GOS is typically given as the likelihood or the likelihood of call experiencing a delay greater than a certain queuing time.

14. Grade of service (GOS)
When the offered traffic exceeds the maximum capacity of the system, the carried traffic becomes limited due to the limited capacity. The maximum possible channel traffic is the total number of channel, C Erlang.
The AMPS cellular system was designed for a GOS of 2% blocking. This implies that the channel allocation for cell sites re designed so that 2 out of 100 calls will be blocked due to channel occupancy during the busiest hour.

15. Grade of service (GOS)
For a lost-call system, the grade of service B may be defined as:
Where, B
is the proportion of time for which congestion exist or
probability of congestion or
probability that a call will be lost due to congestion

16. Grade of service (GOS)
If traffic A Erlang is offered to a group of trunks having a grade of service B, the traffic lost is AB and the traffic carried, A(1-B) Erlang
The larger the value of GOS, the worse is the service given. The grade of service is normally specified for the traffic at busy hour.

17. Quality of service
(i) It is not reasonable to dimension the network for a very small blocking probability, since the call may be unsuccessful due to other reasons with a much higher probability:
Subscriber does not answer
Subscriber busy
One has dialed a wrong number
(ii) Often the set limit for the blocking probability is 1%
There may be reattempts after unsuccessful calls

19. Quality of service
In other networks ( such as data/packet networks), than the traditional POTS, the quality of service is described by many other quantities, in place or in addition to the blocking probability.
In ATM networks and packet networks (i.e., Internet) following may be important:
- Maximum Packet/cell delay
Cell delay variation (Jitter)
The Cell loss ratio
Cell error ratio
Throughput
etc.

20. Key terms
Call arrival/request rate: A arrival from any particular user is generally assumed to occur purely by chance and be totally independent of arrivals from other users. Thus the no. of call arrivals during any particular time interval is indeterminate. The average number of call request per unit time.
Hold time: The time a user engage in talking/ communication. It is also distributed randomly. In some applications this element of randomness can be removed by assuming constant holding time ( i.e., fixed length packet). It is the average duration of a typical call.

22. Key terms
Set up time: The time required to allocate a trunked radio to a requesting user.
Blocked call: Call which can not be completed at time of request due to congestion. Also they are referred as loss call.
Traffic intensity: Measure of channel time utilization, which is the average channel occupancy measured in Erlang.
Load: Traffic intensity across the entire radio system

23. Congestion
When all trunk in a group are busy, and so it can accept no further calls. This state is known as congestion.
In a message switched system, calls that arrive during congestion wait in a queue until an outgoing trunk become free. Such system is called a delayed system.
In circuit switched system, all attempts to make calls over a congested group of trunk are unsuccessful. Such system call loss-call system.

24. The Unit of traffic
One measure of network traffic is the volume of traffic over a period of time. Traffic volume is essentially the sum of all holding times carried during that interval.
Ex.
Observation were made of the no. of busy lines in a group of junctions at intervals of 5-minutes during the busy hour. The result obtained are:
11, 13, 8, 10, 14, 12, 7, 9, 15, 17, 16 & 12
Traffic carried=12 Erlang
So, measuring the traffic carried amounts to counting the calls in progress at regular intervals during busy hours and averaging the results.

25. The Unit of traffic
The traffic intensity (or traffic flow) is defined as the average number of calls in progress. Although it is dimensionless, a name has been given to the unit of traffic and is called Erlang.
The traffic intensity describe the mean no. of simultaneous call in progress.
In north America, traffic is sometimes expressed in terms of century of call seconds per hour (CCS).
1 Erlang= 36 CCS

26. Definition of Erlang
The maximum capacity of a single server (Channel) is 1 Erlang, which is say that the server ( channel) is always busy.
Thus the maximum capacity in Erlang of a group of servers is merely equal to the number of servers.
Since a single truck can not carry more than 1 call. The traffic is a function of an Erlang equal to the average proportion of time for which the truck is busy. This is called occupancy time.

27. Definition of Erlang
1 Erlang represents the amount of traffic intensity carried by a channel that is completely occupied (i.e. One call-hour per hour or one call-minute per minute).
For example, a radio channel that is occupied for thirty minutes during and hour carries 0.5 Erlang of traffic.

29. Traffic Intensity
The traffic intensity offered by each user is equal to the call request rate multiplied by the holding time.
Here, H is the average duration of a call and λ is the average number of call request per unit time for each user.
For a system containing U users and an unspecified number of channels, the total traffic intensity A, is given by,

30. Erlang B formula
The Danish pioneer traffic theorist A. K. Erlang determined the GOS of a lost call system having C trunks when offered traffic A.
The lost call assumption implies that any attempted call which encounters congestion is immediately cleared from the system. When this happens the user is likely to make another attempts shortly afterwards.

34. Erlang B formula
The Erlang B formula determines the probability that a call is blocked and is a measure of the GOS for a trunked system which provides no queuing for blocked calls.
Where, C is the number of trunked channels offered by a trunked radio system and A is the total offered traffic

35. Typical traffic intensities
Typical traffic intensities per single source are( fraction of time they are being used):
Items
Traffic (Erlang)
Private subscriber E
Business subscriber E
Mobile phone E
PABX E
Coin operated phone E

36. Problem
We consider a cellular system with 395 total allocated voice channel frequencies. If the traffic is uniform with an average call holding time of 120 seconds and the call blocking during the system busy hour is 2% calculate:
The number of calls per cell site per hour
Mean S/I ratio for cell reuse factors equal to 4, 7 & 12
Assume omnidirectional antennas with 6 interferer and a slop for the path loss factor 40 dB ( n=4)

37. Solution
For frequency reuse factor N=4, no. of voice channel per cell site = 395/4=99
Q= √(3*4)=3.5
Using 2% blocking for 99 channels traffic =87 erlang
The offered load=(1-0.02)*87=85.26 erlangs
(no. f cells per cell site per hour*120)/3600=85.26
No. of ceels per cell site per hour = 2558
S/I= (3.5)4/6=25 =14 dB
Calculate the same for N=7 & N=12
Observation:
From N= 4 to N=12 S/I increase to 23.3 dB (66.4% improvement). However call capacity of the cell siter is reduced from 2558 to 739 calls per cell ( 72% reduction).

38. Problem
Consider a GSM system with a one way spectrum of 12.5 MHz and channel spacing 200 KHz. There are 3-control ch per cell and the reuse factor is 4. Assuming an omnidirectional antenna with 6 interferers and a slop for path loss 40 db( n=4). Calculate the no. of calls per cell site per hour with 2% blocking during system busy hour and an average call holding time 120 seconds. Also calculate mean S/I ratio

39. Solution
No. of Voice channel per cell site= (12.5 x10e6x8)/(200x10e3x4)=122
Using erlang B traffic table for 122 ch. With 2% blocking, we find a traffic load of 110 Erlang. The offered load will be –(1-0.02)*110= Erlang
(No. of clla per cell site per hourx120)/3600=107.8
No. of calls per cell site per hour =3234
Q= √(3x4)=3.5
Mean S/I ratio= 93.4)e4/6=25=14 dB

40. Problem
Traffic in different cells in a 7-cell cellular system located in a busy metropolitan area are 30.8, 66.7, 48.6, 33.2, 37.7, 38.2, There are 395 total available channels in the system. Assuming each subscriber in the system generates 0.03 Erlanges of traffic with an average holding time of 120 seconds and the system covers an area of 1200 sq miles with cells designed for a GOS 2%.
No. of channels required in each cell
No. of subscribers served by the system
Average no. of subscriber per channel
No. of calls supported by the system
Subscriber density per sq miles
Call density per sq miles
Call radius in miles
Channel reuse factor

41. Solution
Cell no.
Traffic (Er)
No. of Subs. Per cell
No. of call per cell
No. of chs req 1
30.8
1028.7
924 40 2
66.7
2223.3
2001 78 ..
Total
287.9
9597
8637
358
(No. of calls per hour per subscriber/3600)=0.03
No. of calls per hour per subscriber/3600=0.9
Average no. of subscriber per channel=9597/358=26.8
Erlang/mile=287.9/1200=0.20
Subscriber density=9597/1200=8.0 per sq mile
Call density= 8637/1200=7.2 call per mile sq
Area of eacj cell= 1200/7=171.1 sq mile
Ch. Reuse factor=358/395=0.906