Telecommunication Traffic

Trunk: In telecommunication engineering the term

trunk is used to describe any entity that will carry one call.

Erlang: Is the unit of traffic intensity, which is

defined as the average calls in progress.

Busy Hour

The average weekday reading over one or two weeks in the known busy season.

The average of the BH traffic on 30 busiest days of the year.

The average of the BH traffic on the 10 busiest days of the year

The average BH traffic on the 5 busiest days of the year.

Holding time: Is the duration of a call, the call holds the

trunk for that time.CCS: In North America , traffic is sometime

expressed in hundreds of call seconds per hour

(CCS). 1 Erlang =36 CCS

Traffic carried by a group of trunks is A=Ch/TC: average no. of call arrivals during time T.h: average call holding time. Since a single trunk can not carry more

than one call, A<=1 The traffic is a fraction of an erlang equal to

the average proportion of time for which the trunk is busy.

Example

On average, during the busy hour, a company makes 120 outgoing calls of average duration 2 minutes. It receives 200 incoming calls of average duration 3 minutes. Find

(1)The outgoing traffic. (2)The incoming traffic. (3)The total traffic

Solution

The outgoing traffic is 120x2/60=4E.The incoming traffic is 200x3/60=10EThe total traffic is 4+10=14E.

Example

During the busy hour, on average, a customer with a single telephone line makes 3 calls and receive 3 calls. The average call duration is 2 minutes. What is the probability that a caller will find the line engaged.

Solution

Occupancy of line =(3+3)x2/60=0.1E =probability of finding the line engaged

Congestion

*The situation that all trunks in a group of trunks are busy is known as congestion.

*In circuit switched systems, all attempts to make calls over a congested group of trunks are unsuccessful.

*Such systems are called lost-call systems. *In a lost-call system, the result of congestion

is that the traffic actually carried is less than the traffic offered to the system

* Traffic carried=traffic offered-traffic lost

Grade of Service

The proportion of calls that is lost or delayed due to congestion is a measure of the service provided. It is called the grade of service.

For a lost-call system, the grade of service, B, may be defined as

Number of calls lostB =Number of calls offered

Hence, also: B=Proportion of the time for which the

congestion exists.=probability of congestion.=probability that a call will be lost due to

congestionThus 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 is A(1-B)

The larger the GOS, the worse is the service given.

The GOS is normally specified for the traffic at the busy hour.

It varies from 1 in 1000 for cheap trunks inside an exchange to 1 in 100 for inter-exchange connections and 1 in 10 for expensive international routes

Dimensionality Problem

The basic problem of determining the size of a telecommunication systems, known as dimensionality problem is, : Given the offered traffic, A, and the specifies GOS, B, find the No. of trunks, N, that is required

Example During the busy hour, 1200 calls were

offered to a group of trunks and six calls were lost. The average call duration was 3 minutes. Find:

1. The traffic offered. 2. The traffic carried. 3. The traffic lost. 4. The GOS. 5. The total duration of the period of congestion.

Solution

1. A=Ch/T=1200x3/60=60 E. 2. 1194x3/60=59.7 E. 3. 6x3/60=0.3 E. 4. B=6/1200=0.005 5. 0.005x3600= 18 seconds.

Traffic Measurement

It is important for an operating company to know how much BH-traffic its systems are handling.

In particular, it needs to know when a system is becoming overloaded and additional equipment should be installed.

The traffic should be measured regularly and records kept. In modern SPC systems, the central processors generate records of the calls they set up.

Example

Observations were made of the No. of busy lines in a group of junctions at intervals of 5 minutes during the BH. The results obtained were:

11, 13, 10, 14, 12, 7, 9, 15, 17, 16, 12 It is therefore estimated that the traffic

carried in erlangs, was:

11+13+10+14+12+7+9+15+17+16+12=12 E 12

A mathematical Model

A simple model for the traffic offered to telecommunication systems is based on the assumptions:

. Pure-chance traffic. . Statistical equilibrium. Pure-chance traffic assumption means

random call arrivals and terminations. This leads to the following results: