## Info

t (seconds)

Fig. 8.1. Negative distribution function for h = 100 sec. Figure shows that, 50% probability call lasts longer than 70 sec.

3. Distribution of destinations. Number of calls receiving at a exchange may be destined to its own exchange or remoted exchange or a foreign exchange. The destination distribution is described as the probability of a call request being for particular destination. As the hierarchical structure of telecommunication network includes many intermediate exchanges, the knowledge of this parameter helps in determining the number of trunks needed between individual centres.

4. User behavior. The statistical properties of the switching system are a function of the behavior of users who encounter call blocking. The system behaves differently for different users. The user may abonden the request if his first attempt to make a call is failed. The user may makes repeated attempts to setup a call. Otherwise the user may wait some times to make next attempt to setup a call. These behavior varies person to person and also depends on the situation.

5. Average occupancy. If the average number of calls to and from a terminal during a period T seconds is 'n' and the average holding time is 'h' seconds, the average occupancy of the terminal is given by nh . 1 X

Thus, avarage occupancy is the ratio of average arrival rate to the average service rate. It is measured in Erlangs. Average occupancy is also referred as traffic flow or traffic intensity or carried traffic.

### 8.2.2. Traffic Pattern

An understanding of the nature of telephone traffic and its distribution with respect to time (traffic load) which is normally 24 hours is essential. It helps in determining the amount of lines required to serve the subscriber needs. According to the needs of telephone subscribers, the telephone traffic varies greatly. The variations are not uniform and varies season to season, month to month, day to day and hour to hour. But the degree of hourly variations is greater than that of any other period. Fig. 8.2 shows the typical variations of calls from 8.00 A.M. to midnight.

Fig. 8.2. Variations of call from 8 A.M. to midnight.

Fig. 8.2. Variations of call from 8 A.M. to midnight.

If the behavior of the traffic shown above is systematic for period of time or season, good judgement about the design of switching system or lines or trunks or any common shared equipments can be made. Thus, the combination of historical records, experience, location of exchanges (business area or residential area), vacations, govt. policies on holidays etc., decides the design of telecommunication network. Various parameters related to traffic pattern one discussed below :

Busy hour. Traditionally, a telecommunication facility is engineered on the intensity of traffic during the busy hour in the busy session. The busy hour vary from exchange to exchange, month to month and day to day and even season to season. The busy hour can be defined in a variety of ways. In general, the busy hour is defined as the 60 minutes interval in a day, in which the traffic is the highest. Taking into account the fluctuations in traffic, CCITT in its recommendations E.600 defined the busy hour as follows.

1. Busy hour. Continuous 60 minutes interval for which the traffic volume or the number of call attempts is greatest.

2. Peak busy hour. It is the busy hour each day varies from day to day, over a number of days.

3. Time consistent busy hour. The 1 hour period starting at the same time each day for which the average traffic volume or the number of call attempts is greatest over the days under consideration.

In order to simplify the traffic measurement, the busy hour always commences on the hour, half hour, or quarter hour and is the busiest of such hours. The busy hour can also be expressed as a percentage (usually between 10 and 15%) of the traffic occuring in a 24 hour period.

Call completion rate (CCR). Based on the status of the called subscriber or the design of switching system the call attmepted may be successful or not. The call completion rate is defined as the ratio of the number of successful calls to the number of call attempts. A CCR value of 0.75 is considered excellent and 0.70 is usually expected.

Busy hour call attempts. It is an important parameter in deciding the processing capacity of an exchange. It is defined as the number of call attempts in a busy hour.

Busy hour calling rate. It is a useful parameter in designing a local office to handle the peak hour traffic. It is defined as the average number of calls originated by a subscriber during the busy hour.

Day-to-day hour traffic ratio. It is defined as the ratio of busy hour calling rate to the average calling rate for that day. It is normally 6 or 7 for rural areas and over 20 for city exchanges.

8.2.3. Units of Telephone Traffic

Traffic intensity is measured in two ways. They are (a) Erlangs and (b) Cent call seconds (CCS).

Erlangs. The international unit of traffic is the Erlangs. It is named after the Danish Mathematician, Agner Krarup Erlang, who laid the foundation to traffic theory in the work he did for the copenhagen telephone company starting 1908. A server is said to have 1 erlang of traffic if it is occupied for the entire period of observation. More simply, one erlang represents one circuit occupied for one hour.

The maximum capacity of a single server (or channel) is 1 erlang (server is always busy). Thus the maximum capacity in erlangs of a group of servers is merely equal to the number of servers.

Thus, the traffic intensity which is the ratio of the period for which the server is occupied to the total period of observation is measured in erlangs.

Example 8.1. If a group of 20 trunk carries 10 erlangs and the average call duration is 3 minutes, calculate (a) average number of calls in progress (b) total number of calls originating per hour.

traffic intensity = 10 erlangs holding time h = 3 minutes observation period T = 60 minutes (generally).

10 erlangs

Sol. (a) Traffic intensity per trunk =-—-= 0.5 erlangs/trunk.