Voice and Signaling Erlang Calculation

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The objective of teletraffic theory can be formulated as follows:

“To make the traffic measurable in well de fined units through mathematical models and to derive the relationship between grade-of-service and system capacity in such a way that the theory becomes a tool by which investments can be planned.”

The goal when planning a telecommunication system is to adjust the amount of equipment so that variations in the subscriber demand for calls can be satis ed without noticeable inconvenience while the costs of the installations are as small as possible. The equipment must be used as efficiently as possible.

Erlang:

The Erlang (symbol E) as a dimensionless unit is used in telephony as a statistical measure of the volume of telecommunications traffic. It is named after the Danish telephone engineer A. K. Erlang, the originator of traffic engineering and queueing theory. For example, a radio channel that is occupied for thirty minutes during an hour is said to carry 0.5 E of traffic. Traffic measured in erlangs is used to calculate grade of service (GOS) or quality of service (QoS).

Signaling Traffic Measurement

Assumption:

• Link Type : Low Speed link (64kbps)
• Bit transmitted  for 1 hour : 80 MB

Explanation :

Formula for calculating the Erlang is

Erlang =Bit Transmitted/Total Capacity

• Here we have 80 MB traffic / hour, so traffic in bit is 80*1000000
• Total Capacity can transmit for an hour is 64000 per second,  64k*60 per minute, 64k*60*60 per hour

Erlang = 80*1000000 / 64000*60*60

Erlang = 0.347222

Voice Traffic Measurement

Assumption:

• The speech channels carry a traffic load of 0.75 Erl
• The average call duration is 100 seconds
• The signaling link is used at a rate of 0.2 Erl
• each call setup and call release involves the transmission of 14 information blocks with 12 bytes each ( per POTS subscriber ) and 24 bytes ( per ISDN subscriber )

Explanation :

• Per hour every speech channel carries 3600/100 * 0.75 = 27 calls
• per hour every speech channel 27*14*24 = 9072 bytes of info must be transmitted ( 4536 bytes from exchange A to B and 4536 bytes from exchange B to A )
• a circuit transmits 64000 bits/sec or 8000 bytes/sec or 8000*3600*0.2 bytes/hour I.e 5760000 bytes/hour
• with each voice channel transmits 4536 bytes a signaling circuit can support 5760000/4536 = 1269.84 voice circuits.