# Loss system

Traffic balance in communication theory

In traffic theory, a loss system is a system that is not up to the supply at all times . If the performance of the system exceeds (also called the load ), the remaining traffic is rejected because the technical facilities required to establish the connection are not available. These can be lines, channels, coupling arrangements or other resources. The performance is the product of the occupancy per hour and the average occupancy time . ${\ displaystyle A}$${\ displaystyle A}$ ${\ displaystyle y}$${\ displaystyle y}$${\ displaystyle C}$${\ displaystyle t_ {m}}$

${\ displaystyle y = C_ {y} \ cdot t_ {m}}$(in Erlang )

Most switching systems ( e.g. EWSD ) work on the principle of the loss system.

There are two types of loss in a loss system:

1. Loss (market value of the rest / market value of the offer ) and${\ displaystyle B = R / A}$
2. Inhibition (market value of the rest / market value of the service ), obsolete since around 1975.${\ displaystyle H = R / y}$

Both types can be converted into each other:

• ${\ displaystyle W = H / (1 + H)}$ and
• ${\ displaystyle H = B / (1-B)}$

(S technical statement of the German Federal Post TAnw FTZ 136 D 40 R 23 1, briefly.: 1D40) based tolerable losses, the design of bundles made.

## example

• 1000 participants want to make calls per hour. How many free lines must there be so that a maximum of 10 subscribers (B = 0.01) hear a busy tone ?
Approach: = 1000/60 calls / min = 16.7 calls / min${\ displaystyle \ lambda}$
Wanted Poisson distribution with 1-F (x) <0.01${\ displaystyle F _ {\ lambda} (x)}$
Solution: F (26) = 0.988 → 1-F (X) <0.01. If there are 26 lines, less than 1% of the participants receive a busy tone.
• As before, but with the additional information that a conversation (more precisely: an assignment) lasts an average of 2 minutes.
Approach: The offer is (1000 * 2 min) / 60 min = 33 Erlang
Searched Erlang B distribution with B (N, 33) with B (N, 33) <0.01
Solution: B ( 45 , 33) <0.009 (according to 1D40). With a number of 45 lines and an average occupancy of 2 minutes, less than 1% of the participants receive a busy tone

In contrast to waiting systems , lost systems do not have a waiting room for temporarily storing incoming orders.