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Define congestion and grade of service.
Congestion: This is uneconomic to give sufficient equipment to carry all the traffic which could possibly be offered to a telecommunication system. Inside a telephone exchange this is theoretically possible for all subscribers to make a call concurrently. A situation can hence arise that each of the trunks in a group of trunks are busy, and therefore this can accept further calls. This type of state is termed as congestion. Into a message-switched system, calls which arrive throughout congestion wait in a queue till an outgoing trunk becomes free. Therefore, they are delayed but not lost. These systems are so termed as queuing systems or delay system. A telephone exchange, in a circuit-switched system all attempts to make calls over a congested group of trunks is successful. These systems are so termed as lost-call systems. In a lost-call system the result of congestion is which the traffic in fact carried is less than the traffic offered to the system. Therefore we may write:
Grade of Service: In loss systems, the traffic carried through the network is usually lower than the actual traffic offered to the network through the subscribers. The overload traffic is discarded and hence it is not carried with the network. The amount of traffic discarded by the network is an index of the quality of the facility offered through the network. It is known as Grade of Service (GOS) and is defined by the ratio of lost traffic to offered traffic. Offered traffic is the product of the average no. of calls generated through the users and the average holding time per call. Therefore, GOS is specified:
GOS = (A - A0)/A
Here
A= offered traffic
A0 = carried traffic
A-A0= lost traffic
SET 2I OF ALL INTEGERS WITH ZERO IS AN ABELIAN GROUP
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