A telephone exchange has 100 lines (circuits) for connection to the trunk networ

Question

A telephone exchange has 100 lines (circuits) for connection to the trunk network. Calls arrive for these circuits at the rate of 50 calls/minute during busy hours.

a) If the mean call holding time is 2 minutes, how many Erlangs of traffic are being offered to the
exchange?
b) i) Use the Erlang-B formula to calculate the probability that a call is blocked during the busy hour.
ii) Calculate the number of Erlangs of traffic that were carried.

c) i) It is desired that call blocking be no higher than 2 %. Calculate the minimum number of
additional circuits which will be needed to obtain this quality of service.
ii) Calculate in Erlangs the amount of traffic which will then be lost.

d) Erlang's formula is derived assuming that the call holding distribution is exponential.
Will your results above be any different if the call holding distribution is constant?

Explanation / Answer

a)

A=Ch/T

A is traffic intensity , C is Calling rate , h is holding time

A= 100*2/60=3.33 E

b) The probability of finding the trunk busy is equal to the proportion of time for which the trunk is busy.

Probability of finding the line engaged=3.33*2/60=.11

c) i) 100 minimum number of
additional circuits which will be needed to obtain this quality of service.

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