Queues Applied to Telecoms

16Chapter 8 Exercises

EXERCISE 8.1.– Total accessibility with delay (1)

The offered traffic is equal to Erl.

Looking at the Erlang-C table, the probability of waiting corresponding to 30 circuits and an offered traffic of 21 Erl is equal to D = 5%.

The carried traffic is equal to the offered traffic since there is no loss, so Y = 21 Erl. Thus, the average carried traffic per channel is equal to Erl.

The average delay time for all the calls is given by:

The average delay time for calls that must wait is equal to:

EXERCISE 8.2.– Total accessibility with delay (2)

Calls are served in the order of their arrival, so the delay time follows an exponential distribution. The probability that a call will have to wait for more than t seconds is given by: . Calculations give 0.04, 0.03 and 0.02, respectively, as the probabilities that a call will have to wait more than 3, 6 and 12 seconds.

It is the same for the probability of delay times given that a call must wait: . Calculations give 0.78, ...