January 2023
Intermediate to advanced
272 pages
5h 3m
English
Content preview from Queues Applied to Telecoms
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15Chapter 7 Exercises
EXERCISE 7.1.– PABX
The total traffic per switchboard is equal to 0.035 + 0.045 = 0.08 Erl. The total traffic for all of the 200 switchboards is thus 0.08 × 200 = 16 Erl.
The switch only has 30 circuits, so the loss probability is estimated to be 0.1% according to the Erlang-B table.
EXERCISE 7.2.– Erlang-B table
Table 15.1 summarizes the results for this exercise.
Table 15.1. Results for Exercise 7.2
| Loss probability | 1% | 10% | 50% | ||||||
| Circuits | Offered | Lost | Carried | Offered | Lost | Carried | Offered | Lost | Carried |
| 5 | 1.25 | 0.012 | 1.238 | 3 | 0.3 | 2.7 | 9.5 | 4.75 | 4.75 |
| 10 | 4.5 | 0.045 | 4.455 | 7.5 | 0.75 | 6.75 | 18.5 | 9.25 | 9.25 |
| 15 | 8 | 0.08 | 7.92 | 12.5 | 1.25 | 11.25 | 28.5 | 14.25 | 14.25 |
EXERCISE 7.3.– GSM cell
The offered traffic is equal to 
Erl. Offering these 14 Erl to 18 circuits, the blocking rate, according to the Erlang-B table, equals 5%. For type-one pure chance traffic, the blocking rate and the congestion rate are equal; therefore, we also have a congestion rate of 5%.
Thus, 5% of the offered traffic will be lost, or Ap = 5% × 14 = 0.7 Erl. The carried traffic is therefore Y = 13.3 Erl, and the carried traffic per circuit is equal to 
Erl.
The lost traffic of 0.7 Erl corresponds to a number of rejected calls per hour equal to rejected calls/hour.
EXERCISE 7.4.– Authorized traffic ...
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