- Asked 2/22
- 2080 Baisakh · 5 marks
- 2079 Chaitra · 5 marks
Numerical: users supported and market penetration
Short answer
Each user offers 0.1 Erlang. At 2% blocking, 19 channels carry 12.33 Erlangs, so 123 users per cell, giving about 48,462 total users and 2.42% market penetration.
An urban area has a population of two million residents. System A has 394 cells with 19 channels each. Find the number of users that can be supported at 2% blocking if each user averages two calls per hour at average call duration of three minutes. Assuming that trunk systems are operated at maximum capacity, compute the percentage market penetration of cellular provider.
Erlang B Traffic Table (Maximum Offered Load Versus B and N; B is in %):
| N/B | 0.01 | 0.05 | 0.1 | 0.5 | 1.0 | 2 | 5 | 10 | 15 | 20 | 30 | 40 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 16 | 5.339 | 6.250 | 6.722 | 8.100 | 8.875 | 9.828 | 11.54 | 13.50 | 15.18 | 16.81 | 20.30 | 24.54 |
| 17 | 5.911 | 6.878 | 7.378 | 8.834 | 9.652 | 10.66 | 12.46 | 14.52 | 16.29 | 18.01 | 21.70 | 26.19 |
| 18 | 6.496 | 7.519 | 8.046 | 9.578 | 10.44 | 11.49 | 13.39 | 15.55 | 17.41 | 19.22 | 23.10 | 27.84 |
| 19 | 7.093 | 8.170 | 8.724 | 10.33 | 11.23 | 12.33 | 14.32 | 16.58 | 18.53 | 20.42 | 24.51 | 29.50 |
| 20 | 7.701 | 8.831 | 9.412 | 11.09 | 12.03 | 13.18 | 15.25 | 17.61 | 19.65 | 21.64 | 25.92 | 31.15 |
(The Erlang B table was attached to the 2079 Chaitra paper.)
Given: population = 2 000 000; cells = 394; channels per cell C = 19; GOS = 2 % blocking; λ = 2 calls/hour; H = 3 min.
Step 1: Traffic per user
Au = λ × H = 2 × (3/60) = 0.1 Erlang
Step 2: Traffic per cell from Erlang B table For N = 19 channels and B = 2 %:
A (per cell) = 12.33 Erlangs
Step 3: Users per cell
U = A / Au = 12.33 / 0.1 = 123.3 ≈ 123 users per cell
Step 4: Total users supported
Total = 123 × 394 = 48 462 users
(Without rounding: 123.3 × 394 = 48 580)
Step 5: Market penetration
Penetration = 48 462 / 2 000 000 × 100 = 2.42 %
Answer: About 48 462 users (≈ 48 500) can be supported at 2 % blocking, giving a market penetration of about 2.42 %.
✓ Answer checked by Claude Opus 5.5 (high effort)
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