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Numerical: 32-cell system area and channels

Short answer

Each hexagonal cell has area 6.651 km², so total area is 212.8 km². With reuse factor 7 and 336 channels, each cell gets 48 channels, supporting 1536 simultaneous calls.

The cellular system has 32 cells, each cell has a 1.6 km radius and the system reuse factor is 7. The system is to support 336 traffic channels in total. Determine the total geographical area covered, the number of traffic channels per cell and the total number of simultaneous calls supported by this system.

Given: number of cells = 32, R = 1.6 km, N = 7, total traffic channels S = 336.

Area of one hexagonal cell:

A_cell = (3√3/2) R² = 2.598 × 1.6² = 2.598 × 2.56
       = 6.651 km²

Total area covered:

A_total = 32 × 6.651 = 212.83 km²

Traffic channels per cell:

k = S / N = 336 / 7 = 48 channels per cell

Total simultaneous calls:

C = 48 × 32 = 1536 calls

(Number of clusters = 32/7 ≈ 4.57, and C = M × S gives the same value 4.57 × 336 = 1536.)

Answer: Area ≈ 212.8 km², 48 channels per cell, 1536 simultaneous calls.

✓ Answer checked by Claude Opus 5.5 (high effort)

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