Given:
- Bandwidth = 100 Mbps
- Pure ALOHA efficiency (S) = 1 / (2e)
- Slotted ALOHA efficiency (S) = e * e^(-e)
Throughput using Pure ALOHA in the first half: Throughput_Pure_ALOHA_1st_half = (1 / (2e)) * 100 Mbps
Throughput using Slotted ALOHA in the second half: Throughput_Slotted_ALOHA_2nd_half = (e * e^(-e)) * 100 Mbps
Throughput using Slotted ALOHA in both halves: Throughput_Slotted_ALOHA_both_halves = (e * e^(-e)) * 100 Mbps
Now, we need to compare the throughputs to determine the gain or loss.
Gain: Gain = Throughput_Slotted_ALOHA_both_halves - Throughput_Pure_ALOHA_1st_half = [(e * e^(-e)) * 100 Mbps] - [(1 / (2e)) * 100 Mbps] = 100 Mbps * (e * e^(-e) - 1 / (2e))
Loss: Loss = Throughput_Slotted_ALOHA_2nd_half - Throughput_Slotted_ALOHA_both_halves = [(e * e^(-e)) * 100 Mbps] - [(e * e^(-e)) * 100 Mbps] = 0
Therefore, the user gains:
Gain = 100 Mbps * (e * e^(-e) - 1 / (2e))
And there is no loss in throughput by switching from Slotted ALOHA in the second half to Slotted ALOHA in both halves.