Consider a simplified time slotted MAC protocol, where each host always has…
2004
Consider a simplified time slotted MAC protocol, where each host always has data to send and transmits with probability p = 0.2 in every slot. There is no backoff and one frame can be transmitted in one slot. If more than one host transmits in the same slot, then the transmissions are unsuccessful due to collision. What is the maximum number of hosts which this protocol can support, if each host has to be provided a minimum through put of 0.16 frames per time slot?
- A.
1
- B.
2
- C.
3
- D.
4
Attempted by 181 students.
Show answer & explanation
Correct answer: B
Key formula: Throughput per host = p * (1 - p)^(n - 1), where n is the number of hosts.
Substitute p = 0.2 and require throughput ≥ 0.16:
0.2 * (0.8)^(n - 1) ≥ 0.16
Divide both sides by 0.2: (0.8)^(n - 1) ≥ 0.8
Since 0.8^k decreases as k increases and 0.8^1 = 0.8, we need n - 1 ≤ 1, so n ≤ 2.
Therefore the maximum integer number of hosts that can be supported while providing at least 0.16 frames/slot per host is 2.
Answer: 2 hosts.