Consider a simplified time slotted MAC protocol, where each host always has data to send and transmits with probability p = 0.5 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 that this protocol can support if we want the probability that a given slot has a successful transmission to be at least 2/3? A. 1 B. 2 C. 3 D. 4

GATE 2004 · Computer Networks · MAC Protocol · medium

Answer: B. 2 - The maximum number of hosts that can be supported while maintaining P(success) >= 2/3 is 2.

1. Write the conditional success probability formula: With p = 0.5: numerator = N * (1/2)^N, denominator = 1 - (1/2)^N. So P = (N/2^N) / (1 - 1/2^N).
2. Evaluate for N = 1 and N = 2: N=1: P = 1.0 >= 2/3. Satisfied. N=2: P = (1/2)/(3/4) = 2/3 >= 2/3. Satisfied (at boundary).
3. Evaluate for N = 3 and N = 4: N=3: P = 3/7 = 0.429 < 2/3. NOT satisfied. N=4: P = 4/15 = 0.267 < 2/3. NOT satisfied.