Suppose 3 hosts share a 2 Mbps data link. Each host transmits at 1 Mbps when it has access to the link. Also suppose each host transmits 20 percent of the time. You are told to propose an access control mechanism for sharing the 2 Mbps broadcast channel. Clearly explain the data rates achievable with each of the following schemes in this scenario: TDMA, FDMA, slotted ALOHA, pure ALOHA),
Try an answer before revealing the guidance below.
Key Concepts
- Channel partitioning
- Idle slots
- Transmission probability p = 0.2
- Success probability
- Offered load
Answer Approach
- For TDMA and FDMA, divide the 2 Mbps channel into 3 fixed shares.
- Compare each share with what a host actually needs.
- For slotted ALOHA, compute the chance that exactly one host transmits in a slot.
- For pure ALOHA, extend the vulnerable period and repeat.
Full Answer
Answer status: Draft answer (unofficial). Revision notes, not an official marking scheme.
Direction (assumes each host needs on average 0.2 × 1 Mbps = 0.2 Mbps, and ALOHA hosts send in a slot with p = 0.2). TDMA: each host gets every third slot of the 2 Mbps channel, 2/3 ≈ 0.67 Mbps on average, but slots of idle hosts are wasted. FDMA: each host gets a fixed 2/3 ≈ 0.67 Mbps band, so it cannot even reach its 1 Mbps sending rate, and unused bands are wasted. Slotted ALOHA: a host succeeds in a slot with probability 0.2 × 0.8² = 0.128, so all three together succeed 3 × 0.128 = 0.384 of the time → about 0.384 × 2 ≈ 0.77 Mbps of useful throughput in total (≈ 0.26 Mbps per host). Pure ALOHA: the vulnerable period is two frame times, so success per host is 0.2 × 0.8⁴ ≈ 0.082 and the total is ≈ 0.246 → about 0.49 Mbps (≈ 0.16 Mbps per host). For comparison, the textbook maximum efficiencies are 1/e ≈ 37% (slotted) and 1/(2e) ≈ 18% (pure). Channel partitioning guarantees each host a share; ALOHA lets a lone host use the full rate but loses capacity to collisions.
Slotted: P(success) = Np(1 − p)^(N−1)Pure: P(success) = Np(1 − p)^(2(N−1))Shortcuts: K concepts · A approach · F answer · R reviewed · B bookmark · ← / → previous / next