Computer Networks · TEE · papers
Q2(b) · Slotted ALOHA rates
2024-02-06 · 2022-23
Actual paper; 100 marks attempted. Current-syllabus alignment is stated per question.
Q2(b). A slotted ALOHA network transmits 150-bit frames using a shared channel with a 400-kbps bandwidth. Calculate the throughput and how many frames will survive if the system (all stations together) produces i) 800 frames per second ii) 400 frames per second [10 marks]
Answer
Given
Frame length L = 150 bits; link rate R = 400,000 bit/s; attempted rates λ = 800, 400 frames/s.
To find
Normalized throughput S and successful frames per second for each offered load.
Formula and why
LaTeX: T_f=L/R,\quad G=\lambda T_f,\quad S=Ge^{-G},\quad \lambda_{success}=S/T_f=\lambda e^{-G}G counts attempted frames per frame time, including retransmissions if present. S is not measured in frames/s. Multiply by the frame rate capacity 1/Tf to obtain surviving frames/s.
Step 1. Convert the link rate and compute frame time
Tf = 150/400000 = 0.000375 s. Capacity = 1/Tf = 2666.66667 frames/s.
Step 2. Offered rate 800 frames/s
G = 800 × 0.000375 = 0.3.
e−1G = e−0.3 = 0.740818221.
S = 0.3 × 0.740818221 = 0.222245466.
Successful frames/s = 800 × 0.740818221 = 592.654577. Successful bit/s = 592.654577 × 150 = 88898.1865.
Step 3. Offered rate 400 frames/s
G = 400 × 0.000375 = 0.15.
e−1G = e−0.15 = 0.860707976.
S = 0.15 × 0.860707976 = 0.129106196.
Successful frames/s = 400 × 0.860707976 = 344.283191. Successful bit/s = 344.283191 × 150 = 51642.4786.