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A sender uses the Selective Repeat ARQ protocol.

  • Frame size $=2000 \text{bits}$
     
  • Sender transmission rate $=500 \mathrm{Kbps}$ $(1 \mathrm{Kbps}=1000 \mathrm{bps})$
     
  • ACK size $=20 ~\text{bytes}$
     
  • Receiver ACK transmission rate $=100 \mathrm{Kbps}$
     
  • One-way propagation delay $=50 \mathrm{~ms}$
     
  • Sender window size $W_s=5 ~\text{frames}$
     

Assuming no losses or errors, what is the sender's throughput in $\textbf{Kbps}$?

3 Answers

1 1 vote

Frame size $L_{\text {frame }}=2000 ~\text{bits}$

Sender data rate $R_{\text {data }}=500 \mathrm{Kbps}=500,000 \mathrm{bps}$

ACK size $L_{\text {ack }}=20 ~\text{bytes} = 160 ~\text{bits}$

ACK transmission rate $R_{\text {ack }}=100 \mathrm{Kbps}=100,000 \mathrm{bps}$

One-way propagation delay $T_p=50 \mathrm{~ms}=0.05 \mathrm{~s}$

Sender window size $W=5$ frames

$$
\begin{aligned}
T_{\text {tx-data }} & =\frac{L_{\text {frame }}}{R_{\text {data }}}=\frac{2000}{500000}=0.004 \mathrm{~s} \\\\
T_{\text {tx-ack }} & =\frac{L_{\text {ack }}}{R_{\text {ack }}}=\frac{160}{100000}=0.0016 \mathrm{~s}
\end{aligned}
$$

First frame sent at $t=0$, last bit at $t=0.004$.

It arrives at receiver at $t=0.004+T_p=0.054 \mathrm{~s}$.

Receiver sends ACK: transmission time of ACK $=0.0016 \mathrm{~s}$, so ACK last bit sent at $t=0.054+ 0.0016=0.0556$.

ACK arrives at sender at $t=0.0556+T_p=0.1056 \mathrm{~s}$.

So:

$$
\begin{gathered}
T_{\text {firstACK }}=0.1056 \mathrm{~s} \\\\
\mathrm{BDP}(\text { frames })=\frac{T_{\text {firstACK }}}{T_{\mathrm{tx} \text {-data }}}=\frac{0.1056}{0.004}=26.4 \text { frames }
\end{gathered}
$$


Our window size $W=5$ is less than $\mathbf{26.4}$, so throughput is limited by window size.

$$
\begin{aligned}
\text { Throughput } & =\frac{W \times L_{\text {frame }}}{T_{\text {firstACK }}}=\frac{5 \times 2000}{0.1056} \mathrm{bps} \\\\
= & \frac{10000}{0.1056} \approx 94696.97 \mathrm{bps} \\\\
& \approx 94.697 \mathrm{Kbps}
\end{aligned}
$$

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