Efficiency of Stop and Wait Protocol - ARQ
Duration: 6 min
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The lecture provides a comprehensive derivation of the efficiency formula for Stop-and-Wait ARQ protocols and demonstrates how to calculate effective bandwidth or throughput. The instructor begins by defining efficiency ($\eta$) as the ratio of useful transmission time to the total cycle time. He breaks down the total cycle time into transmission time ($T_t$) and waiting time ($2 * T_p$), where $T_p$ is propagation delay. Through algebraic manipulation, he derives the standard efficiency equation $\eta = 1 / (1 + 2a)$, defining $a$ as the ratio of propagation delay to transmission time. The session concludes by introducing the throughput formula, which is the product of efficiency and bandwidth, and sets up a numerical example to illustrate the concept.
Chapters
0:00 – 2:00 00:00-02:00
The instructor introduces the concept of efficiency ($\eta$) using a slide titled 'Efficiency($\eta$)'. The slide displays the formula: 'Useful Time / Total Cycle time = $T_t / T_t + 2 * T_p$'. He explains that the useful time in the entire cycle is $T_t$, while the remaining $2 * T_p$ time is spent waiting for processing. He notes that during this waiting period, more packets could have been sent. He then proceeds to simplify the fraction by dividing both the numerator and the denominator by $T_t$, leading to the expression $\eta = 1 / (1 + 2 * T_p / T_t)$.
2:00 – 5:00 02:00-05:00
The instructor moves to the whiteboard to visually demonstrate the derivation. He writes the total time equation $T_T = T_t + 2 * T_p$ and the efficiency definition $\eta = UT / TT$. He substitutes the time components into the efficiency formula, resulting in $\eta = T_t / (T_t + 2 * T_p)$. He then performs the division by $T_t$ on both the numerator and denominator, explicitly showing the term $T_p / T_t$. He defines this ratio as $a$, finalizing the formula as $\eta = 1 / (1 + 2a)$. After establishing the efficiency formula, he transitions to a new slide titled 'Effective Bandwidth / Throughput / Bandwidth Utilization is calculated as:', introducing the formula Throughput = $\eta * B$.
5:00 – 5:43 05:00-05:43
The instructor begins a practical example to calculate throughput. He writes $\eta$ and $B$ on the board. He assigns a value of 0.5 to efficiency ($\eta$) and 10 Mbps to the bandwidth ($B$). He writes the multiplication $\eta * B$ and prepares to calculate the final throughput value. He also draws a simple diagram of packets to visualize the data flow. This section connects the theoretical efficiency formula to a practical calculation of effective bandwidth, showing how the theoretical efficiency directly impacts the actual data rate achieved on the network.
The video progresses logically from theoretical definition to algebraic derivation and finally to practical application. It starts by defining efficiency in terms of time components ($T_t$ and $T_p$), derives the standard $1/(1+2a)$ formula, and then applies this efficiency to calculate throughput by multiplying it with the channel bandwidth.