Why 10Gbps Links Feel Slow: Stop-and-Wait ARQ Efficiency Formula Explained
Why 10Gbps Links Feel Slow: Stop-and-Wait ARQ Efficiency Formula Explained When deploying high-speed fiber links across continents, engineers often discover a paradoxical reality: upgrading bandwidth from 1 Gbps to 10 Gbps yields almost zero throughput improvement for single-packet protocols. The culprit is the fundamental physics governing Stop-and-Wait ARQ Link Efficiency . 1. Transmission…
In the realm of high-speed fiber networking, a common observation is that scaling bandwidth from 1 Gbps to 10 Gbps often results in negligible gains in throughput for single-packet protocols. This seeming paradox stems from the core principles of Stop-and-Wait Automatic Repeat reQuest (ARQ) and its efficiency formula.
At the heart of network exchanges lie two key metrics: Transmission Delay (T_t) and Propagation Delay (T_p). T_t represents the duration required to push all L bits of a frame onto the transmission medium at a given bandwidth B, calculated as T_t = (L / B). T_p, on the other hand, quantifies the time a single electromagnetic bit takes to traverse a physical distance d, moving at the speed of light in the medium (approximately 2 × 10⁸ m/s in glass), equating to T_p = (d / v).
In Stop-and-Wait ARQ, the sender dispatches one frame before pausing until acknowledgment (ACK) is received. Assuming ACK transmission time is inconsequential, the overall roundtrip cycle time equates to T_t + 2 · T_p. The efficiency of this protocol, or channel utilization (U), elucidates the proportion of total cycle time devoted to actual data transmission. This metric is expressed as U = (T_t / T_t + 2 · T_p), simplifying to U = (1 / 1 + 2 · (T_p / T_t)).
By introducing the dimensionless ratio a = (T_p / T_t), the equation for channel efficiency becomes U = (1 / 1 + 2a). The ramifications of varying 'a' are profound. Within Local Area Networks (LANs), where physical distances are relatively short, T_p remains negligible compared to T_t. Consequently, utilization nears 100%.
Conversely, in Wide Area Networks and Satellite Links, where distances are vast, T_p dominates over T_t. In this scenario, utilization dwindles towards 0%, rendering such links incredibly inefficient under Stop-and-Wait ARQ. To circumvent this inefficiency, contemporary transport layers employ Sliding Window Protocols, such as Go-Back-N, Selective Repeat, and TCP, enabling continuous pipelining of multiple frames.
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