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 Delay vs Propagation Delay

Every network exchange is governed by two distinct physical metrics:

  • Transmission Delay (T_t): The time required to inject all L bits of a frame into the transmission medium at bandwidth B: 
T_t = (L / B)
  • Propagation Delay (T_p): The time taken by a single electromagnetic bit to travel across physical distance d at propagation speed v (approx. 2 × 10⁸ m/s in glass): 
T_p = (d / v)

In Stop-and-Wait ARQ, the sender transmits one frame and then completely halts until receiving an acknowledgment (ACK). Assuming ACK transmission time is negligible, the total roundtrip cycle time is:

Total Cycle Time = T_t + 2 · T_p

2. Deriving the Efficiency Formula: U = (1 / 1 + 2a)

Channel utilization (U) represents the fraction of total cycle time spent doing useful work (transmitting data):

U = (T_t / T_t + 2 · T_p) = (1 / 1 + 2 · left(fracT_p)T_tright)

Defining the dimensionless ratio a = (T_p / T_t):

U = (1 / 1 + 2a)

The Implications of a:

  1. When a ll 1 (Local Area Networks): Propagation distance is short, T_p is tiny compared to T_t. Utilization approaches 100\%.
  2. When a gg 1 (Wide Area & Satellite Links): Physical distance is large, so T_p dominates. Utilization collapses towards 0\%.

3. The Bandwidth-Delay Product (BDP)

Upgrading bandwidth B reduces T_t, which actually increases a. The pipe can hold vast amounts of data in transit, but Stop-and-Wait leaves the entire link starved.

To saturate high-latency links, modern transport layers use Sliding Window Protocols (Go-Back-N, Selective Repeat, and TCP) to pipeline multiple frames continuously.

Explore our interactive space-time protocol ladder with live packet flights at Binary Dose.