Token Bucket Regulation: Duration of Full-Rate Transmission

In a token bucket regulator, the system “spends” tokens to allow sending at the link’s line rate (here $6$ Mbps). Tokens are generated continuously at a fixed token generation rate and stored up to a maximum bucket capacity.

Key idea: when the computer transmits at full $6$ Mbps, it consumes tokens at $6$ Mbps; meanwhile, new tokens are added at $1$ Mbps. Thus, the bucket level decreases at the net rate $(6-1)=5$ Mbps. The time you can keep transmitting at full $6$ Mbps is determined by how long it takes for the initial stored tokens (capacity) to be depleted.

Model the token level in bits:

• Initial tokens: $8$ megabits
• Token arrival (fill) rate: $1$ Mbps
• Token consumption at full send: $6$ Mbps

So, $\text{time}=\frac{\text{initial tokens}}{\text{consumption rate}-\text{fill rate}}=\frac{8\ \text{Mb}}{6\ \text{Mbps}-1\ \text{Mbps}}=\frac{8}{5}\ \text{s}=1.6\ \text{s}$

Mermaid intuition (token level over time while sending at full rate):

Therefore, the computer can transmit at the full $6$ Mbps for $1.6$ seconds.