Distance-vector control traffic: In a 50-router network, each router records delays as 10-bit numbers and exchanges its entire delay vector twice per second. Approximately how much bandwidth is consumed per full-duplex line by the routing exchanges (ignoring headers)?

Introduction / Context:Distance-vector routing protocols periodically exchange vectors of path metrics (for example, delays). Estimating the bandwidth consumed by these control messages is useful for capacity planning on low-speed links and for understanding protocol overheads relative to user traffic.

Given Data / Assumptions:

• Number of routers (and destinations) = 50.
• Each delay is encoded as a 10-bit value.
• Each router sends its full vector twice per second.
• We ignore protocol headers and assume one neighbor per link for a simple per-link estimate.

Concept / Approach:

On a single link between two routers, each side sends a vector containing one entry per known destination. Bits per vector equals entries * bits per entry. Multiply by update frequency to get bits per second in one direction. A full-duplex line has independent capacities in each direction, but per-direction bandwidth is usually quoted.

Step-by-Step Solution:

Verification / Alternative check:

If you summed both directions, the pair would total ~2000 bps, but per-direction accounting (the usual convention) yields 1000 bps. Including headers would raise the figure slightly but not change the order of magnitude.

Why Other Options Are Wrong:

a: 500 bps accounts for one update per second, not two.

b: 1500 bps does not follow directly from the provided numbers.

c: 5 bps is far too low; it ignores vector length and frequency.

e: Not applicable because 1000 bps is the consistent per-direction estimate.

Common Pitfalls:

Confusing per-direction (full-duplex) bandwidth with the sum of both directions; forgetting to multiply by update frequency; or miscounting destinations in the vector length.

Final Answer:

1000 bps