### End to End Throughput and Bottleneck Links

Consider the scenario shown below, with four different servers connected to four different clients over four three-hop paths.
The four pairs share a common middle hop with a transmission capacity of R = 400 Mbps.
The four links from the servers to the shared link have a transmission capacity of R_{S} = 20 Mbps.
Each of the four links from the shared middle link to a client has a transmission capacity of R_{C} = 40 Mbps.

You might want to review Figure 1.20 in the text before answering the following questions

### Question List

1. What is the maximum achievable end-end throughput (in Mbps) for each of four client-to-server pairs, assuming that the middle link is fairly shared (divides its transmission rate equally)?

2. Which link is the bottleneck link? Format as Rc, Rs, or R

3. Assuming that the servers are sending at the maximum rate possible, what are the link utilizations for the server links (R_{S})? Answer as a decimal

4. Assuming that the servers are sending at the maximum rate possible, what are the link utilizations for the client links (R_{C})? Answer as a decimal

5. Assuming that the servers are sending at the maximum rate possible, what is the link utilizations for the shared link (R)? Answer as a decimal

### Solution

1. The maximum achievable end-end throughput is the capacity of the link with the minimum capacity, which is 20 Mbps

2. The bottleneck link is the link with the smallest capacity between R_{S}, R_{C}, and R/4. The bottleneck link is Rs.

3. The server's utilization = R_{bottleneck} / R_{S} = 20 / 20 = 1

4. The client's utilization = R_{bottleneck} / R_{C} = 20 / 40 = 0.5

5. The shared link's utilization = R_{bottleneck} / (R / 4) = 20 / (400 / 4) = 0.2

That's incorrect

That's correct

The answer was: 20

The answer was: Rs

The answer was: 1

The answer was: 0.5

The answer was: 0.2