Regarding Scenario 7, the bottleneck in the system is the 64kbps full-duplex link 2 3. We will assume that all acknowledgment rates are limited by their respective data rates by
where denotes a data flow from source x to destinationy and denotes the corresponding acknowledgment flow in the reverse direction.
At time t=0, the flows and commence. The optimum rates for both are:
| Time | Optimum Rate (bps) | |
| 0<=t | 64,000 | 1706.66 |
At time t=12, the flows and commence. As the link 2 3 is the bottleneck, we can write
Obviously (2) is the limiting equation, and by sharing bandwidth equally to the flows, we obtain the rates:
| Time | Optimum Rate (bps) | |||
| 0<=t<12 | 64,000 | 1706.66 | ||
| 12<=t | 32,000 | 853.33 | 32,000 | 853.33 |
At time t=18, the flows and commence. Here, the flows are in the opposite directions to the previous four flows. We can write:
Distributing bandwidth fairly, we have and . Assume both links are fully utilised and substituting for the acknowledgment rates using (1), we have:
Substituting (8) into (6) gives , and the table:
| Time | Optimum Rate (bps) | |||||
| 0<=t<12 | 64,000 | 1706.66 | ||||
| 12<=t<18 | 32,000 | 853.33 | 32,000 | 853.33 | ||
| 18<=t | 31,168.83 | 831.2 | 31,168.83 | 831.2 | 62,337.66 | 1,662.34 |
The six flows continue to transmit until time t=12 when the flows and commence. Again, distributing bandwidth fairly, we have and . Assume both links are fully utilised and substituting for the acknowledgment rates using (1), we have:
Substituting (11) into (9) gives , and the table:
| Time | Optimum Rate (bps) | |||||||
| 0<=t<12 | 64,000 | 1706.66 | ||||||
| 12<=t<18 | 32,000 | 853.33 | 32,000 | 853.33 | ||||
| 31,168.83 | 831.2 | 31,168.83 | 831.2 | 62,337.66 | 1,662.34 | |||
| 20,779.2 | 554.1 | 20,779.2 | 554.1 | 62,337.66 | 1,662.34 | 20,779.2 | 554.1 | |
As flow only has 100 packets to send, it finishes quickly, and the rates return to the values before flow started:
| Time | Optimum Rate (bps) | |||||||
| 0<=t<12 | 64,000 | 1706.66 | ||||||
| 12<=t<18 | 32,000 | 853.33 | 32,000 | 853.33 | ||||
| 31,168.83 | 831.2 | 31,168.83 | 831.2 | 62,337.66 | 1,662.34 | |||
| 20,779.2 | 554.1 | 20,779.2 | 554.1 | 62,337.66 | 1,662.34 | 20,779.2 | 554.1 | |
| 31,168.83 | 831.2 | 31,168.83 | 831.2 | 62,337.66 | 1,662.34 | |||
Similarly, flow has most of the bandwidth across 3 2, so it is the next to finish, and the rate return to the values before flow started:
| Time | Optimum Rate (bps) | |||||||
| 0<=t<12 | 64,000 | 1706.66 | ||||||
| 12<=t<18 | 32,000 | 853.33 | 32,000 | 853.33 | ||||
| 31,168.83 | 831.2 | 31,168.83 | 831.2 | 62,337.66 | 1,662.34 | |||
| 20,779.2 | 554.1 | 20,779.2 | 554.1 | 62,337.66 | 1,662.34 | 20,779.2 | 554.1 | |
| 31,168.83 | 831.2 | 31,168.83 | 831.2 | 62,337.66 | 1,662.34 | |||
| 32,000 | 853.33 | 32,000 | 853.33 | |||||
The flows and continue at this rate until one or both finish.