Question

Consider a residential network that connects to the internet with a DSL link that has a download rate of 4 Mb/s. Assume that there are three UDP flows sharing the link and the remote hosts are sending at rates of 1 Mb/s, 2 Mb/s and 3 Mb/s. Assume that the ISP router has a link buffer that can hold 300 packets (assume all packets have the same length).

a) For each flow, what fraction of the packets it sends are discarded?

b) For each flow, about how many packets does it have in the queue.

c) Now, suppose the queue at the ISP router is replaced by three queues that can each hold 100 packets and that the queues are scheduled using weighted-fair queueing, where the weights are all 0.33. In this case, what fraction of packets are discarded from each flow?

d) How many packets does each flow have in the queue?

e) Now, suppose the weights are 0.2 for the first flow, 0.6 for the second and 0.2 for the third. In this case, what fraction of packets are discarded from each flow?

f) How many packets does each flow have in the queue?

Answer 1

a) The UDP flows are sending data at (1 + 2 + 3) Mbps and the DSL link can download data only at 4 Mbps. Since packats from all the flows are being held together, for ach flow the fraction of lost packets

= (6-4)/6

= 2/6

= 1/3

b) Total 300 packets can be queued at the buffer. Among these,

Packets belonging to 1 Mbps flow

= 1x 300/(1 + 2 + 3)

= 300/6

= 50

Packets belonging to 2 Mbps flow

= 2x 300/(1 + 2 + 3)

= 600/6

= 100

Packet belonging to 1 Mbps flow

= 3x 300/(1 + 2 + 3)

= 900/6

= 150

c) Each queue is scheduled with 0.33 weight.

Therefoe the first flow consumes a share of the bandwidth equal to min(1Mbps, 4*0.33 Mbps)=1Mbps. It loses 0% of it's packets.

The second and third flows equally share the remaining 4-1 = 3 Mbps of bandwidth, and therefore each get 1.5 Mbps.

The second flow loses 100%x(2-1.5)/2 = 25% of its packets

The third flow loses 100%x(3 - 1.5)/3 = 50% of its packets.

d) The first flow’s queue is empty or close to empty. The other two each have about 100 packets in their queues which is the maximum capacity of their queues.
e) Second flow queue has 0.6 weight, therefore it gets min(2 Mbps, 4*0.6 Mbps)= 2 Mbps of the dowanload capacity.

None of second flow packets are discarded.

The remaining (4-2) Mbps = 2 Mbps is equally shared by the first and third flow, each getting 1 Mbps.

Since first flow bandwidth share exactly matches it's data rate, none of it's packets are discarded.

Third flow gets 100%x(3 - 1)/3 = 67% packets discarded

f) First flow has no packets in queue (assuming packets arrive at regular intervals)

The second flow has none or close to no packts in the queue.

The third flow has about 100 packets in queue which is the maximum capacity of it's queue.