Consider the queuing delay in a router buffer, where the packet experiences a delay as it waits to be transmitted onto the link. The length of the queuing delay of a specific packet will depend on the number of earlier-arriving packets that are queued and waiting for transmission onto the link. If the queue is empty and no other packet is currently being transmitted, then our packet’s queuing delay will be zero. On the other hand, if the traffic is heavy and many other packets are also waiting to be transmitted, the queuing delay will be long.
Assume a constant transmission rate of R = 900000 bps, a constant packet-length L = 4100 bits, and a is the average rate of packets/second. Traffic intensity I = La/R, and the queuing delay is calculated as I(L/R)(1 - I) for I < 1.
1. In practice, does the queuing delay tend to vary a lot? Answer with Yes or No
2. Assuming that a = 26, what is the queuing delay? Give your answer in milliseconds (ms)
3. Assuming that a = 87, what is the queuing delay? Give your answer in milliseconds (ms)
4. Assuming the router's buffer is infinite, the queuing delay is 1.0899 ms, and 1681 packets arrive. How many packets will be in the buffer 1 second later?
5. If the buffer has a maximum size of 655 packets, how many of the 1681 packets would be dropped upon arrival from the previous question?
1. Yes, in practice, queuing delay can vary significantly. We use the above formulas
as a way to give a rough estimate, but in a real-life scenario it is much more complicated.
2. Queuing Delay = I(L/R)(1 - I) * 1000 = 0.1184*(4100/900000)*(1-0.1184) * 1000 = 0.4755 ms.
3. Queuing Delay = I(L/R)(1 - I) * 1000 = 0.3963*(4100/900000)*(1-0.3963) * 1000 = 1.0899 ms.
4. Packets left in buffer = a - floor(1000/delay) = 1681 - floor(1000/1.0899) = 764 packets.
5. Packets dropped = packets - buffer size = 1681 - 655 = 1026 dropped packets.
The answer was: Yes
The answer was: 0.4755
The answer was: 1.0899
The answer was: 764
The answer was: 1026