Homework Assignments: 22C:178 & 055:134

Computer Communications Spring 1998

Assignment 7

[9 March]

Packet Size Problems

First Problem. Suppose we have a file of size 40MB to send over a store and forward sequence of 8 hops. The problem is to send the file from node A to textttnode B.

  A --- X --- X --- X --- X --- X --- X --- X --- B

Each of the X-nodes is a store and forward node that can read a frame and send another frame concurrently (this is often called pipelining ). The 40MB will be split into frames, so that each frame has the form:

   | Header (32 bytes) |  Data (p bytes)           |

Each link has raw bandwidth of 200kbps. There is a negligible propagation delay on each link. What value of p will minimize the total time to send the file?

(Solution technique for the above problem was given in class on Monday 9 March).

Second Problem. This is a problem of evaluating the effective bandwidth for the stop & wait protocol in the presence of errors. Suppose the loss of a frame, in either direction on a full-duplex link, occurs with probability (frameSize)*1e-8, where frameSize is the number of bits in a frame. Thus small frames are less likely to be lost than large frames. Every frame contains a header of 24 bytes. We have software with these characteristics: the frame size can either be 1KB, 2KB, or 32 bytes -- the 32 byte frame is only used as an ACK0 or ACK1 frame. The link speed is 10Mbps. The propagation delay on the link is 2.5 microseconds. We can specify the frame size to be used for sending data, either 1KB or 2KB. Which will give us the highest effective bandwidth?

Hints: to solve this problem we need to calculate the expected effective bandwidth for each case, 1KB and 2KB frame lengths. The following formula proves useful in calculations:

 1 + 2R + 3R^2 + 4R^3 + 5R^4 + ...  =  1/(1-R)^2

where R is a value between 0 and 1.

Ted Herman