EE132B-HW Set #5 UCLA 2014 Fall Prof. Izhak Rubin

Problem 1Consider a selective-repeat ARQ in which the window size N is equal to 4 (i.e.,

the time out duration allows the transmission of four data frames, including itself).Assume that the originating node wishes to transmit 10 data frames which are labeledD1, D2, . . . , D10. In this particular session, frames D3, D4, D8, D10 are retransmittedonce, while Frame D2 is retransmitted three times. Other frames do not requireretransmission. Draw a simple time diagram demonstrating the correct sequence ofevents, identifying the timeout threshold used.

Problem 2In a sequence of frame transmissions, data frame D0 has just been positively ac-

knowledged. Four more frames - D1, D2, D3, and D4 - are transmitted. The nextreturned transmission, received after D4 has been transmitted, is a negative acknowl-edgement toD2. Assume that this implicitly acknowledges any previously transmittedbut unacknowledged data frames.(a) What action does a go-back-N protocol take?

(b) What action does a selective-repeat-N protocol take?

Problem 3Compute the throughput rate attained across a communications link when using

a stop-and-wait ARQ scheme assuming the following parameters: a 64 kbps link, allcharacters are eight bits long, 200 data characters per frame, six characters for dataframe headers and for acknowledgement frames, 10 msec (one way) propagation timeand 20 msec turn-around time, and a bit error rate of 104.

Problem 4A 1 MByte file is to be transmitted over a 1 Mbps communication line that has a

bit error rate of p = 106.(a) What is the probability that the entire file is transmitted without errors? Note:

For n large and p very small, we have: (1 p)n enp.(b) The file is broken up into N equal-sized blocks that are transmitted separately.

What is the probability that all the blocks arrive without error? Was it usefulto divide the file into blocks?

(c) Suppose that the propagation delay is negligible and the ACK packet size isnegligible. Explain how the stop-and-wait ARQ scheme can help deliver the filein an error-free form. On the average, how long does it take to deliver the fileif the whole file is transmitted once and the ARQ scheme causes the entire fileto be retransmitted if there is error?

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EE132B-HW Set #5 UCLA 2014 Fall Prof. Izhak Rubin

(d) Now consider breaking up the file into N blocks. (Neglect the overhead for theheader and CRC bits.) On the average how long does it take to deliver thefile if the ARQ transmits the blocks one at a time? Evaluate your answer forN = 80, 800, and 8000.

(e) Explain qualitatively to the impact on the answer to part (d) when frame over-head is taken into account.

Problem 5Use Dijkstras algorithm, showing all steps, to derive the shortest path tree rooted

at node A for the network graph with indicated link weights as shown in Figure. 1.

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A

B

C

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Figure 1: The network graph with indicated link weights

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