ee132b-hw4

EE132B-HW Set #4 UCLA 2014 Fall Prof. Izhak Rubin

Problem 1

Consider an ARQ stop-and-wait scheme between stations A and B.

(a) If station A intends to transmit a single data frame, what is the average numberof retransmissions required for the successful transport of data frames? (Hint:Let p denote the probability that the transmit frame is received with error.Express the average number of retransmissions in terms of p.)

(b) If station a intends to transmit M data-frames, where M 2, what is theprobability that the number of retransmissions NR(M) is equal to 2? (Hint:Express the probability in terms of M and p.)

Problem 2

Consider an ARQ stop-and-wait scheme which is similar to the scheme describedin Problem 1 but a distinct feature: suppose that an acknowledgement can be lostduring its transmissions with probability q. If an acknowledgement is lost, station Awill retransmit the data-frame after time-out. Such retransmission process continuesuntil station A receives an acknowledgement.

(a) If station A intends to transmit a single data frame, what is the average numberof retransmissions required for the successful delivery of data frames? (Hint:Express the average number of retransmissions in terms of p and q.)

(b) Find the probability that station A retransmits exactly twice. (Hint: expressthe probability in terms of p and q. You do not need to simplify your answer.)

Problem 3

Let T and S denote two independent exponentially distributed random variableswith parameter T and S, respectively.

(a) Show that the random variable T is memoryless (i.e., P (T t | T > s) =P (T t s), t s 0).

(b) Set Y = min{T, S}. Show that the random variable Y is exponentially dis-tributed, and find its parameter.

(c) LetX denotes a Poisson random variable with parameter T , where T is an expo-nentially distributed random variable with parameter T . Find the distributionfor X (i.e., P (X = n), for n = 0, 1, . . . ).

Problem 4

Figure ?? illustrates the first two messages exchanged in the course of a telephonecall from user A to user B. extend this diagram to include the following messages (with

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first two already illustrated: A Off-Hook; Dial Tone to A; Dialed digits from A; CalledRequest signals; Call Accept signal; Conversation with B answering, A responding,and one more response from B; B On-Hook, Disconnect signals (originating fromlocation of first user to hang up); and finally A On-hook. (This is an arbitrary choiceof the order of actions during disconnect; for example, either user could equally wellhang up first.)

Local Loop Telephone network Local loop

User A Network interface User BNetwork interface

Off-hook signal

Dial tone

Dialed digits

Figure 1: The first two messages exchanged in the course of a telephone call fromuser A to user B

Problem 5

Compare virtual circuit and datagram service with respect to the following:

(a) Ability to survive link or node failure.

(b) Ability to deal with congestion in the network.

(c) Applicability for use with the following types of traffic: (i) voice, (ii) interactivedata traffic, and (iii) file transfer.

Problem 6

(a) Compute the total delays to transfer a message 10000 (eight bit) characters longacross the three hop communications path under the following timing assump-tions. Assume that all links operate at 4800 bps, with a 20 msec delay per linkfor propagation delays plus reaction time at the receiver. (Timings given aretypical, though they are so highly variable that results of this problem shouldbe treated with caution.)

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(i) For circuit switching assume 3 sec per link connection delay (time huntingfor an outgoing trunk, or dialing and associated delays) and 100 msecdurations of call request or accept signal (times to put signals on thecommunications lines, for example, number of bits divided by line ratein bps).

(ii) For message switching, assume 50 bytes per message of header (routinginformation, identification, sequencing information, and so forth) and (ar-bitrarily) 300 msec processing plus queuing time at each node.

(iii) for packet switching, assume the message is divided into 20 equal lengthpackets with 50 bytes of header information per packet, 300 msec process-ing plus queuing time at each node and 20 msec between packets.

(c) Discussing your results and indicate reasonable conditions under which the rel-ative rankings of the delays might change.

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ee132b-hw4

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