Question 1. (10 points) Describe the operation of a Time-Slot-Interchange (TSI) switch. Determine the number of 64Kbps voice connections such a switch can support . Question 2. ( 20 points) Consider p-persistent CSMA-CD protocol,

i) Describe the operation of this protocol. ii) Assuming that there are n users contending during a contention interval, derive the

expression for maximum success probability during a minislot. Determine the maximum success probability as n increases.

iii) Derive the expression for the maximum throughput for this protocol. Question 3. (25 points) A 128,000bytes message will be transmitted from the source to the destination in the network shown below. Assume that the signal propagates at a speed of

km/second and each hop has a bit error rate of . The network limits the packets to a maximum

Course Number Section Telecommunication Networks ELEC 463 Examination Date Time # of pages Final Examination December 12, 2002 3 Hours 4 Instructor (s) Dr. M. Mehmet Ali Material allowed : No Yes Calculators allowed : No Yes

Special Instructions: Attempt all six questions. Handwriting should be clear and readable. Whenever possible include diagrams to make solutions more clear. Students should return the question paper after the exam. All the answers should be in the answering book. Some formulas that may be needed are provided at the end of the exam.

510*2610−=p

X

X

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size of 2,000bytes and each packet has a 32-byte header. Assume that the size of ACK/NACK packet is 40bytes and that the transmission of ACK/NACK packets are error free. There are no queueing delays, the processing times are negligible and the time out duration has been chosen to expire at the arrival time of ACK/NACK. Determine the average time it will take to transmit the message from source to destination in each of the following cases,

i) Assuming that hop-by-hop Stop-and-Wait ARQ protocol is being used. A switch may begin the transmission of a packet at the second hop as soon as it has been received error free from the first hop and similarly source begins the transmission of the next packet.

ii) Assuming that end-to-end Stop-and-Wait ARQ is being used. As soon as the last bit of

a packet arrives at the switch, its transmission over the second link begins. ACK/NACK are sent by the destination and the source doesnot begin the transmission of the next packet until the present packet is received error free by the destination.

Note: You have to show the intermediate steps in your calculations. 1000km 1500km 1Mbps 2Mbps Question 4. (15 points) Suppose that we wish to transmit a large message over a link and that the message will be broken into 100Kbits packets. A packet is transmitted simultaneously over two independent channels as shown in the figure below. If a packet is received error free in at least in one of the channels, then the transmission of the packet is successful otherwise the packet will require retransmission. Assume that the probability of bit error on each channel is . Determine the average number of bits that it will take to transmit the message from the source to the destination,

i) Assuming that Stop-and Wait ARQ is used between source and destination. ii) Assuming that the original Go-Back N ARQ is used with N= 5 between source and

destination. Compare and explain this result with that of part i) .

MbitsL 10=

510−=p

Source

Switch

Destination

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Channel 1 Channel 2

Question 5. ( 15 points) Assume that the path from a source to a destination station consists of L links, signal propagation time on each link is p and the transmission rate on each link is same. Assume that the transmission time of a message on a link is T, ignoring the queueing and retransmission delays,

i) Derive the end to end message delay from source to destination. ii) Derive the end to end delay for transmitting the message assuming that message has

been divided into k packets. iii) Derive the expresssion for the end to end delay assuming that message has been divided

into k packets and cut through switching is used. ( Show your derivations and illustrate each mode of message transmission through a figure)

Question 6. ( 15 points) Determine the spanning tree for the following network, explain your steps. Costs assigned to each LAN are assumed to be equal.

Source

Destination

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Formulas: - Poisson distribution:

- Binomial distribution:

- Geometric distribution:

,

Expected number of trials for the first success to occur =

!)( ) arrivals ( Pr

k

tektkobλλ −

=

knk ppkn

nkob −−⎟⎟⎠

⎞⎜⎜⎝

⎛= )1( trials)in successes ( Pr

1)1( trial)' on the occurs successfirst ( Pr −−= kppthkob

pkE 1][ =

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