Suppose five stations are waiting for another packet to fin

Suppose five stations are waiting for another packet to finish on… Suppose five stations are waiting for another packet to finish on an Ethernet. Alltransmit at once when the packet is finished and collide.  (a) Simulate this situation up until the point when one of the five waiting stationssucceeds. Use coin flips or some other genuine random source to determinebackoff times. Make the following simplifications: Ignore interframe spacing,ignore variability in collision times (so that retransmission is always after anexact integral multiple of the 51.2-µs slot time), and assume that each collisionuses up exactly one slot time.(b) Discuss the effect of the listed simplifications in your simulation versus thebehavior you might encounter on a real Ethernet.51 Write a program to implement the simulation discussed above, this time with Nstations waiting to transmit. Again model time as an integer, T, in units of slottimes, and again treat collisions as taking one slot time (so a collision at timeT followed by a backoff of k = 0 would result in a retransmission attempt attime T + 1). Find the average delay before one station transmits successfully, forN = 20, N = 40, and N = 100. Does your data support the notion that the delayis linear in N? Hint: For each station, keep track of that station’s NextTimeToSendand CollisionCount. You are done when you reach a time T for which there is onlyone station with NextTimeToSend == T. If there is no such station, increment T. Ifthere are two or more, schedule the retransmissions and try again.52 Suppose that N Ethernet stations, all trying to send at the same time, require N/2slot times to sort out who transmits next. Assuming the average packet size is 5slot times, express the available bandwidth as a function of N.53 Consider the following Ethernet model. Transmission attempts are at randomtimes with an average spacing of ? slot times; specifically, the interval betweenconsecutive attempts is an exponential random variable x = -? log u, whereu is chosen randomly in the interval 0 = u = 1. An attempt at time t results in a collision if there is another attempt in the range from t – 1 to t + 1,where t is measured in units of the 51.2-µs slot time; otherwise the attemptsucceeds.(a) Write a program to simulate, for a given value of ?, the average number of slottimes needed before a successful transmission, called the contention interval.162 2 Direct Link NetworksFind the minimum value of the contention interval. Note that you will haveto find one attempt past the one that succeeds, in order to determine if therewas a collision. Ignore retransmissions, which probably do not fit the randommodel above.(b) The Ethernet alternates between contention intervals and successful transmissions. Suppose the average successful transmission lasts 8 slot times (512bytes). Using your minimum length of the contention interval from above,what fraction of the theoretical 10-Mbps bandwidth is available for transmissions?54 What conditions would have to hold for a corrupted frame to circulate forever ona token ring without a monitor? How does the monitor fix this problem?55 An IEEE 802.5 token ring has five stations and a total wire length of 230 m. Howmany bits of delay must the monitor insert into the ring? Do this for both 4 Mbpsand 16 Mbps; use a propagation rate of 2.3 × 108 m/s.56 Consider a token ring network like FDDI in which a station is allowed to hold thetoken for some period of time (the token holding time, or THT). Let RingLatencydenote the time it takes the token to make one complete rotation around thenetwork when none of the stations have any data to send.(a) In terms of THT and RingLatency, express the efficiency of this network whenonly a single station is active.(b) What setting of THT would be optimal for a network that had only one stationactive (with data to send) at a time?(c) In the case where N stations are active, give an upper bound on the tokenrotation time, or TRT, for the network.57 Consider a token ring with a ring latency of 200 µs. Assuming that the delayedtoken release strategy is used, what is the effective throughput rate that can beachieved if the ring has a bandwidth of 4 Mbps? What is the effective throughputrate that can be achieved if the ring has a bandwidth of 100 Mbps? Answer forboth a single active host and for “many” hosts; for the latter, assume there aresufficiently many hosts transmitting that the time spent advancing the token canbe ignored. Assume a packet size of 1 KB.[07/07, 7:41 pm] +254 720 476419: The IP datagram for a TCP ACK message is 40 bytes long: It contains 20 bytes ofTCP header and 20 bytes of IP header. Assume that this ACK is traversing an ATMnetwork that uses AAL5 to encapsulate IP packets. How many ATM packets willit take to carry the ACK? What if AAL3/4 is used instead?27 The CS-PDU for AAL5 contains up to 47 bytes of padding, while the AAL3/4 CSPDU only contains up to 3 bytes of padding. Explain why the effective bandwidthof AAL5 is always the same as, or higher than, that of AAL3/4, given a PDU of aparticular size.28 How reliable does an ATM connection have to be in order to maintain a lossrate of less than one per million for a higher-level PDU of size 20 cells? AssumeAAL5.29 Assuming the 20-cell AAL5 packet from the previous problem, suppose a final cellis tacked on the end of the PDU, and that this cell is the XOR of all the previouscells in the PDU. This allows recovery from any one lost cell. What cell loss ratenow would yield a net one-per-million loss rate for 20-data-cell PDUs?30 Recall that AAL3/4 has a CRC-10 checksum at the end of each cell, while AAL5has a single CRC-32 checksum at the end of the PDU. If a PDU is carried in12 AAL3/4 cells, then AAL3/4 devotes nearly four times as many bits to errordetection as AAL5.(a) Suppose errors are known to come in bursts, where each burst is small enoughto be confined to a single cell. Find the probability that AAL3/4 fails to detectExercises 231an error, given that it is known that exactly two cells are affected. Do the samefor three cells. Under these conditions, is AAL3/4 more or less reliable thanAAL5? Assume that an N-bit CRC fails to detect an error with probability1/2N (which is strictly true only when all errors are equally likely).(b) Can you think of any error distribution in which AAL3/4 would be more likelythan AAL5 to detect an error? Do you think such circumstances are likely?31 Cell switching methods essentially always use virtual circuit routing rather thandatagram routing. Give a specific argument why this is so.32 Suppose a workstation has an I/O bus speed of 800 Mbps and memory bandwidthof 2 Gbps. Assuming DMA in and out of main memory, how many interfaces to45-Mbps T3 links could a switch based on this workstation handle?33 Suppose a workstation has an I/O bus speed of 1 Gbps and memory bandwidthof 2 Gbps. Assuming DMA in and out of main memory, how many interfaces to45-Mbps T3 links could a switch based on this workstation handle?34 Suppose a switch can forward packets at a rate of 100,000 per second, regardless(within limits) of size. Assuming the workstation parameters described in the previous problem, at what packet size would the bus bandwidth become the limitingfactor?35 Suppose that a switch is designed to have both input and output FIFO buffering.As packets arrive on an input port they are inserted at the tail of the FIFO. Theswitch then tries to forward the packets at the head of each FIFO to the tail of theappropriate output FIFO.(a) Explain under what circumstances such a switch can lose a packet destinedfor an output port whose FIFO is empty.(b) What is this behavior called?(c) Assuming the FIFO buffering memory can be redistributed freely, suggest areshuffling of the buffers that avoids the above problem, and explain why itdoes so.Computer Science Engineering & Technology Networking INTERNET 2

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