Section 5.9. Exercises

5.9. Exercises

1.	Consider the transfer of a file containing 1 million characters from one computer to another. Transfer consists of a sequence of cycles. For one cycle, a = (time for data packet + propagation) + (time for ack packet + propagation). The throughput refers to the number of sequences required to transfer 1 million characters. Each character in its digital form requires 8 bits. The two computers are D = 1 km apart, and each generates a data rate of b = 1 Mb/s, with a packet size s = 256 bits, which includes 80 bits of overhead. The propagation speed on the bus is 200 m/ ¼ sec. Find the total elapsed time using throughput and C for the following two cases. A bus topology, with each frame acknowledged with an 88-bit frame before the next frame is sent. A ring topology having a total circular length of 2 D , with the two computers D distance apart. Acknowledgment is achieved by allowing a frame to circulate past the destination user back to the source user . The ring has N = 100 repeaters, each of which introduces a delay of 1 bit time.
2.	We want to design a coaxial LAN for 12 offices arranged on three similar floors, each floor having two rows with 2 offices and the rows separated by a hallway. Each office is 5 m x 5 m with a height of 3 m. The LAN center is in the center of the ground floor beneath the three office floors. Assume that each office requires two IP telephone lines and retrieves two Web pages per minute at the average rate of 22 K per page. Estimate the distance from each office to the LAN center. Estimate the required available bit rate for the LAN.
3.	Consider a 100 m bus LAN with a number of equally spaced computers with a data rate of 100 Mb/s. Assume a propagation speed of 200 m/ ¼ s. What is the mean time to send a frame of 1,000 bits to another computer, measured from the beginning of transmission to the end of reception ? Assume a mean distance between pairs of computers to be 0.375 km, an approximation based on the following observation: For a computer on one end, the average distance is 0.5 km. For a computer in the center, the average distance is 0.25 km. With this assumption, the time to send is transmission time plus propagation time. If two computers with a mean distance of 0.37 km start transmitting at the same time, their frames interfere with each other. If each transmitting computer monitors the bus during transmission, how long does it take before it notices a collision? Show your answer in terms of both time and bit time.
4.	Consider a 100 Mb/s 100BaseT Ethernet LAN with four attached users, as shown in Figure 5.5. In a nonpersistent CSMA/CD algorithm, a user normally waits 512 g bit times after a collision before sending its frame, where g is drawn randomly . Assume that a 96 bit times of waiting period are needed for clearing the link from the jammed signal in the 100BaseT Ethernet LAN. Assume that only user 1 and user 4 are active and that the propagation delay between them is 180 bit times. Suppose that these two users try to send frames to each other and that their frames collide at the half-way LAN link. User 1 then chooses g = 2, whereas user 4 picks g = 1, and both retransmit. How long does it take for user 1 to start its retransmission? How long does it take for user 4 to start its retransmission? How long does it take the frame from user 4 take to reach user 1?
5.	For a CSMA/CD system, consider the throughput derived from Equation (5.15). Set two parameters in this equation: ± = t p /T and ² = »T . Rewrite the throughput in terms of ± and ² , and denote it by U n . Comment why R n is in terms of frames/time slot and why ² can be called " offered load" in this case. Using a computer, sketch four plots all in one chart for U n in terms of ² , given ± ={0.001, 0.01, 0.1, 1.0}, and comment on the behavior of the normalized throughput, U n .
6.	For a local area network using CSMA/CD, assume a 12 percent frame error rate owing to noise and errors resulting from collisions. Discuss how the throughput U could be affected.
7.	A 10 Gb/s Ethernet LAN with ten users attached to it uses CSMA/CD. The bus is about 10 meters , and users' frames are restricted to a maximum size 1,500 bytes. Based on the statistics, four users in average are active at the same time. Find the frame propagation and transmission times. Find the average utilization of the bus. Find the probability that a user attempts to transmit frames in an empty time slot. Find the probability that a user attempts seven different times in seven different empty slots to transmit its frame and is not successful, owing to collision, but is successful on the eighth attempt. Find the average number of contentions.
8.	Using the CSMA details discussed in this chapter, sketch a block diagram that represents the implementation of this algorithm for the following cases: Nonpersistent CSMA p -persistent CSMA
9.	Design (show only the network) a LAN system for a small five-story building. One floor is dedicated to two mail servers and separated three database servers. Each of remaining floor has four computers with broadband access. Your design should meet the following restrictions and conditions: three-input hubs, one bridge, and unlimited Ethernet buses. The incoming broadband Internet access must be connected to a six-repeater ring, no bus LAN is allowed outside of a floor, and a traffic analyzer must be attached to the network.