Exercise 2 -- Network Interconnections

Due: Thursday, March 9, 2000 (in class)

1. Sometimes the best way to understand how something works is to think about what might happen when it doesn't work. So, for this exercise, I'd like you to think about how the various approaches to constructing a multi-machine network discussed in class might react to a bad situation.

   Suppose you had a token ring network and a bus network using the CSMA/CD protocol organized as shown in the diagrams below. The most obvious way one of these networks might get "damaged" is to have one of the wires accidentally cut. So, assume that in each network something accidentally damages the wire between machines "C" and "D," severing the connection.

   

   In a real network, an accidental cable break might cause electrical damage to the machines connected to the broken cable or other secondary problems. For this question, however, assume that the damage done is so clean that the only thing interrupted is the ability to send data along the wire between C and D. Everything else works as well as it possibly could after the break.

   On the other hand, in real implementations of these networks, the machines follow special instructions when they detect connection problems in an attempt to recover from any damage. For this problem, I want you to instead assume the machines act as if nothing special has happened.

   With these assumptions:

   1. Which, if any, machines would be able to continue to communicate after the accident in the CSMA/CD network? Briefly justify your answer.
   2. Which, if any, machines would be able to continue to communicate after the accident in the token ring network? Briefly justify your answer.

2. Engineers and scientists often use odd units to measure things. If you don't believe this, you should learn about the use of smoots as a unit of distance before dealing with the rest of this problem.

   A better known example of an odd unit of measure for distance is the "light year." Since when is a "year" a unit of distance?

   When measuring networks, a very good unit of measure might be called the "light bit." The idea is to choose the distance that a signal traveling through the network traverses in the time spent sending one bit's worth of data as the basic unit of distance. Since electrical signals and light in fiber travel at just about the speed of light, this is basically the distance light travels in the time it takes to send one bit.

   The actual length of this unit depends, of course, on the data transmission rate of the network considered. For example, when data is sent through a 10 Megabit per second Ethernet, the time required to send a bit is 1/10,000,000 of a second. The speed of light is about 3 x 10⁸meters/sec. So, the length of a "bit" sent through an Ethernet is:

   (3 x 10⁸)/(10⁷) = 30 meters

   I'd like you to do some measuring in these units.

   1. The fastest modems one can buy transmit data at the rate of 56,000 bits per second. How long is a "light bit" sent through such a modem. That is, how far can light travel in the time it takes such a modem to send one bit.

   2. The fiber network between buildings on the campus operate at a rate of 100 million bits per second. How long is a bit on these parts of the network?

   3. Given the size of the campus, its probably reasonable to say that the longest stretch of fiber between buildings is under one kilometer long. How would you express this length in bits? (i.e. how many bits would fit on one kilometer of fiber given a data rate of 100 million bits per second).

3. Now, to understand why measuring a network in bits makes sense, let's consider the efficiency of some of the networks discussed in class.

   When a network tries to deliver a packet, the efficiency of the process can be measured by dividing the time spent actually sending the bits of a packet by the total time from when the system starts trying to send the packet to the point when the last bit is sent. If no time is wasted, the efficiency will be 1. If something delays the beginning of the transmission of the packet, the efficiency will be:

   time-spent-sending/(length-of-delay + time-spent-sending)

   Obivously, if the delay is greater than 0, the efficiency will be less than 1.

   In Ethernet, the main cause of inefficient transmission is collisions. If a station encounters one or more collisions before it manages to send a packet successfully, the efficiency will be less than one.

   Suppose that on some Ethernet, two computers, A and B, both have a packet to send. Assume that A starts sending before B, but not long enough before B to avoid a collision. Also assume that after detecting the collision, A attempts to send its packet again as soon as it detects that the network is again idle and that nothing collides with this second attempt allowing A to deliver its packet successfully.

   1. Assuming the network is 1 kilometer long, that the packet is 1000 bits long and that the data rate is 100 million bits per second, what would be the highest and lowest possible efficiency values for A's transmission. (Hint: The efficiency will depend on how far apart you assume A and B are on the network.)

   2. Now, again compute the minimum and maximum efficiency values for A, but this time assume the data rate is 10 million bits per second.

4. Having seen how efficient (or inefficient) an Ethernet can be we might as well do a similar inspection of Token Ring.

   The basic cause of inefficiency on a token ring is the time spent waiting for the token to arrive. So, assume that just one station, A, on a token ring has a packet to send. Assume that the total circumference of the ring is 1 kilometer and that the data rate of the ring is 100 million bits per second.

   packet A wants to send is 1000 bits long.

   1. Determine the minimum and maximum possible efficiency values for A's transmission assuming that the message A wants to send is 1000 bits long. (Hint: The efficiency value will depend on where you assume the token was situated when A first got the urge to send a packet.)
   2. Determine the minimum and maximum possible efficiency values for A's transmission assuming that the message A wants to send is 10,000 bits long.

If you have questions, you are encouraged to ask them through the discussion area for this homework assignment