Vehicular traffic networks

Recall that latency is the time it takes to get from one place to another (measured in seconds, minutes, or hours), and bandwidth is the amount of something that can pass through a point in a given amount of time (measured in cars per minute, bits per second, etc.).

Consider this road network with six cities. Single lines represent 1 lane in each direction, and double lines represent 2 lanes in each direction.

• There are four different routes to get from A to B (without going in circles). What are the four routes? (In graph theory language, you would say there are four distinct paths that go from A to B without cycles.)
• What is the total length of the shortest route?
• Assume all the roads have speed limit 30 miles per hour.
  • What is the latency of a car traveling from A to B along route ACDB?
  • What is the latency of a car traveling from A to B along route AEDB?
• Assume everyone follows the 2-second rule for following distance.
  • What is the bandwidth of the route ACDB? (Hint: the bandwidth of a route is limited by the lowest bandwidth of any link in the path.)
  • What is the bandwidth of the route AEDB?
• Challenge problem: Now suppose we want to build a house in city B using materials in city A. We have 10000 bricks that we have to get from A to B as fast as possible. Assume a car can carry 10 bricks, cars always follow the 2-second rule, and there is no other traffic on the road. What is the total time it will take to get all the bricks from A to B? You will have to consider both latency and bandwidth. Show your work; explain the steps of your calculation; list any assumptions you had to make.
• How long does it take 1 bit to get from A to B?
• How long does it take 2 bits to get from A to B? Hint: The second bit can follow right after the first bit. You don’t have to wait for the first bit to reach B before A sends the second bit.
• How many bytes are in the file?
• How many bits are in the file?
• Use the formula to find the total amount of time it will take to send the file over the network. Make sure the units are consistent.

Data networks

Latency and bandwidth are used to measure speed in computer networks. The latency (sometimes called the ping) is how long it takes one bit to get across the network. The bandwidth is how many bits can go by in a second. The bandwidth is analogous to the 2-second rule in the vehicular traffic example.

Suppose two computers (A and B) are connected in a network.The latency of the connection is 20 ms (0.020 seconds), and the bandwidth of the connection is 40 kbps (40000 bits per second). (This is a pretty typical latency, but it’s a very low bandwidth these days. It’s like dial-up rate.)

The formula to find the total amount of time it takes to get a file across the network is

For example, if you are sending an 80000 bit file across the network described above, the formula says the time required is 2.02 seconds:

This formula works because it takes 0.02 seconds for the first bit to get across the network (the latency). Then all the other bits are following right after it, one after the other as fast as the bandwidth allows. Since the bandwidth is 40 kbps, 40000 bits are arriving at computer B every second. In this example, it takes 2 full seconds to get all the bits into computer B.

1 MB

Now suppose you want to send a 1 megabyte file across the computer network above.