*In this post:** A detailed, step-by-step guide demonstrating the steps I use to solve a problem similar to one encountered in my CS 372 Intro to Networking class.*

Given an effective delay of 99ms when network usage is 76%, what is the effective delay when network usage is 53%?

Suppose they want the answer in milliseconds rounded to 1 decimal place.

You might’ve seen a variation of this problem where the delay is given in ms and the network usage is 0%. If you’re given a delay with a network that’s in-use, you have to first figure out what the the delay would be if the network congestion was 0%.

Let’s call that value x and solve for it.

We will use the same D = Do/(1-U) formula we would use if we already knew the delay for a zero-congestion network, but we will put our 99 ms delay where D goes and our unknown “x” value for Do.

Do / (1 - U) = D x / (1- 0.76) = 99ms x / (0.24) = 99

Multiply both sides by 0.24 to turn that into a value for x:

x = 0.24 * 99 x = 23.76 <-- network delay in ms when congestion is at 0%

Now that we know the delay in ms when congestion is at 0%, we can plug it into the D = Do/(1-U) formula again.

D = 23.76 / (1 - .53)D = 50.6 ms

It’s not a difficult problem but my class’s materials only covered the “easy” version so I wanted to demonstrate the “missing steps” for anyone else who might be wondering what to do when they give you the delay for a partially-congested network instead.

Thank you!