# Data link layer Sliding Window utilization formula query

In the data link layer, the Sliding Window is used for flow control.

There are two link utilization formula that can be use. They are :

U = 1, for N > 2a + 1

OR

U = N/(1+2a), for N < 2a + 1

In both formula, N denotes the window size and a = Propagation time / transmission time

I am not really understanding which formula to use in what situation although the condition is specified. What does 2a+1 actually mean? Can anyone help me to understand it in simple term. Thanks!

• What is $a$? And no, you can not use one or the other; they are one formula, defining $U$ in a piecewise fashion. – Raphael Nov 14 '16 at 19:47

If it is about how we got to the formula, link utilization is the ratio of the time that the link is active to the total time.

total time being the sum of transmission time and propagation time.

link active time = time taken to transmit N packets = N * TransmissionDelay

Hence, the formula to calculate link utilization(or efficiency) is

N/(1+2a)

However, in practice, the link utilization cannot exceed 1 (ie link cannot be active for more than 100% of the time). Hence, whenever N>(1+2a), we restrict the value to 1 only.