# Average transmission rate on IEEE 802.11 wireless network

So, here's the problem:

An access point is alternately sending L-sized packets to 2 stations, A and B.

The access point is transmitting to A at 10 MBits /s and to B at 2 MBit/s.

What's the average rate the access point is transmitting at?

The answer is not 10 + 2 / 2 = 6, but instead it's 3.33 Mbit/s.

How?

• Unfortunattely that will not be possible, since classes are over. Do you know any kind of webpages where I can read and try to figure out the question? Commented Jan 19, 2016 at 20:34
• Resource recommendations are off-topic. Commented Jan 19, 2016 at 20:41
• Ok then, so any clue on how to think or what to search? Commented Jan 19, 2016 at 20:45
• You'd have to ask whoever screwed up the math. If it sent 10Mb in the 1st second, and 2Mb in the 2nd second, then over 2sec the average rate is 6Mb. Commented Jan 19, 2016 at 21:44

First, an example:

Suppose the frames are 1500 bytes long, it is the same as 12000 bits.

The transmission of the frame to A at 10 Mb/s takes 1.2 milliseconds.

The transmission of the same size frame to B takes 6 milliseconds.

In total, to transmit 24000 bits took 7.2 milliseconds. It gives an speed of 3.33 Mb/s.

The result isn't the arithmetic mean, is the Harmonic Mean.

The harmonic mean can be expressed as the reciprocal of the arithmetic mean of the reciprocals.

For our case:

=1/(((1/10)+(1/2))/2) =1/((6/10)/2) = (2/1)/(6/10) = 20/6 = 3.33

In general, for two speeds s1 and s2 will be:

``````=(2*s1*s2)/(s1+s2)
``````

In this case `=(2*10*2)/(10+2) =(40/12) =3,33`