# Padhye et. al. Equation and TCP performance

## September 3, 2011

If you are not familiar with the **Mathis Equation**, I **recommend** you quickly go over my post article Mathis Equation and TCP Performance. This is necessary since the Padhye et. al. Equation is an extension to the Mathis Equation for accuracy of TCP throughput calculation over multiple scenario of packet loss.

As simply put, the Padhye et. al. Equation Equation is exactly the same concept as the Mathis Equation but taking in consideration the Maximum TCP Window size affected by received/lost/duplicate ACK, the initial retransmit timer and the effect of the TCP timeout mechanism on the total throughput.

The approximative equation model deferred by a 2 conditional throughput equation as to whether $$W\left (p \right ) < Wmax$$ or not is

$$B(p) \approx \left ( \frac{Wmax}{RTT}, \frac{1}{RTT\sqrt{\frac{2bp}{3}}+Tomin\left ( 1,3\sqrt{\frac{3bp}{8}} \right )p\left ( 1+32p^{2} \right )} \right )$$

First of all, it is important to keep in mind that Padhye et. al.’s formula relays on the concept that the Windows size ($$W$$) increases per $$W+ 1/b$$ “(b) being the number of packets acknowledge per each received ACK”.

(b) Some hosts send an ack for each X amount of packet received depending on the ACK delay value. For most configuration, an ACK is sent for each 2 packets received.

“Padhye” study centers around different models and scenarios, for instance, packet lost is accounted when triple ack are received and the Window Size of the sender remains un-influenced by the window scaling etc.

Keep in mind that these scenarios do not take for most part some of the TCP model features such as Fast Recovery or the Sender window adjustment by the receiver’s advertised window size. The Padhye equation is one of many models used these days to calculate the TCP throughput.

For more information, refer to the whitepaper @ http://www.sigcomm.org/sigcomm98/tp/paper25.pdf