# Mathis Equation and TCP performance

## September 16, 2009

As simple as possible laid off, the Mathis equation goes as follow

Rate <= (MSS/RTT)*(1 / p)

MSS

This is the Maximum Segment Size, which is the MTU excluding the TCP/IP headers.

MSS = MTU - TCP/IP headers - for example 1460 with an MTU of 1500 (20b IP and 20b TCP headers)

RTT

RTT is the Round Trip Time as measured by TCP. The round trip is the time it would take a packet to travel from endpoint A to B and from endpoint B to A.

On average, RTT = (Physical Distance * 20ms) / 1609 , that is to say, for each 1 609 km, you should expect an RTT of 20ms

_p _

p is the probability percentage of packet lost per physical segment. A fiber BER would typically be of 10⁻¹³%.

Before we go on, it is first important to understand how TCP evaluates packet loss. As simple as it can be, packet loss is simply based on late delivered ACKs. The more acknowledgment are being sent late, the more the % of packet lost increases.

Let’s get more serious

As explained earlier, the Mantis Equation allows to locate the rate or so to say throughout we can use based on the MSS, RTT and the probability % of packet loss on the link.

Imagine we have an E3 link. For those new to WAN technology, an E3 link uses an M3 signaling type as opposed to an E1 which uses a ZM signaling type. Getting back to the speed line, an E3 is the equivalent of  16*E1 ~= 34.064 Mbps (including management overhead)

1. Line is E3 with a bw of 34.064 Mbps
2. Our endpoint is roughly 3000 km from us
3. We are using a default MSS of 1460
4. An E3 would have a typical packet loss percentage of 10⁻³ = 0.001 (1 packet lost each 1000 packets)

Based on 3000 km, we could assume that the average RTT would be of 37.29 ms = 0.03729 s

Mantis Eq : (1460 / 0.03729) * (1/0.001) ~=  1.23 Mbps

Now if we had no packet loss, our throughout would have been

Throughput = TCPWindow / RTT

(65535 / 0.03729) * 8 ~= 14Mbits

An original bandwidth line of 14 Mbps and an actual throughput of 1.23Mbps over 3000km with a packet lost of one packet each 1000.

How to do you increase rate?

In a perfect world, you would of course need to reduce each value variable of the equation such as decreasing RTT, decreasing the loss probability and increase the MMS (which btw you cannot on the internet, as all routers are configured with a static MTU of 1500)

I hope that was informative on how packet loss can affect throughput.

Reference

The Macroscopic Behavior of the TCP Congestion Avoidance Algorithm (1997) http://citeseer.ist.psu.edu/old/mathis97macroscopic.html