Editing End-to-end delay (section)

===Estimate===
Transmission between two network nodes may be asymmetric, and the forward and reverse delays are not equal. Half the RTT value is the average of the forward and reverse delays and so may be sometimes used as an approximation to the end-to-end delay. The accuracy of such an estimate depends on the nature of delay distribution in both directions. As delays in both directions become more symmetric, the accuracy increases.

The [[probability mass function]] (PMF) of absolute error, ''E'', between the smaller of the forward and reverse OWDs and their average (i.e., RTT/2) can be expressed as a function of the network delay distribution as follows:<ref name="Abdou"/>

<math display=block>\Pr(E = x) = \begin{cases}\displaystyle\sum_{i=0}^\infty f_i(a).f_i(b), &x=0,\\\displaystyle\sum_{i=0}^\infty f_i(a).f_{2x+i}(b) + \sum_{i=0}^\infty f_i(b).f_{2x+i}(a), &x>0,\end{cases}</math>

where ''a'' and ''b'' are the forward and reverse edges, and ''f<sub>y</sub>''(''z'') is the PMF of delay of edge ''z'' (that is, {{nowrap|1=''f<sub>y</sub>''(''z'') = Pr{delay on edge ''z'' = ''y''}).}}