# Round-trip delay time

In telecommunications, the round-trip delay time (RTD) or round-trip time (RTT) is the length of time it takes for a signal to be sent plus the length of time it takes for an acknowledgement of that signal to be received. This time delay includes the propagation times for the paths between the two communication endpoints.

In the context of computer networks, the signal is generally a data packet, and the RTT is also known as the ping time. An internet user can determine the RTT by using the ping command.

End-to-end delay is the length of time it takes for a signal to travel in one direction and is often approximated by half the RTT.

## Protocol design

Network links with both a high bandwidth and a high RTT (and thus high bandwidth-delay product) can have a very large amount of data "in flight" at any given time. Such "long fat pipes" require a special protocol design.[1] One example is the TCP window scale option.

The RTT was originally estimated in TCP by:

${\displaystyle \mathrm {RTT} =\alpha \cdot \mathrm {old\_RTT} +(1-\alpha )\cdot \mathrm {new\_round\_trip\_sample} }$

where α is constant weighting factor (${\displaystyle 0\leq \alpha <1}$).[2] Choosing a value for α close to 1 makes the weighted average immune to changes that last a short time (e.g., a single segment that encounters long delay). Choosing a value for α close to 0 makes the weighted average respond to changes in delay very quickly. This was improved by the Jacobson/Karels algorithm, which takes standard deviation into account as well. Once a new RTT is calculated, it is entered into the equation above to obtain an average RTT for that connection, and the procedure continues for every new calculation.

## End-to-end delay 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:[3]

${\displaystyle \Pr(E=x)={\begin{cases}\displaystyle \sum _{i=0}^{\infty }f_{i}(a).f_{i}(b),&x=0,\\\displaystyle \sum _{i=0}^{\infty }f_{i}(a).f_{2x+i}(b)+\sum _{i=0}^{\infty }f_{i}(b).f_{2x+i}(a),&x>0.\end{cases}}}$

where a and b are the forward and reverse edges, and fy(z) is the PMF of delay of edge z (that is, fy(z) = Pr{delay on edge z = y}).

## Wi-Fi

In IEEE 802.11mc, round-trip time over Wi-Fi provides a method for precise indoor positioning.