# Round-trip delay time

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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 acknowledgment of that signal to be received. This time delay therefore consists of the propagation times between the two points of a signal.

## Computer networks

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.

## Space technology

In space technology, the round-trip delay time or round-trip light time is the time light (and hence any signal) takes to go to a space probe and return.

## Protocol design

Network links with both a high bandwidth and a high RTT can have a very large amount of data (the bandwidth-delay product) "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.

## Half the RTT as a OWD estimate

Delays between two network nodes are often asymmetric, i.e., the forward and reverse delays are not equal. Half the RTT value is the average of the forward and reverse delays, and may thus be sometimes used as an approximation to the one-way delay (OWD). 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}).

## References

1. ^ Brian Heder (May 6, 2014), "Are your pipes too big?", Network World, retrieved 2016-01-09
2. ^ Comer, Douglas. Internetworking with TCP/IP. Page 226. Upper Saddle River, N.J.: Prentice Hall, 2000. Print.
3. ^ Abdou, AbdelRahman; Matrawy, Ashraf; van Oorschot, Paul (May 2015). "Accurate One-Way Delay Estimation with Reduced Client-Trustworthiness". IEEE Communications Letters. doi:10.1109/LCOMM.2015.2411591.