Cumulative Acknowledgement (TCP)

network-protocols tcp

Definition

Cumulative Acknowledgement (TCP)

A TCP cumulative acknowledgement is the least byte index not yet received in order.

For received byte indices $R\subseteq \mathbb{N}$,

$$\mathrm{ACK}(R)=\min \{i\in \mathbb{N}\mid i\notin R\}.$$

Hence

$$\mathrm{ACK}(R)=k⟺\{0,\dots ,k-1\}\subseteq R\wedge k\notin R.$$

A segment $(q,L)$ contributes

$$[q,q+L)=\{q,q+1,\dots ,q+L-1\},R^{\prime }=R\cup [q,q+L).$$

For $k=\mathrm{ACK}(R)$,

$${\mathrm{ACK}}_{\text{new}}=\mathrm{ACK}(R^{\prime })=\{\begin{array}{ll}\ge k+L,& q=k,\\ k,& q>k.\end{array}$$

The case $q>k$ produces a duplicate ACK.