# Minimizing the In-Cloud Bandwidth for On-Demand Reactive and Proactive Streaming Applications
## 3 Optimizing Cloud-Based Streaming Internal Bandwidth: Case of an Unpopular Video  
For unpopular content streaming, in this section we present a new variant of the protocol Slotted Stream Tapping called SASST. We consider the on-demand scenario (not the live scenario) where video and/or audio files stored in the cloud storage nodes are requested.  
First, we describe the SASST principle. Then, we evaluate the performances of SASST in terms of the average consumed bandwidth for both cases of (1) a deterministic high load and (2) a Poisson load of SN request arrivals.  
\begin{table}
\begin{tabular}{l l l l} \hline \hline  & **Principle** & **Bandwidth** & **Implementation** \\ \hline _Reactive_ & & & \\ \hline \multirow{4}{*}{Unicast} & & \(B=\lambda D\) & \multirow{4}{*}{Easy.} \\  & & \(\lambda\) is the request & \\  & & for each client request. & rate, & \\  & & \(D\) is the video & & \\  & & duration. & \\ \hline \multirow{4}{*}{ST [15]} & & \(\begin{array}{c}\text{Makes clients sharing}\\ \text{one main stream (TS)}\\ \text{and provides the missed}\\ \text{part by an additional}\\ \text{unicast stream (FTS)}.\end{array}\) & \multirow{4}{*}{\(B=\sqrt{\lambda D+1}-1\)} & \multirow{4}{*}{Medium.} \\ \hline \multirow{4}{*}{SST [11, 23]} & \(\begin{array}{c}\text{In addition to what ST}\\ \text{does, SST groups}\\ \text{client request per slots}\\ \text{to be served through}\\ \text{the same streams}.\end{array}\) & & \\ \hline \multirow{4}{*}{Dyadic [8]} & \(\begin{array}{c}\text{Allows clients to share}\\ \text{all opened streams in a}\\ \text{pseudo-optimal way.}\\ \text{The arrival sequence}\\ \text{should be known in}\\ \text{advance to be optimal}.\end{array}\) & & \multirow{4}{*}{\(B=\sqrt{2D}-\frac{1}{2}\)} & \multirow{4}{*}{Medium.} \\ \hline \multirow{4}{*}{Dyadic [8]} & \(\begin{array}{c}\text{Allows clients to share}\\ \text{all opened streams in a}\\ \text{pseudo-optimal way.}\\ \text{The arrival sequence}\\ \text{should be known in}\\ \text{advance to be optimal}.\end{array}\) & & \multirow{4}{*}{\(\begin{array}{c}\text{No analytical}\\ \text{expression.}\\ \text{expression.}\\ \text{expression.}\\ \text{\end{array}}\)} & \multirow{4}{*}{Hard.} \\ \hline _Proactive_ & & & \\ \hline \multirow{4}{*}{SB [6, 18, 44, 45, 46]} & \(\begin{array}{c}\text{Divides the movie into }n\\ \text{equally-sized segment}\\ \text{and broadcasts each}\\ \text{segment repeatedly in}\\ \text{a channel.}\end{array}\) & & \multirow{4}{*}{\(B=n\)} & \multirow{4}{*}{Easy.} \\ \hline \multirow{4}{*}{Pyramid} & \(\begin{array}{c}\text{Divides the movie into}\\ \text{$n$ segments with size}\\ \text{growing geometrically.}\\ \text{Each segment is}\\ \text{broadcast repeatedly}\\ \text{in a channel.}\end{array}\) & & \multirow{4}{*}{\(B=n\)} & \multirow{4}{*}{\(\begin{array}{c}\text{Easy.}\\ \text{$n$ segments with size}\\ \text{$D$ is the video}\\ \text{duration,}\\ \text{$w$ is the client}\\ \text{waiting time.}\end{array}\)} \\ \hline \multirow{4}{*}{Harmonic [21, 51]} & \(\begin{array}{c}\text{Divides the movie into }n\\ \text{equally-sized segment}\\ \text{$S_{1}$, $S_{2}$, $\dots$ }S_{n}\text{and broadcast}\\ \text{them such as $S_{1}$ is}\\ \text{broadcast in channel 1}\\ \text{with rate $b$, $S_{2}$ in channel 2}\\ \text{with rate $\frac{b}{2}$, $\dots$ }S_{n}\text{in}\\ \text{channel $n$ with rate $\frac{b}{n}$.}\end{array}\) & & \multirow{4}{*}{\(B=n(\sqrt{\frac{\frac{\overline{D}}{\overline{w}}}}-1)\)} & \multirow{4}{*}{\(\begin{array}{c}\text{Hard.}\\ \text{$\text{It is rather used}$}\\ \text{$\text{as lower bound}$}\\ \text{benchmark.}\end{array}\)} \\ \hline \hline \end{tabular}
\end{table}
Table 1: Summary of representative works, their principles and performances.