multipath transmission and svc

 The blog is a record of the paper[1].
 The paper models the multipath transmission as a non convex discrete optimization problem. The video streaming flows in internet can be classified into two categories:skip based and no skip based. The former is for real tine media, and chunks are not received by the their deadlines will be skipped. While for non-skipped streaming, if chunk cannot received by its deadline, a stall will occur until it is fully received.Both these situation deteriorates user experience.
 假设一段视频被分成了C个chunks。一个chunk的长度是L秒，基于svc编码，分成一个base layer和n个enhanced layer，base layer的速率为$r_0$，enhanced layer的速率分别为$r_1,...,r_n$。

符号	含义
i	chunk的序号
j	时间片序号
k	路径序号
n	视频layer的序号
$Y_n$	层n的大小
$z_n^{(k)}(i,j)$	段i的layer n使用时间片j在路径k上进行数据传输的大小
$s$	startup delay

 假设一个chunk中的一个layer为元数据，只能在一条链路上传输。在这里可以使用数学语言表示这个约束。$\left(\sum_{j=0}^{(i-1)L+s}z_n^{(1)}(i,j)\right)\left(\sum_{j=0}^{(i-1)L+s}z_n^{(2)}(i,j)\right)=0$
 优化目标：
$\max \sum\limits_{n=0}^{N}\gamma^n\sum\limits_{i=1}^{C}Z_{n,i}\tag{2}$
约束：
$\sum_{j=0}^{(i-1)L+s}z_n^{(1)}(i,j)+z_n^{(2)}(i,j)=Z_{n,i} \forall i,n\tag{3}$
$Z_{n,i}\leq\frac{Y_n}{Y_{n-1}}Z_{n-1,i}\tag{4}$
$\sum\limits_{n=0}^{N}\sum\limits_{i=1}^{C}z_n^{(k)}(i,j)\leq B^{k}(j)\tag{5}$
$\left(\sum_{j=0}^{(i-1)L+s}z_n^{(1)}(i,j)\right)\left(\sum_{j=0}^{(i-1)L+s}z_n^{(2)}(i,j)\right)=0\tag{6}$
$z_n^{(k)}(i,j)\ge0 \forall k\in\{1,2\}\tag{7}$
$z_n^{(k)}(i,j)=0 \forall \{i:(i-1)L+s>j\} \forall k\in\{1,2\}\tag{8}$
$Z_{n,i}\in \mathcal{Z}\triangleq\{0,Y_n\}\tag{9}$
 其中(4)保证高的layer不能在低的layer之前下载。(8)则是时间约束。
[1]Optimized Preference-Aware Multi-path Video Streaming with Scalable Video Coding