$4.$ Consider distributing a file held by a server to $15$ peers. The server can upload the file in $1$ unit of time, and each peer has sufficient download bandwidth to download the file in $1$ unit of time. Each peer takes $2$ units of time to upload the file. A peer must receive the entire file before it can start to send it to another peer. Each participant can send to or receive from only one other participant at a time.

$($a$)$ Using client$-$server distribution, how much time does it take for all $15$ peers to get the file?

Consider distributing a file held by a server to $15$ peers. The server can upload the file in $1$ unit of time, and each peer has sufficient download bandwidth to download the file in $1$ unit of time. Each peer takes $2$ units of time to upload the file. A peer must receive the entire file before it can start to send it to another peer. Each participant can send to or receive from only one other participant at a time.

$($a$)$ Using client$-$server distribution, how much time does it take for all $15$ peers to get the file?

$($b$)$ Describe a P$2$P distribution scheme to get the file to all peers faster than the client$/$server distribution in $($a$).$ How much time does it take for all $15$ peers to get the file? Show the details in a chart similar to that below in which the leftmost column identifies the server or peer sending the file and the entries in the other columns show which peer is receiving the file.

$\backslash$table$[[$sender$,t=1,t=2,t=3,t=4,t=5,$dots