P$23.$ Consider distributing a file of FFF bits to NNN peers using a client$-$server architecture. Assume a fluid model where the server can simultaneously transmit to multiple peers, transmitting to each peer at different rates, as long as the combined rate does not exceed usu$\_$sus$.$

a$.$ Suppose that us$/$N$$dminu$\_$s$/$N $\backslash$leq d$\_\{\backslash$text$\{$min$\}\}$us$/$N$$dmin$.$ Specify a distribution scheme that has a distribution time of NF$/$usNF$/$u$\_$sNF$/$us$.$

b$.$ Suppose that us$/$N$$dminu$\_$s$/$N $\backslash$geq d$\_\{\backslash$text$\{$min$\}\}$us$/$N$$dmin$.$ Specify a distribution scheme that has a distribution time of F$/$dminF$/$d$\_\{\backslash$text$\{$min$\}\}$F$/$dmin$.$

c$.$ Conclude that the minimum distribution time is in general given by max$\{$NF$/$us$,$F$/$dmin$\}\backslash$max $\backslash \{$ NF$/$u$\_$s$,$ F$/$d$\_\{\backslash$text$\{$min$\}\}\backslash \}$max$\{$NF$/$us$,$F$/$dmin$\}.$