A Data Centre network using Ethernet switching and TPC$/$IP protocol is formed of $4$ racks each hosting $16$ servers. $($a$)$ Having a subscription ratio of $32$ downlinks to $20$ uplinks, each link connecting a different spine switch, $($i$)$ draw the topology and calculate the blocking probability under $60\%$ load. $($ii$)$ Measure the total number of crosspoints required for the whole network. $[3$ marks$][2$ marks$]($b$)$ Form a strictly non$-$blocking network and re$-$calculate the number of crosspoints, the subscription ratio and blocking probability under $90\%$ load. $[5$ marks$]($c$)$ Assume a time$-$division multiplexed circuit switched network with $200$ timeslots per link and a maximum of $8$ slots given to any connection. Calculate the number of leaf switches needed to design a strictly non$-$blocking network?