Consider an ad hoc network in which communication (message or packet transfer) is to take place from node X to node Y. The route has already been established, and a data packet is to be transferred over n hops. To transfer the packet, the k th node uses the following medium-access protocol:

• It waits for time t(k) after which the channel becomes free. t(k) = kα time units.
• It transfers the data packet to the next hop. This takes α time units.
• It receives an acknowledgment. This takes another α/2 time units.

The time t(k) before the k th node actually transmits the data packet is given by t(k) = kα time units.
(a) Find an expression for time taken for the data to cover n hops (i.e., from node 1 to node n + 1).

(b) If the time taken to traverse n hops is T = 2n √nα, what is the value of n?