Suppose that Bob sends 𝑁 back-to-back packets to Alice over two links (shown below), with the transmission rate of the link between Bob and the router being 𝑅 bits/sec (bps) and the transmission rate of the link between the router and Alice being 2𝑅 bps. Suppose that the 𝑁 packets sent by Bob are numbered 1 to 𝑁. Suppose that every odd-numbered packet (i.e., packet 1, packet 3, packet 5, and so on) is composed of 𝐿 bits and that every even-numbered packet (i.e., packet 2, packet 4, packet 6, and so on) is composed of 2𝐿 bits. Considering only the transmission delay that occurs in sending packets, answer the following:
a) Find a formula, in terms of 𝑁, 𝐿, and 𝑅, that characterizes the end-to-end delay of sending the 𝑁 packets to Alice (i.e., the time needed for the last bit of the 𝑁th packet to arrive at Alice since Bob starts transmitting the first bit of the first packet). Also, using your formula, find the end-to-end delay of sending 𝑁 = 95 packets considering 𝐿 = 2000 bits and 𝑅 = 10,000 bps. Show your work in detail.
b) For 𝑛 ∈ {1, ⋯ , 𝑁}, find a formula, in terms of 𝑛, 𝐿, and 𝑅, that characterizes the end-to-end delay experienced by the 𝑛th packet (i.e., the time needed for the last bit of the 𝑛th packet to arrive at Alice since Bob starts transmitting the first bit of the 𝑛th packet). Also, using your formula, find the end-to-end delay experienced by the 95th packet considering 𝐿 = 2000 bits and 𝑅 = 10,000 bps. Show work in detail.