Chapter 1, Problem P6P

This elementary problem begins to explore propagation delay and transmission delay, two central concepts in data networking. Consider two hosts, A and B, connected by a single link of rate R bps. Suppose that the two hosts are separated by m meters, and suppose the propagation speed along the link is s meters/sec. Host A is to send a packet of size L bits to Host B.

1. a. Express the propagation delay, d_prop, in terms of m and s.
2. b. Determine the transmission time of the packet, d_trans, in terms of L and R.
3. c. Ignoring processing and queuing delays, obtain an expression for the end-to-end delay.
4. d. Suppose Host A begins to transmit the packet at time t = 0. At time t = d_trans, where is the last bit of the packet?
5. e. Suppose d_prop is greater than d_trans. At time t = d_trans, where is the first bit of the packet?
6. f. Suppose d_prop is less than d_trans. At time t = d_trans, where is the first bit of the packet?
7. g. Suppose s = 2.5 · 10⁸, L = 120 bits, and R = 56 kbps. Find the distance m so that d_prop equals d_trans.