Suppose one bit stream arrives at a buffer. The rate of the bit stream is a periodic function of time with period T = 1 second. During [0, T/4], the rate is equal to 10 Mbps and during (T/4,T), it is equal to zero. A transmitter with rate R bps serves the buffer by sending the bits whenever available.
(a) Draw a diagram that shows the occupancy of the buffer as a function of time, for different ranges of values for R.
(b) What is the minimum value R0 of R so that this occupancy does not keep growing?
(c) For 10 ³ R ³ R0, express the average delay D(R) per bit as a function of R.
(d) For 10 ³ R ³ R0, express the average buffer occupancy (over time) L(R) as a function of R.
(e) Show that L(R) = l D(R), where l = 2.5 Mbps is the average arrival rate of the bits. This is an example of the Little's Formula.