4. P4.4 Consider the Markov chain model due to G. Bianchi [G. Bianchi, Performance analysis of the IEEE 802.11 distributed coordination func- tion, IEEE Journal on Selected Areas in Communications, 18(3), March 2000. DOI: 10.1109/49.840210. 53, 54, 56, 57, 65] discussed in the chapter for the scenario where only the Access Point and a single WiFi device have unlimited data to send to each other. Assume that C Wmin D C Wmax D 1 and Slot Time D 20s.

a) Draw the transition probability diagram for the Markov chain.

(b) Derive the invariant distribution for the Markov chain.

(c) Calculate the probability that a duration between two consecutive epochs of the Markov chain would have a successful transmission.

(d) Assume that each WiFi data frame transports 1,000 bytes of payload. Furthermore, assume that a duration between two consecutive Markov chain epochs with a suc- cessful transmission is 60 Slot Time long, while that with a collision is 50 Slot Time long. Calculate the network throughput in Mbps as seen by the upper layers.