Assignment:
Consider a wireless system where a random number of mobile users share a common transmission channel with capacity of C = 1 Mbit/s. We assume that the new requests for data transmission generated over the time by the mobile users form a Poisson process with parameter λ [request/s]. Each request consists of the transmission of a random number of data bits, with distribution approximately exponential and mean value L bits. (For simplicity, assume that system can transmit even fractions of bit.) The channel allocation is operated by a central controller, named base station (BS) on a periodic base, with period T = 10 ms. At the beginning of each period, the BS divides the channel capacity equally among all the active users, that is to say, users that have data to transmit. Therefore, denoting by Xn the number of active users at the beginning of the nth allocation period, each user is given a budget of C/Xn bits untill the following allocation period.
a) Prove that Xn is a MC.
b) Determine the transition matrix P.