Determine a variation of the smux device of problem


Assignment:

Consider a variation of the SMUX device of Problem 7.20 in which packets are generaed and get served in pairs, so that the process Ym that counts the number of packet in the buffer at the beginning of each slot evolves according to the following equation

Ym+1 = Ym +2vm - 2X{Ym > 0)

where vm is statistically independent of Ym. Suppose that the initial state of the process can either be Y0 = 0 or Y0 = 1, with equal probability. Determine whether Ym is a MC and, in this case, classify it and write its transition matrix.

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