Consider one communication link from node A to node B. Each data packet over this link needs one timeslots to be transmitted. Let An be the number of packets that arrive at node A during timeslot n. Assume that {An: n = 0,1,2,...,} is an iid sequence with distribution P{Aj = 0} = 3/5, P{Aj = 1} = 1/5, P{A1 = 2} = 1/5. (1) To make the counting of packets easier, assume the following sequence of events in each timeslot: packets arrive during the timeslot (waiting in a common buffer of infinite size if necessary), packets in transmission leave the system at the end of this timeslot if they reach the destination, a new packet starts transmission over a link at the beginning of next timeslot (equal to the end of current timeslot) if the link is free and there is a packet in the buffer to transmit. Let Xn be the number of packets in system at the beginning of time slot n before any packets are transmitted. (a) Prove that X = {Xnin = 0,1, ...} is a DTMC. (b) Specify the state space and the transition matrix Consider one communication link from node A to node B. Each data packet over this link needs one timeslots to be transmitted. Let An be the number of packets that arrive at node A during timeslot n. Assume that {An: n = 0,1,2,...,} is an iid sequence with distribution P{Aj = 0} = 3/5, P{Aj = 1} = 1/5, P{A1 = 2} = 1/5. (1) To make the counting of packets easier, assume the following sequence of events in each timeslot: packets arrive during the timeslot (waiting in a common buffer of infinite size if necessary), packets in transmission leave the system at the end of this timeslot if they reach the destination, a new packet starts transmission over a link at the beginning of next timeslot (equal to the end of current timeslot) if the link is free and there is a packet in the buffer to transmit. Let Xn be the number of packets in system at the beginning of time slot n before any packets are transmitted. (a) Prove that X = {Xnin = 0,1, ...} is a DTMC. (b) Specify the state space and the transition matrix