Consider one communication link from node A to node B. Each data packet over this link...

 

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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{A = 0} = 3/5, P{A = 1} = 1/5, P{A = 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 {Xn: n = 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{A = 0} = 3/5, P{A = 1} = 1/5, P{A = 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 {Xn: n = 0, 1,...} is a DTMC. (b) Specify the state space and the transition matrix. =

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To prove that X show two properties 0 1 2 is a DiscreteTime Markov Chain DTMC we need to 1 Markov Pr... View the full answer