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20092ee132B_1_hw8 - UCLA Electrical Engineering Department...

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UCLA Electrical Engineering Department EE132B HW Set #8 Professor Izhak Rubin Problem 1 Consider a communication system which queues arriving messages and then transmits them on a first-come first- served (FCFS) basis across a single outgoing link. Messages arrive in accordance with a geometric point process, and the number of packets in each message is geometrically distributed. The transmission time of one packet is equal to the slot length. a. Let the service rate be equal to 0.85 messages / slot. Calculate the mean queue size and the mean message waiting time for three cases: i. Message arrival rate = 0.4 messages / slot. ii. Message arrival rate = 0.8 messages / slot. iii. Message arrival rate = 10.0 messages / slot. b. For each of the three arrival rate cases considered in part a. above, compute the probability that a message will have to wait for the start of its transmission for longer than 5 slots. Problem 2 Consider the following communications system. Messages arrive in accordance with a geometric point process at a transmission node that is served by a single transmission channel. Messages are queued in the nodal buffer until they
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