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UNIVERSITY OF SOUTHERN CALIFORNIA, FALL 2008 1 EE 550: Problem Set # 5 Due: Wednesday Oct. 13, 2008 I. B OOK P ROBLEM 3.14 II. J ACKSON N ETWORK Consider a simple Jackson network consisting of two queues in tandem. The input to the first queue is Poisson with rate λ , and departures from this queue enter the second queue. There are no other arrival processes. Service times in both queues are i.i.d. exponential with rate μ , where λ < μ . Recall that we use the Kleinrock independence approximation, so that service times of the same packet in the two queues are independent. Let ( N 1 , N 2 ) represent the state of the system (representing the number of packets currently in node 1 and 2 ). a) Suppose ( N 1 , N 2 ) = (1 , 1) , so that there is exactly one packet in each queue. The next transition corresponds to a “single event.” List the possible single events. b) Assuming the state in part (a), what is the expected time to the next transition? c) Is the process N 1 ( t ) , treated alone, reversible? Is N 2 ( t ) reversible? d) Show that the 2 -d process ( N 1 ( t ); N 2 ( t )) is not reversible, even though in steady state the current number of packets in node 1
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