# queue - Queueing Theory(Fall 2010 Final Homework(Due Day 1...

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Queueing Theory (Fall 2010) Final Homework (Due Day: 2011/1/17) 1. Consider the following closed queueing network (Figure 1) with only two customers; find P(k 1 ,k 2 ,k 3 ) explicitly in terms of μ . Figure 1 2. Persons arrive at a Xerox machine according to a Poisson process with rate one per minute. The number of copies to be made by each person is uniformly distributed between 1 and 10. Each copy requires 3 sec. Persons with no more than 3 copies to make are given preemptive priority over other persons. Find the average waiting time in queue for two-priorities persons (denoted by W 1 and W 2 ). 3. Consider an open queueing network of three queues, as shown in Figure 2. The output of Queue 1 is split by a probability p into two streams; one goes into Queue 2 and the other goes into Queue 3 together with the output of Queue 2. If the arrival to Queue 1 is a Poisson process with rate l and the service times at all queues are exponentially distributed with the rates shown in the diagram, find the mass function of the state probability for the whole network.

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