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# hwk2 - 1 CSE 422 Name Practice Problems Spring 2008 1(22...

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1 CSE 422 Practice Problems Spring 2008 Name: 1. (22 points total) Consider a checkout lane in the supermarket. Customer arrivals are Poisson with a mean arrival rate of one customer every four minutes. The service times are exponen- tially distributed about a mean of 225 seconds. (Recall that in an M/M/1 queue: N = ρ 1 - ρ . Also recall the formula for a Poisson process: P k ( t ) = e - ( λt ) ( λt ) k k ! .) (a) (2 points) What is the arrival rate, λ , in customers/minute? (b) (2 points) What is the service rate, μ , in customers/minute? (c) (4 points) What is the average number of customers in the system?

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Name: 2 (d) (4 points) What is the average length of time a customer spends in the system? (e) (6 points) Assume that a new customer has just joined the queue. What is the probability that no additional customers will join the queue in the next 6 minutes? (f) (4 points) On average, how many minutes per hour is the system empty?
Name: 3 2. (10 points total) Consider an infinite-population slotted ALOHA system in which each frame lasts for two slots. That is, transmission of each frame must begin on a slot boundary, but the duration of the frame is two slots. A few definitions:

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hwk2 - 1 CSE 422 Name Practice Problems Spring 2008 1(22...

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