IE143-LQ4reviewprobs

# IE143-LQ4reviewprobs - University of the Philippines...

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University of the Philippines – Diliman Department of Industrial Engineering and Operations Research IE 143 Long Quiz 4 Long Quiz 4 Review Problems 1. Mom-and-Pop’s Grocery Store has a small adjacent parking lot with three parking spaces reserved for the store’s customers. During store hours, cars enter the lot and use one of the spaces at a mean rate of 2 per hour. For n = 0, 1, 2, 3, the probability P n that exactly n spaces currently are being used is P 0 = 0.2, P 1 = 0.3, P 2 = 0.3, P 3 = 0.2. a) Determine the basic measures of performance – L, L q , W, and W q – for this queuing system. (+) b) Determine the average length of time that a car remains in a parking space. (+) 2. You are given two queuing systems, Q 1 and Q 2 . The mean arrival rate, the mean service rate per busy server, and the steady-state expected number of customers for Q 2 are twice the corresponding values for Q 1 . Let W i = the steady-state expected waiting time in the system for Q i , for i = 1, 2. Determine W 2 /W 1 . (+) 3. Consider a self-service model in which the customer is also the server. Note that this corresponds to having an infinite number of servers available. Customers arrive according to a Poisson process with parameter λ, and service times have an exponential distribution with parameter μ. a) Find L q and W q . (+) b) Construct the rate diagram for this queuing system. (+) c) Use the balance equations to find the expression for P n in terms of P 0 . (++) d) Find P 0 . (++) {Use a familiar Taylor series expansion} e) Find L and W. (+++) 4. Suppose that a single-server queuing system fits all the assumptions of the birth-and-death process except that customers always arrive in pairs . The mean arrival rate is 2 pairs per hour (4 customers per hour) and

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## This note was uploaded on 05/19/2011 for the course IE 2 taught by Professor A during the Spring '11 term at University of the Philippines Diliman.

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IE143-LQ4reviewprobs - University of the Philippines...

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