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# hmwk11 - ISyE 3232 Stochastic Manufacturing and Service...

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ISyE 3232 Stochastic Manufacturing and Service Systems Spring 2011 Drs. Hayriye Ayhan and Jim Dai Homework 11 April 12, 2011 (Due on Tuesday, April 19) 1. Suppose customer arrive to a bank according to a Poisson process but the arrival rate fluctuates over time. From the opening time at 9 a.m. until 11, customers arrive at a rate of 10 customers per hour. From 11 to noon, the arrival rate increases linearly until it reaches 20 customers per hour. From noon to 1pm, it decreases linearly to 15 customers per hour, and remains at 15 customers per hour until the bank closes at 5 p.m. For notation, let N ( t ) be the number of arrivals in the t hours since the bank opened and λ ( t ) the arrival rate at t hours after opening. (a) What is the arrival rate at 12:30pm? (b) What is the average number of customers per day? (c) What is the probability of k arrivals between 11:30 and 11:45? (d) What is the probability of k arrivals between 11:30 and 11:45 given that there were 7 arrivals between 11:00 and 11:30?

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• Spring '07
• Billings
• Probability theory, Markov chain, Continuous-time Markov process, arrival rate, Continuous Time Markov, time Markov chain

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