final_2000

# final_2000 - EES&OR 222 Introduction to Stochastic...

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EES&OR 222 Page 1 of 2 Introduction to Stochastic Processes & Models March 13, 2000 Instructor: Sandeep Juneja Winter Quarter 1999-2000 1 FINAL EXAM 1. Consider a single server queue with no waiting room. Two independent Poisson arrival streams visit this queue. The first stream customers arrive at a rate of 1/hour and require exponentially distributed service with mean time equaling 30 minutes. The second stream customers arrive at a rate of 2 per hour and they require exponential amount of service with rate 1/3 per hour. No waiting is allowed in this system so the customer forced to wait leaves the system. The first stream customers have pre-emptive priority over second stream customers, i.e., if an arriving first stream customer sees the second stream customer at service it immediately displaces it and starts service while the displaced customer leaves the system. a) What are the states for this CTMC? (2 points) b) Draw the rate diagram for this CTMC (3 points) c) Find the steady state probabilities for this CTMC (3 points) d) What is the rate at which customers of stream 2 complete service (i.e., on average how

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final_2000 - EES&OR 222 Introduction to Stochastic...

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