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Unformatted text preview: Jacobs University Bremen School of Engineering and Science Peter Oswald Fall Term 2010 120201 ESM3A — Problem Set 11 Issued: 23.11.2010 Voluntary submission: Monday 6.12.2010 (in class) This homework deals with material on stochastic processes. Its submission is voluntary (submis sion is another chance to improve on your homework percentage). Doing it (and more problems from the literature) is however strongly recommended. Read carefully : If you submit, don’t submit solutions to more than 6 problems. To get full credit, you have to correctly solve at least 5 problems, among them at least two problems from problems 11.14, and at least two problems from 11.58. Problems on counting processes (Pois son, queuing systems, and alike) and Markov chains (random walk on graphs, ergodic theorem) will be on the final, solve more problems to practice! Calculations can be done by software, state what you have computed! 11.1. In a small IT company, there are three servers. They operate properly (independendently of each other, and independently of whether they have been previously repaired or not) for a exponentially distributed random time with parameter λ = 1. When a server fails, it is repaired, the maintenance time is uniformly distributed (independently of the server to be repaired) in a contractually agreed upon service time interval t min ≤ t ≤ t max . Denote....
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 Spring '11
 Prof. Dr. Peter Oswald
 Probability theory, Stochastic process, Poisson process, Markov chain, Random walk, Compound Poisson process

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