IEOR 4404 Assignment #7 Simulation October 19, 2006 Prof. Mariana Olvera-Cravioto Page 1 of 1 Assignment #7 – due October 27th, 2006 1. (From Ross) Suppose that jobs arrive at a single server queueing system according to a nonhomogeneous Poisson process, whose rate is initially 4 per hour, increases steadily until it hits 19 per hour after 5 hours, and then decreases steadily until it hits 4 per hour after an additional 5 hours. The rate then repeats indeﬁnitely in this fashion — that is, λ ( t + 10) = λ ( t ). Suppose that the service distribution is exponential with rate 25 per hour. Suppose also that whenever the server completes a service and ﬁnds no jobs waiting he goes on break for a time that is uniformly distributed on (0, 0.3). If upon returning from his break there are no jobs waiting, then he goes on another break. Use simulation to estimate the expected amount of time that the server is on break in the ﬁrst 100 hours of operation. Do 500 simulation runs. 2. (From Ross) Consider a single-server queueing model in which customers arrive according to
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Probability theory, Exponential distribution, Poisson process, 5 hours, 100 hours, Prof. Mariana Olvera-Cravioto