2008 Operation Research 2 Assignment 12 Due day: 2008/06/02 Problems: 1. (Hillier 7th edition, 17.6-36) Consider a single-server queueing system. It has been observed that (1) this server seems to speed up as the number of customers in the system increases and (2) the pattern of acceleration seem to fit the state-dependent model. Furthermore, it is estimated that the expected service time is 8 minutes when there is only 1 customer in the system. Determine the pressure coefficient c for this model for the following cases: (a) The expected service time is estimated to be 4 minutes when there are 4 customers in the system. (b) The expected service time is estimated to be 5 minutes when there are 4 customers in the system. 2. (Hillier 7th edition, 17.6-32) At the Forrester Manufacturing Company, one repair technician has been assigned the responsibility of maintaining three machines. For each machine, the probability distribution of the running time before a breakdown is exponential, with a mean of 9 hours. The repair time also has an exponential distribution, with a mean of 2 hour. (a) Which queueing model fits this queueing system? (b) Use this queueing model to find the probability distribution of the number of machines not running, and the mean of this distribution. (c) Use this mean to calculate the expected time between a machine breakdown and the completion of the repair of that machine. (d) What is the expected fraction of time that the repair technician will be busy? (e) As a crude approximation, assume that the calling population is infinite and that machine breakdowns occur randomly at a mean rate of 3 every 9 hours. Compare the result from while using (i) the M/M/s model and (ii) the finite queue variation of the M/M/s/GD/c model with c=3 (f) Repeat part (b) when a second repair technician is made available to repair a second machine whenever more than one of these three machines require repair. 注意: 請用A4紙張作答，不用A4作答不予計分,並在作業的最上方標明「學號」及「姓名」。 --

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