Q15 - (10 pts) In a manufacturing system, we have 3 parallel machines as presented below where a part can randomly choose one of the machines to be processed regardless of their status of being idle, working or under repair. The machines have their own queues in front of them. The inter-arrival times of the parts are distributed with exponential distribution with a mean of 10 minutes whereas the processing times of the parts are exponentially distributed with a mean of 20 minutes. Machines, independent of each other, fail according to an exponential distribution with a mean of 30 minutes. When they fail, they are repaired by a single repairman whose repair time is exponentially distributed with a mean of 50 minutes. If there is a part at the machine when it fails, for simplicity, you can assume that the processing of the part has finished. For simplicity, you can assume that, when a machine fails, all parts waiting in the queue of that failed machine stay in that queue until repair. As the decision maker of this simple system, you are trying to analyze whether the current queuing disciplines, the current number of machines and the current number of repairman are enough for reasonable waiting time, moderate utilization and etc. and you want to simulate the operation of this system. M1 M2 M3 Simulate the operation of the system starting with an empty system until at least 2 parts leave the system. Using simulation, estimate the utilization of M2; the utilization of the repairman and estimate the average number of parts that are waiting in the queue of M2. Use the following sequence of random variates (for simplicity, I dropped the decimal points for the exponential random variates): Exponential(10): 28 10 2 46 20 16 41 3 8 8 9 12 7 16 4 18 9 10 11 9 1 Exponential(20): 4 27 8 20 4 14 7 17 24 33 33 8 24 12 7 20 3 11 15 3 Exponential(30) (for M1): 21 42 32 35 30 11 Exponential(30) (for M2): 3 32 19 5 11 11 Exponential(30) (for M3): 6 37 10 17 18 14 Exponential(50): 11 3 32 788 1 65 69 7 15 100 222 6 81 60 21 63 38 137 1 Uniform(0,1); 0.52 0.34 0.43 0.23 0.58 0.76 0.53 0.64 0.21 0.38 0.78 0.68 Q15 - (10 pts) In a manufacturing system, we have 3 parallel machines as presented below where a part can randomly choose one of the machines to be processed regardless of their status of being idle, working or under repair. The machines have their own queues in front of them. The inter-arrival times of the parts are distributed with exponential distribution with a mean of 10 minutes whereas the processing times of the parts are exponentially distributed with a mean of 20 minutes. Machines, independent of each other, fail according to an exponential distribution with a mean of 30 minutes. When they fail, they are repaired by a single repairman whose repair time is exponentially distributed with a mean of 50 minutes. If there is a part at the machine when it fails, for simplicity, you can assume that the processing of the part has finished. For simplicity, you can assume that, when a machine fails, all parts waiting in the queue of that failed machine stay in that queue until repair. As the decision maker of this simple system, you are trying to analyze whether the current queuing disciplines, the current number of machines and the current number of repairman are enough for reasonable waiting time, moderate utilization and etc. and you want to simulate the operation of this system. M1 M2 M3 Simulate the operation of the system starting with an empty system until at least 2 parts leave the system. Using simulation, estimate the utilization of M2; the utilization of the repairman and estimate the average number of parts that are waiting in the queue of M2. Use the following sequence of random variates (for simplicity, I dropped the decimal points for the exponential random variates): Exponential(10): 28 10 2 46 20 16 41 3 8 8 9 12 7 16 4 18 9 10 11 9 1 Exponential(20): 4 27 8 20 4 14 7 17 24 33 33 8 24 12 7 20 3 11 15 3 Exponential(30) (for M1): 21 42 32 35 30 11 Exponential(30) (for M2): 3 32 19 5 11 11 Exponential(30) (for M3): 6 37 10 17 18 14 Exponential(50): 11 3 32 788 1 65 69 7 15 100 222 6 81 60 21 63 38 137 1 Uniform(0,1); 0.52 0.34 0.43 0.23 0.58 0.76 0.53 0.64 0.21 0.38 0.78 0.68
