3. Consider a repair shop where 3 repairmen work. The rate at which the jobs to...

 

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3. Consider a repair shop where 3 repairmen work. The rate at which the jobs to be repaired at the system depends on the number of jobs currently in the system. Jobs arrive at the shop, according to a Poisson process with a mean rate of 0.1*(5-k) jobs per minute when there are k jobs in the system (no job arrives when k > 4). The time to repair a job is exponentially distributed with a mean of 5 minutes. a. Model the repair shop as a queueing system by (i) providing an appropriate state description and 1 IE 361 Study Set 2 state space, (ii) specifying birth and death rates at each state and drawing the rate diagram. b. What is the average time spent by each job in the repair shop? c. What is the average time spent by each job while waiting in the queue? d. Let c be unit net profit per job. Express the long-run daily expected profit. Fall 2020 3. Consider a repair shop where 3 repairmen work. The rate at which the jobs to be repaired at the system depends on the number of jobs currently in the system. Jobs arrive at the shop, according to a Poisson process with a mean rate of 0.1*(5-k) jobs per minute when there are k jobs in the system (no job arrives when k > 4). The time to repair a job is exponentially distributed with a mean of 5 minutes. a. Model the repair shop as a queueing system by (i) providing an appropriate state description and 1 IE 361 Study Set 2 state space, (ii) specifying birth and death rates at each state and drawing the rate diagram. b. What is the average time spent by each job in the repair shop? c. What is the average time spent by each job while waiting in the queue? d. Let c be unit net profit per job. Express the long-run daily expected profit. Fall 2020 3. Consider a repair shop where 3 repairmen work. The rate at which the jobs to be repaired at the system depends on the number of jobs currently in the system. Jobs arrive at the shop, according to a Poisson process with a mean rate of 0.1*(5-k) jobs per minute when there are k jobs in the system (no job arrives when k > 4). The time to repair a job is exponentially distributed with a mean of 5 minutes. a. Model the repair shop as a queueing system by (i) providing an appropriate state description and 1 IE 361 Study Set 2 state space, (ii) specifying birth and death rates at each state and drawing the rate diagram. b. What is the average time spent by each job in the repair shop? c. What is the average time spent by each job while waiting in the queue? d. Let c be unit net profit per job. Express the long-run daily expected profit. Fall 2020