Question: 1. Computer programs are submitted for execution according to a Poisson distribution with mean arrival rate of 90 per hour. Execution times are exponentially distributed,

1. Computer programs are submitted for execution according to a Poisson

1. Computer programs are submitted for execution according to a Poisson distribution with mean arrival rate of 90 per hour. Execution times are exponentially distributed, with jobs requiring an average of 38 seconds. Users complain of long waiting times. Management is considering the purchase of a faster CPU that would decrease the average execution time to 30 seconds per job. This expense can be justified only if, under the current system, the average number of jobs waiting exceeds 5. Also, if a new CPU is to be purchased, its percentage of idle time should not exceed 30%. Can the new CPU be justified? Explain all considerations fully. Make the necessary calculations, and then make an appropriate recommendation to management. 1. Computer programs are submitted for execution according to a Poisson distribution with mean arrival rate of 90 per hour. Execution times are exponentially distributed, with jobs requiring an average of 38 seconds. Users complain of long waiting times. Management is considering the purchase of a faster CPU that would decrease the average execution time to 30 seconds per job. This expense can be justified only if, under the current system, the average number of jobs waiting exceeds 5. Also, if a new CPU is to be purchased, its percentage of idle time should not exceed 30%. Can the new CPU be justified? Explain all considerations fully. Make the necessary calculations, and then make an appropriate recommendation to management

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