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Virginia's Ron McPherson Electronics Corporation retains a service crew to repair machine breakdowns that occur on an average of λ = 4 per 8-hour workday (approximately Poisson in nature). The crew can service an average of μ = 6 machines per workday, with a repair time distribution that resembles the negative exponential distribution. a) The utilization rate of this service system = 0.67 (round your response to two decimal places). b) The average downtime for a broken machine 0.50 days (round your response to two decimal places). c) The average number of machines waiting receive service t any given time 1.33 machines (round your response to three decimal places). d) The probability that there is more than one machine that is in the system = 0.444 (round your response to three decimal places). The probability that there are more than two machines that are in the system = 0.296 (round your response three decimal places). (round your response to three decimal places). The probability that there are more than three machines that are in the system =

Virginia's Ron McPherson Electronics Corporation retains a service crew to repair machine breakdowns that occur on an average of λ = 4 per 8-hour workday (approximately Poisson in nature). The crew can service an average of μ = 6 machines per workday, with a repair time distribution that resembles the negative exponential distribution. a) The utilization rate of this service system = 0.67 (round your response to two decimal places). b) The average downtime for a broken machine 0.50 days (round your response to two decimal places). c) The average number of machines waiting receive service t any given time 1.33 machines (round your response to three decimal places). d) The probability that there is more than one machine that is in the system = 0.444 (round your response to three decimal places). The probability that there are more than two machines that are in the system = 0.296 (round your response three decimal places). (round your response to three decimal places). The probability that there are more than three machines that are in the system =

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter12: Queueing Models
Section12.5: Analytic Steady-state Queueing Models
Problem 26P
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Virginia's Ron McPherson Electronics Corporation retains a service crew to repair machine breakdowns that occur on an average of λ = 4 per 8-hour workday (approximately Poisson in nature). The crew can service an average of µ = 6 machines per workday, with a repair time distribution that resembles the negative exponential distribution. a) The utilization rate of this service system = 0.67 (round your response to two decimal places). b) The average downtime for a broken machine = 0.50 days (round your response to two decimal places). c) The average number of machines waiting to receive service at any given time = 1.33 machines (round your response to three decimal places). d) The probability that there is more than one machine that is in the system = 0.444 (round your response to three decimal places). The probability that there are more than two machines that are in the system = 0.296 (round your response to three decimal places). The probability that there are more than three machines that are in the system = (round your response to three decimal places).
Transcribed Image Text:Virginia's Ron McPherson Electronics Corporation retains a service crew to repair machine breakdowns that occur on an average of λ = 4 per 8-hour workday (approximately Poisson in nature). The crew can service an average of µ = 6 machines per workday, with a repair time distribution that resembles the negative exponential distribution. a) The utilization rate of this service system = 0.67 (round your response to two decimal places). b) The average downtime for a broken machine = 0.50 days (round your response to two decimal places). c) The average number of machines waiting to receive service at any given time = 1.33 machines (round your response to three decimal places). d) The probability that there is more than one machine that is in the system = 0.444 (round your response to three decimal places). The probability that there are more than two machines that are in the system = 0.296 (round your response to three decimal places). The probability that there are more than three machines that are in the system = (round your response to three decimal places).
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