Virginia's Ron McPherson Electronics Corporation retains a service crew to repair machine breakdowns that occur on an average of λ = 3 per 8-hour workday (approximately Poisson in nature). The crew can service an average of μ = 10machines per workday, with a repair time distribution that resembles the negative exponential distribution. a) The utilization rate of this service system? b) The average downtime for a broken machine? c) Average number of machines waiting to be serviced at any given time? d) The probability that more than 1 machine is in the system? The probability that more than 2 machine is in the system? The probability that more than 3 machine is in the system? The probability that more than 4 machine is in the system?

Virginia's Ron McPherson Electronics Corporation retains a service crew to repair machine breakdowns that occur on an average of λ = 3 per 8-hour workday (approximately Poisson in nature). The crew can service an average of μ = 10machines per workday, with a repair time distribution that resembles the negative exponential distribution. a) The utilization rate of this service system? b) The average downtime for a broken machine? c) Average number of machines waiting to be serviced at any given time? d) The probability that more than 1 machine is in the system? The probability that more than 2 machine is in the system? The probability that more than 3 machine is in the system? The probability that more than 4 machine is in the system?

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 9P

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12-11 The Rockwell Electronics Corporation retains a service crew to repair machine breakdowns that occur on an average of λ=3 per day (approximately Poisson in nature). The crew can service an average of μ=8 machines per day, with a repair time distribution that resembles the exponential distribution. a. What is the utilization rate of this service system? b. What is the average downtime for a machine that is broken? c. How many machines are waiting to be serviced at any given time? d. What is the probability that more than one machine is in the system? Probability that more than two are broken and waiting to be repaired or being serviced? More than three? More than four?
Virginia's Ron McPherson Electronics Corporation retains a service crew to repair machine breakdowns that occur on an average of λ = 2 per 8-hour workday (approximately Poisson in nature). The crew can service an average of μ = 10 machines per workday, with a repair time distribution that resembles the negative exponential distribution. a) The utilization rate of this service system = 0.200.20 (round your response to two decimal places). b) The average downtime for a broken machine = 0.130.13 days (round your response to two decimal places). c) The average number of machines waiting to receive service at any given time = nothing machines (round your response to three decimal places).
Virginia's Ron McPherson Electronics Corporation retains a service crew to repair machine breakdowns that occur on an average of λ = 2 per 8-hour workday (approximately Poisson in nature). The crew can service an average of μ = 10 machines per workday, with a repair time distribution that resembles the negative exponential distribution. a) The utilization rate of this service system = 0.200.20 (round your response to two decimal places). b) The average downtime for a broken machine = . 40.40 days (round your response to two decimal places).
Benny’s Arcade has six video game machines. The average time between machine failures is 50 hours. Jimmy, the maintenance engineer, can repair a machine in 15 hours on average. The machines have an exponential failure distribution, and Jimmy has an exponential service-time distribution.a. What is Jimmy’s utilization?b. What is the average number of machines out of service, that is, waiting to be repaired or being repaired?c. What is the average time a machine is out of service?
4) Repair calls are handled by one repairman at a photocopy shop. Repair time, including travel time, is exponentially distributed, with a mean of two hours per call. Requests for copier repairs come in at a mean rate of three per eight- hour day (assume Poisson). Determine:1. The average number of customers awaiting repairs.2. System utilization.3. The amount of time during an eight-hour day that the repairman is not out on a call. 4. The probability of two or more customers in the system.
Benny's arcade has six video game machines. The average time between machine failures is 50 hours. Jimmy, the maintenance manager can repair a machine in 5 hours on average. The machines have an exponential failure distribution, and Jimmy has an exponential service-time distribution. a. Jimmy's utilization is? b. what is the average number of machines out of service, that is, waiting to be repaired or being repaired? c. what is the average time a machine is out of service?.