A crew of mechanics at the Department of Transportation garage make minor repairs to snowplows during the winter. The snowplows break down at an average rate of 5 vehicles per day and breakdowns are distributed according to the Poisson distribution. The mechanic can service an average of 8 vehicles per day with a repair time distribution that approximates a negative exponential distribution. Assume an 8 hour day. What are the chances that 3 vehicles are in the service system? Group of answer choices 9% 38% 63% 19%

A crew of mechanics at the Department of Transportation garage make minor repairs to snowplows during the winter. The snowplows break down at an average rate of 5 vehicles per day and breakdowns are distributed according to the Poisson distribution. The mechanic can service an average of 8 vehicles per day with a repair time distribution that approximates a negative exponential distribution. Assume an 8 hour day. What are the chances that 3 vehicles are in the service system? Group of answer choices 9% 38% 63% 19%

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 30P

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A system operational history provides the following data: Service Time = 780 hrs Available time = 8000 hrs %3D # of starts = 52 # of outages = 5 Forced Outage Time = 150 hrs Probability of system failure at start is zero. Find: a. Average service time b. Average available time c. Mean Time To Repair d. Mean Time To Failure e. Forced outage rate
Martin Weir is studying a waiting line for a 9 server system at Market Fresh Foods. The company wants to be sure that its customers enjoy a quality service experience. Martin has studied operations for the past 2 weeks and has determined that on average, a customer arrives every 0.0061 Minute(s) and the average service is completed in 0.0282 Minute(s). Answer the following:. Offered workload rate =
A crew of mechanics at the Department of Transportation garage make minor repairs to snowplows during the winter. The snowplows break down at an average rate of 4 vehicles per day and breakdowns are distributed according to the Poisson distribution. The mechanic can service an average of 10 vehicles per day with a repair time distribution that approximates a negative exponential distribution. Assume an 8 hour day. What is the system utilization? Group of answer choices 0.60 0.17 0.40 0.67
Q2. Customers visit an astrologer at a rate of 4/hour (Poisson) and take and average of 12 minutes (Exponential). Compute the probability that: a) There are three or less people in the system b) There are 5 or more people in the system c) The astrologer is free
Eastern Motors Auto Dealership wanted to estimate the average CLV over a 5 year time horizon of a customer who purchases a new vehicle. The average vehicle sells for $28,939 and has a margin of 6%. Based on historical averages, 83 of people buying a new vehicle at Eastern will return for service 9 times over the next 5 years. Though it varies considerably, Eastern generates approximately $92 in margin on each service visit after accounting for parts and direct labor costs. What is the estimated 5 year value of the service component (only) of a customer who purchases a new vehicle at Eastern Motors?
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The average response time for http requests at a web server is 2.5 seconds. The system idle time was measured to be 12 seconds during a one minute observation interval. Use an M/M/1 model for the system to determine the following (a) system utilization (b) average service time per transaction (c) probability that the number of jobs in the system exceeds 10
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…
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Consider the order delivery system of Heartha Hardware and Construction Supplies:- Customers (whether by bulk or retail) would line up in a counter where sales representatives will entertain them. It would take about 15 minutes before a customer will be entertained due to the number of customers being served by the sales representative and only about 4 sales representatives are on duty every day.- The sales representative will take down the customer’s order in the order slip with corresponding prices. On some cases, she will ask the person in-charge in the warehouse if the items are available. She then forwards the order slip to the cashier.- The cashier would sum-up again manually the order slip from the sales representative to check the accuracy of the footing of the totals as well as the prices indicated. This would take about 10 minutes, depending on the bulk of the order being placed.- The official receipt will be printed and will be given to the…