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Exam 22: Waiting Lines

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Question 61

Multiple Choice

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Customers arrive at the one remaining full-service gas station in the country at the rate of 45 per minute and are served by the first available of three pump jockeys who can dole out gas and check oil at the rate of 20 customers per minute. Both service and interarrival times are governed by the exponential distribution. The probability that no pump jockey is busy is 0.0748. -Use the information in Scenario C.3.What is the probability that an arrival at the gas station must wait?

A) Less than or equal to 0.50
B) Greater than 0.50 but less than or equal to 0.60
C) Greater than 0.60 but less than or equal to 0.70
D) Greater than 0.70

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Question 62

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A trucking firm has five trucks that each requires service at an average rate of once every 50 hours, according to an exponential distribution. The firm has a mechanic who needs five hours to complete the average job with exponential service times. -Use the information in Scenario C.5.What is the probability that there will be no trucks in the system?

A) Less than or equal to 0.50
B) Greater than 0.50 but less than or equal to 0.60
C) Greater than 0.60 but less than or equal to 0.70
D) Greater than 0.70

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Question 63

Short Answer

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A(n)________ is one or more "customers" waiting for service.

With a single-server model,increasing the arrival rate by 10 percent and also increasing the service rate by 10 percent will result in

With a single-server model,increasing the service rate while holding all other factors constant will

Customers arrive according to a Poisson distribution.The average number of customer arrivals per hour is three.The probability that four customers will arrive in the next two hours is

Weary travelers arrive at Will Rogers International Airport, pick up their luggage, stumble to their cars, and proceed to the parking lot attendant to pay for their parking. Traveler interarrival times are exponentially distributed, as are the service times of the attendant. On average, travelers arrive every 25 seconds. The attendant can process three travelers per minute. -Use the information in Scenario C.2.What is the average number of customers in the system?

The Jackson Machine Company has four cutting tools that need to be refurbished after an average of 30 hours, according to an exponential distribution. The single machine that refurbishes the tools needs 15 hours for each tool on the average, with exponential service times. -Use the information in Scenario C.6.What is the average waiting time of tools in line?

Customers arrive at the local grocery store every 30 seconds on average.Thirty percent of these customers spend an average of 15 minutes shopping and purchase 10 items or less.These lucky customers go to the express line where they enjoy an average checkout time of 5 minutes.Customers that don't meet the express line criterion average 40 minutes in the store and go to checkout line #2 where they spend an average of 10 minutes checking out.How many people are shopping at any given time?