Exam 13: Queuing Theory

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Which type of queuing system are you likely to encounter at an ATM?

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Which of the following is a reason to employ queuing theory?

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Exhibit 13. The following questions refer to the information and output below. A tax accountant has found that the time to serve a customer has a mean of 30 minutes or 0.5 hours)and a standard deviation of 6 minutes or 0.1 hours).Customer arrivals follow a Poisson distribution with an average of 60 minutes between arrivals.The following queuing analysis spreadsheet was developed from this information. Exhibit 13. The following questions refer to the information and output below. A tax accountant has found that the time to serve a customer has a mean of 30 minutes or 0.5 hours)and a standard deviation of 6 minutes or 0.1 hours).Customer arrivals follow a Poisson distribution with an average of 60 minutes between arrivals.The following queuing analysis spreadsheet was developed from this information.    -Refer to Exhibit 13.7.Based on this report what is the probability that a customer does not have to wait for assistance with his or her taxes? -Refer to Exhibit 13.7.Based on this report what is the probability that a customer does not have to wait for assistance with his or her taxes?

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Customers arrive at a store randomly,following a Poisson distribution at an average rate of 90 per hour.How many customers would you expect to arrive in a 20 minute period?

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The amount of time a customer spends with the server is referred to as

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Joe's Copy Center has 10 copiers.They break down at a rate of 0.02 copiers per hour and are sent to the service facility.What is the average arrival rate of broken copiers to the service facility?

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Exhibit 13. The following questions refer to the information and output below. A computer printer in a large administrative office has a printer buffer memory to store printing jobs)capacity of 3 jobs.If the buffer is full when a user wants to print a file the user is told that the job cannot be printed and to try again later.There are so many users in this office that we can assume that there is an infinite calling population.Jobs arrive at the printer at a Poisson rate of 55 jobs per hour and take an average of 1 minute to print.Printing times are exponentially distributed.The following queuing analysis spreadsheet was developed from this information. Exhibit 13. The following questions refer to the information and output below. A computer printer in a large administrative office has a printer buffer memory to store printing jobs)capacity of 3 jobs.If the buffer is full when a user wants to print a file the user is told that the job cannot be printed and to try again later.There are so many users in this office that we can assume that there is an infinite calling population.Jobs arrive at the printer at a Poisson rate of 55 jobs per hour and take an average of 1 minute to print.Printing times are exponentially distributed.The following queuing analysis spreadsheet was developed from this information.    -Refer to Exhibit 13.5.Based on this report what is the average number of jobs waiting to be printed? -Refer to Exhibit 13.5.Based on this report what is the average number of jobs waiting to be printed?

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Exhibit 13.3 The following questions refer to the information below. A company has recorded the following customer inter-arrival times and service times for 10 customers at one of its single teller service lines.Assume the data are exponentially distributed and the 10 data points represent a reasonable sample. All time in minutes Customer Inter-arrival Service 1 11.08 2.20 2 2.50 2.50 3 6.00 1.10 4 5.75 14.50 5 8.50 2.00 6 4.15 2.70 7 15.50 5.00 8 13.00 8.50 9 10.50 5.00 10 6.00 1.50 -Refer to Exhibit 13.3.What is the average time a customer spends in the service line?

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Exhibit 13. The following questions refer to the information and output below. A computer printer in a large administrative office has a printer buffer memory to store printing jobs)capacity of 3 jobs.If the buffer is full when a user wants to print a file the user is told that the job cannot be printed and to try again later.There are so many users in this office that we can assume that there is an infinite calling population.Jobs arrive at the printer at a Poisson rate of 55 jobs per hour and take an average of 1 minute to print.Printing times are exponentially distributed.The following queuing analysis spreadsheet was developed from this information. Exhibit 13. The following questions refer to the information and output below. A computer printer in a large administrative office has a printer buffer memory to store printing jobs)capacity of 3 jobs.If the buffer is full when a user wants to print a file the user is told that the job cannot be printed and to try again later.There are so many users in this office that we can assume that there is an infinite calling population.Jobs arrive at the printer at a Poisson rate of 55 jobs per hour and take an average of 1 minute to print.Printing times are exponentially distributed.The following queuing analysis spreadsheet was developed from this information.    -Refer to Exhibit 13.5.What is the Kendall notation for this system? -Refer to Exhibit 13.5.What is the Kendall notation for this system?

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Exhibit 13.2 The following questions refer to the information and output below. A barber shop has one barber who can give 12 haircuts per hour.Customers arrive at a rate of 8 customers per hour.Customer inter-arrival times and service times are exponentially distributed.The following queuing analysis spreadsheet was developed from this information. -Refer to Exhibit 13.2.Based on this report what percent of the time is the barber busy cutting hair?

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Which of the following is the typical operating characteristic for the probability an arriving unit has to wait for service?

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Exhibit 13.1 The following questions are based on the output below. A store currently operates its service system with 1 operator.Arrivals follow a Poisson distribution and service times are exponentially distributed.The following spreadsheet has been developed for the system. Exhibit 13.1 The following questions are based on the output below. A store currently operates its service system with 1 operator.Arrivals follow a Poisson distribution and service times are exponentially distributed.The following spreadsheet has been developed for the system.    -Refer to Exhibit 13.1.What is the probability that a customer must wait in queue before being served? -Refer to Exhibit 13.1.What is the probability that a customer must wait in queue before being served?

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A common queue discipline used in practice is

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Exhibit 13. The following questions refer to the information and output below. A tax accountant has found that the time to serve a customer has a mean of 30 minutes or 0.5 hours)and a standard deviation of 6 minutes or 0.1 hours).Customer arrivals follow a Poisson distribution with an average of 60 minutes between arrivals.The following queuing analysis spreadsheet was developed from this information. Exhibit 13. The following questions refer to the information and output below. A tax accountant has found that the time to serve a customer has a mean of 30 minutes or 0.5 hours)and a standard deviation of 6 minutes or 0.1 hours).Customer arrivals follow a Poisson distribution with an average of 60 minutes between arrivals.The following queuing analysis spreadsheet was developed from this information.    -Refer to Exhibit 13.7.Based on this report what is the average number of customers waiting to be helped? -Refer to Exhibit 13.7.Based on this report what is the average number of customers waiting to be helped?

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Customers arrive at a store randomly,following a Poisson distribution at an average rate of 90 per hour.How many customers arrive per minute,on average?

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Which of the following is the typical operating characteristic for average number of units in a queue?

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The standardized queuing system notation such as M/M/1 or M/G/2 is referred to as

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If the arrival process is modeled as a Poisson random variable with arrival rate λ,then the average time between arrivals is

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Exhibit 13. The following questions refer to the information and output below. A grocery store can serve an average of 360 customers per hour.The service times are exponentially distributed.The store has 4 checkout lines each of which serves 90 customers per hour.Customers arrive at the store at a Poisson rate of 240 customers per hour.The following queuing analysis spreadsheet was developed from this information. Exhibit 13. The following questions refer to the information and output below. A grocery store can serve an average of 360 customers per hour.The service times are exponentially distributed.The store has 4 checkout lines each of which serves 90 customers per hour.Customers arrive at the store at a Poisson rate of 240 customers per hour.The following queuing analysis spreadsheet was developed from this information.    -Refer to Exhibit 13.4.Based on this report what percent of the time is a grocery clerk busy serving a customer? -Refer to Exhibit 13.4.Based on this report what percent of the time is a grocery clerk busy serving a customer?

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For a Poisson random variable,λ represents the number of arrivals per time period

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