Exam 13: Queuing Theory

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

Exhibit 13.5 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?

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

A Poisson distribution shape can be described as

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. $\quad$$\quad$$\quad$$\quad$$\underline{\text { 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 10 600 150 -Refer to Exhibit 13.3. What is the mean arrival rate per hour?

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. $\quad$$\quad$$\quad$$\quad$$\underline{\text { 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 10 600 150 -Refer to Exhibit 13.3. What is the average time a customer spends in the service line?

Which type of queuing system are you likely to encounter at a Wendy's restaurant?

Exhibit 13.5 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?

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 is the average total time spent waiting for a haircut and getting a haircut?

A jockey refers to

A grocery clerk can serve 20 customers per hour on average and the service time follows an exponential distribution. What is the probability that a customer's service time is less than 2 minutes?

Customers arrive at a store randomly, following a Poisson distribution at an average rate of 20 per hour. What is the probability of exactly 0, 1 2, and 3 arrivals in a 15 minute period?

If a service system has a constant service time, Poisson arrival rates and 2 servers its Kendall notation is

What is the mean arrival rate based on the following 10 arrival rate observations? Number of arrivals per hour 16 15 14 15 17 16 14 15 13

The customer service desk at Joe's Discount Electronics store receives 5 customers per hour on average. On average, each customer requires 10 minutes for service. The customer service desk is staffed by a single person. What is the average number of customers in the customer service area, if modeled as an M/M/1 queuing system?

Exhibit 13.4 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?

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. What is the Kendall notation for this system?

Exhibit 13.7 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?

The service times for a grocery store with one checkout line have a mean of 3 minutes and a standard deviation of 20 seconds. Customer arrivals at the checkout stand follow a Poisson distribution. What type of system is it?

What is the service policy in the queuing systems presented in this chapter that is considered "fair" by the customers?