Exam 13: Queuing Theory

A barber shop has one barber, a Poisson arrival rate and exponentially distributed service times. 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 percent of the time is the barber busy cutting hair?

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 waiting time before the barber begins a customer's haircut?

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 is the average total time spent in line and being checked out?

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

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 time a customer spends in the customer service area if modeled as an M/M/1 queuing system?

If cell B2 contains the value for  and cell A5 contains the value for T, what formula should go in cell B5 to compute the P(Service time)  T for this exponential distribution?

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 service rate per hour?

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 average amount of time spent waiting in line?

What is the mean arrival rate based on the following 8 arrival rate observations? Number of arrivals per hour: 6, 5, 3, 4, 7, 6, 4, 5

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 number of customers in the service line?

Exhibit 13.6 The following questions refer to the information and output below. The university computer lab has 10 computers which are constantly being used by students. Users need help from the one lab assistant fairly often. Students ask for help at a Poisson rate of with an average of 4 requests per hour for any one computer. The assistant answers questions as quickly as possible and the service time follows an exponential distribution with mean of 1 minute per help session. The following queuing analysis spreadsheet was developed from this information. -Refer to Exhibit 13.6. What is the Kendall notation for this system?

What is the probability that it will take less than or equal to 0.25 hours to service any call based on the following exponential probability distribution with rate $\mu$ = 5? Average Service Rate \mu =5 per hour ( service time \leq) 0.00 0.00 0.05 0.22 0.10 0.39 0.15 0.53 0.20 0.63 0.25 0.71 0.30 0.78 0.35 0.83 0.40 0.86 0.45 0.89 0.50 0.92 0.55 0.94 0.60 0.95 0.65 0.96

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

If the service rate decreases as the arrival rate remains constant, then, in general

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. 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 average number of customers waiting to be helped?

Which of the following best describes queuing theory?

Exhibit 13.6 The following questions refer to the information and output below. The university computer lab has 10 computers which are constantly being used by students. Users need help from the one lab assistant fairly often. Students ask for help at a Poisson rate of with an average of 4 requests per hour for any one computer. The assistant answers questions as quickly as possible and the service time follows an exponential distribution with mean of 1 minute per help session. The following queuing analysis spreadsheet was developed from this information. -Refer to Exhibit 13.6. Based on this report how much time do students spend getting help before they can resume work on their computers?

An arrival process is memoryless if