Exam 12: Waiting Lines and Queuing Theory Models

At a local fast food joint, cars arrive randomly at a rate of 12 every 30 minutes.The fast food joint takes exactly 2 minutes (this is constant).The average total time in the system is

Which of the following distributions is most often used to estimate service times?

What is the difference between a transient state and a steady state? How could you as a manager distinguish between the two?

There is a tutoring lab at a university that holds 20 students.Due to the popularity of the 3 tutors, the lab is always at capacity.Each student approaches a tutor an average of 2 times per hour, and a tutor spends on average 5 minutes per question from a student.The service time follows an exponential distribution. (a)What proportion of the time are the tutors busy? (b)What is the average waiting time for students in queue?

Which of the following distributions is most often used to estimate the arrival pattern?

Customers arrive at a bank at a rate of one every minute.The bank has 3 tellers and on average, it takes two minutes to service a customer. (a)What proportion of time are the tellers busy? (b)What is the average number of customers in the bank? (c)What is the average weight time?

A goal of many waiting line problems is to help a firm find the ideal level of services that minimize the cost of waiting and the cost of providing the service.

Table 12-2 -According to the information provided in Table 12-2, which presents a queuing problem solution, on average, how many units are in the line?

An automatic car wash is an example of a constant service time model.

At the start of football season, the ticket office gets busy the day before the first game.Customers arrive at the rate of four every ten minutes.A ticket seller can service a customer in four minutes.Traditionally, there are two ticket sellers working.The university is considering an automated ticket machine similar to the airlines' e-ticket system.The automated ticket machine can service a customer in 2 minutes. (a)What is the average length of the queue for the in-person model? (b)What is the average length of the queue for the automated system model? (c)What is the average time in the system for the in-person model? (d)What is the average time in the system for the automated system model? (e)Assume the ticket sellers earn $8 per hour and the machine costs $20 per hour (amortized over 5 years).The wait time is only $4 per hour because students are patient.What is the total cost of each model?

Table 12-6 Customers arrive at coffee shop at a rate of 40 per hour.There are 2 servers available and it takes an average of 1 minute to serve each customer. -Using Table 12-6, what is the average number of customers in the coffee shop?

Table 12-4 The sentient car wash in Luther knows she is in for a busy day when dawn breaks on a gorgeous spring morning.She is capable of washing a car every four minutes, and by the looks of things, it is reasonable to expect a steady stream of twelve cars per hour arriving.Because she is fully automatic, she knows that the four-minute estimate is accurate and invariant.She values her time at $10 per hour.Yes, it seems low, but as a single bay car wash, there are few other jobs in town she is qualified for.(We won't get into her unsuccessful turn at the beauty salon.)She estimates that customer time can be valued at $15 per hour. -According to the information provided in Table 12-4, how much time will the average customer spend waiting in line?

Lines at banks where customers wait for a teller window are usually representative of a

Table 12-4 The sentient car wash in Luther knows she is in for a busy day when dawn breaks on a gorgeous spring morning.She is capable of washing a car every four minutes, and by the looks of things, it is reasonable to expect a steady stream of twelve cars per hour arriving.Because she is fully automatic, she knows that the four-minute estimate is accurate and invariant.She values her time at $10 per hour.Yes, it seems low, but as a single bay car wash, there are few other jobs in town she is qualified for.(We won't get into her unsuccessful turn at the beauty salon.)She estimates that customer time can be valued at $15 per hour. -According to Table 12-4, what is the total number of cars in the system?

Table 12-4 The sentient car wash in Luther knows she is in for a busy day when dawn breaks on a gorgeous spring morning.She is capable of washing a car every four minutes, and by the looks of things, it is reasonable to expect a steady stream of twelve cars per hour arriving.Because she is fully automatic, she knows that the four-minute estimate is accurate and invariant.She values her time at $10 per hour.Yes, it seems low, but as a single bay car wash, there are few other jobs in town she is qualified for.(We won't get into her unsuccessful turn at the beauty salon.)She estimates that customer time can be valued at $15 per hour. -According to the information provided in Table 12-4, how many minutes per hour will the car wash be idle and able to ponder the meaning of life?

Two characteristics of arrivals are the line length and queue discipline.

Percent idle time plus percent utilization equals one.

A post office has a single line for customers waiting for the next available postal clerk.There are two postal clerks who work at the same rate.The arrival rate of customers follows a Poisson distribution, while the service time follows an exponential distribution.The average arrival rate is three per minute and the average service rate is two per minute for each of the two clerks.What proportion of time are both clerks idle?

A new shopping mall is considering setting up an information desk operated by two employees.Based on information obtained from similar information desks, it is believed that people will arrive at the desk at the rate of 20 per hour.It takes an average of 4 minutes to answer a question.It is assumed that arrivals are Poisson and answer times are exponentially distributed. (a)Find the proportion of the time that the employees are busy. (b)Find the average number of people waiting in line to get some information. (c)Find the expected time a person spends just waiting in line to have his question answered.

Four thousand students are admitted each year at a large regional university.The average time to complete a degree is six years and the university's retention rate initiative achieves 100% (no students drop out or transfer).What is the student population?