Exam 12: Waiting Lines and Queuing Theory Models

Table 12-5 -According to the information provided in Table 12-5, which presents the solution for a queuing problem with a constant service rate, on average, how many customers are in the system?

Thanks to a generous and eccentric donor, the school of business has 3 fax machines.The toner in each machine needs to be changed after about 5 hours of use.There is one unit secretary who is responsible for the fax machine maintenance.It takes him 15 minutes to replace the toner cartridge.What is the average waiting time in the queue?

An (M/D/1)queuing model is classified as probabilistic.

A queue system is in a transient state before the steady state is reached.

An arrival in a queue that reneges is one who

A queuing system with a normally distributed arrival pattern, exponential service times, and three servers would be described as

A professor holds office hours during final exam week and discovers much to his dismay that his sudden popularity affords him little time to engage in his favorite activity, watching cat videos.Fifteen students per hour arrive at his office and he patiently answers questions, averaging three minutes per student.A student joins the line at 9:45 am and the test is at 10:00 am the same morning.How much time does the student have after getting his question answered to get to the exam room?

Table 12-5 -According to the information provided in Table 12-5, which presents the solution for a queuing problem with a constant service rate, on average, how much time is spent waiting in line?

Table 12-3 -According to the information provided in Table 12-3, which presents a queuing problem solution, what is the utilization rate of the service facility?

A dry cleaner has a single drive-thru window for customers.The arrival rate of cars follows a Poisson distribution, while the service time follows an exponential distribution.The average arrival rate is 16 per hour and the average service time is three minutes. (a)What is the average number of cars in the line? (b)What is the average time spent waiting to get to the service window? (c)What percentage of time is the dry cleaner's drive-thru window idle? (d)What is the probability there are more than 2 cars at the drive-thru window?

Customers enter the waiting line at a cafeteria on a first-come, first-served basis.The arrival rate follows a Poisson distribution, while service times follow an exponential distribution.If the average number of arrivals is four per minute and the average service rate of a single server is seven per minute, what is the average number of customers in the system?

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 is the average length of the line?

Thanks to a generous and eccentric donor, the school of business has 3 fax machines.The toner in each machine needs to be changed after about 5 hours of use.There is one unit secretary who is responsible for the fax machine maintenance.It takes him 15 minutes to replace the toner cartridge.What is the average number of fax machines in the queue?

Many real-world systems are too complex to be handled analytically.In this case a simulation model is the most appropriate analysis tool.

Table 12-1 -According to the information provided in Table 12-1, what is the average amount of time a customer waits and is served?

In a single-channel, single-phase system, reducing the service time only reduces the total amount of time spent in the system, not the time spent in the queue.

Table 12-1 -According to the information provided in Table 12-1, what is the hourly total cost of the system for customers and servers? Assume that servers are paid only when they are helping customers.

The term queue "discipline" describes the

A professor decides to hold a three-hour window open for student advising.The professor has 15 advisees.He's unsure if each advisee will show up, and it's possible that a single advisee could show up multiple times during the 3-hour window.On average, the professor will spend 12 minutes with each student.He usually expects each student to arrive once during the 3-hour window. (a)What proportion of the time can the professor expect to be busy during the window? (b)What is the expected number of students in queue during the window? (c)What is the expected wait time in queue during the window?

On a practical note-if we are using waiting line analysis to study customers calling a telephone number for service, balking is probably not an issue.