Exam 12: Waiting Lines and Queuing Theory Models

An "infinite calling population" occurs when the likelihood of a new arrival depends upon the number of past arrivals.

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 time spent in the system?

In queuing analysis, total expected cost is the sum of expected ________ plus expected ________.

Table 12-2 -According to the information provided in Table 12-2, which presents a queuing problem solution, there are two servers in this system.Counting each person being served and the people in line, on average, how many people would be in this 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 Table 12-4, what is the total hourly cost of the system for customers and the car wash herself? Assume the car wash is paid only when she is washing cars.

Customers enter the waiting line to pay for food as they leave 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 proportion of the time is the server busy?

One difficulty in waiting line analysis is that it is sometimes difficult to place a value on customer waiting time.

Table 12-3 -According to the information provided in Table 12-3, which presents a queuing problem solution, what proportion of time is the system totally empty?

What is the difference between customers balking and customers reneging? If you managed a retail store how would you track and differentiate between customers that balked and reneged?

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.If the dry cleaner wants to accommodate (have enough room for)all of the waiting cars at least 96 percent of the time, how many car-lengths should they make the driveway leading to the window?

Assume that we are using a waiting line model to analyze the number of service technicians required to maintain machines in a factory.Our goal should be to

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.If the average cat video is 60 seconds, how many videos can the professor watch in an hour?

A finite population model differs from an infinite population model because there is a random relationship between the length of the queue and the arrival rate.

Table 12-2 -According to the information provided in Table 12-2, which presents a queuing problem solution, what proportion of time is at least one server busy?

A hospital ward with only 30 beds could be modeled using a finite population model.

Table 12-1 -According to the information provided in Table 12-1, what percentage of the total available service time is being used?

A new shopping mall is considering setting up an information desk manned by one employee.Based upon information obtained from similar information desks, it is believed that people will arrive at the desk at the rate of 15 per hour.It takes exactly two minutes to answer each question.It is assumed that arrivals are Poisson. (a)Find the probability that the employee is idle. (b)Find the proportion of time that the employee is busy. (c)Find the average number of people receiving and waiting to receive information. (d)Find the average number of people waiting in line to get information. (e)Find the average time a person seeking information spends at the desk. (f)Find the expected time a person spends waiting in line to have his question answered.

At a local fast food joint, cars arrive randomly at a rate of 12 every 30 minutes.Service times are random (exponential)and average 2 minutes per arrival.The average time in the queue for each arrival is

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 a normal distribution.What type of queuing model applies here?

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 probability of no customers in the system?