Exam 12: Waiting Lines and Queuing Theory Models

A bank with a single queue to move customers to several tellers is an example of a single-channel system.

Cars arrive at a local JLUBE franchise at the rate of 1 every 12 minutes.Service times are exactly 15 minutes.Jack Burns,the JLUBE owner,has decided to open a second work bay,i.e. ,make the shop into a two-channel system.Under this new scheme,the average customer will wait in an ________ line.

The Basic Kendall notation is based on arrival time distribution,service time distribution,and cost characteristics.

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?

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?

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?

Cars arrive at a local JLUBE franchise at the rate of 1 every 12 minutes.Service times are exponentially distributed with an average of 15 minutes.Jack Burns,the JLUBE owner,has decided to open a second work bay,i.e. ,make the shop into a two-channel system.Under this new scheme,the average customer will wait in line

At an automatic car wash,cars arrive randomly at a rate of 7 every 30 minutes.The car wash takes exactly 4 minutes (this is constant).On average,how long would each driver have to wait before receiving service?

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 transient state is the normal operating condition of the queuing system.

Customers arrive at a bank at a rate of 50 per hour.The bank has 3 tellers and on average,it takes 2 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?

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?

On a practical note-if we were to study the waiting lines in a hair salon that had only five chairs for patrons waiting,we should use an infinite queue waiting line model.

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 its 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?

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

What is meant by a multiphase system?

The analytic technique used to analyze complex queuing models that cannot be captured in closed-form expressions is called

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 probability that 2 fax machines need toner at the same time?

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?

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 an average of two minutes to answer a question.It is assumed that arrivals are Poisson and answer times are exponentially distributed. (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.