Exam 6: A: Advanced Waiting Line Theory and Simulation Modeling
Which of the following statements about simulation is BEST?
B
What is Monte Carlo simulation and how is one conducted?
Monte Carlo simulation is a form of simulation modeling called mathematical simulation,where mathematical formulas and statistical processes are used to simulate activities,decisions,and the like.In Monte Carlo simulation,statistical sampling is used to generate outcomes for a large number of trials.The results of these trials are then used to gain insight into the system of interest.
Monte Carlo simulation is used to simulate all types of systems and many types of statistical distributions.
The modeler must map the random numbers to the outcomes of events under study,then generate a stream of numbers that can be interpreted by the mapping so that the events are interpretable.The stream of numbers could be mined from a page turner such as A Million Random Digits with 100000 Normal Deviates by the RAND Corporation or more commonly,from a computer program.
It is more costly to create a more realistic simulation than one that is less realistic.
True
The bank manager of a busy downtown location found herself unable to find good teller help so she invested in an ATM to handle the routine withdrawals that tended to occupy an inordinate amount the teller's time.Before she installed the ATM she found that customers were arriving on average every 2 minutes (Poisson distributed)and it took a teller 30 seconds (exponentially distributed)to process their request.The ATM is able to maintain a constant 30 second service time.What is the impact on the number of customers waiting in line?
Barber College is the best deal in town! For only $5,you can get a shampoo and cut by any one of four untrained stylists completed in 7.5 minutes on average.Perhaps this is why customers show up on average two minutes apart (both arrival times and service times are exponentially distributed). What percentage of the time are the four stylists working with customers?
Each outcome of flipping a fair coin is completely independent of the previous flip.This outcome is known as:
It's a beautiful sunny day after a week of rainy weather and both of the local car washes are busy.One car wash is fully automated,touchless,and can wash a vehicle of any size to a dazzling luster in 5 minutes flat.The other car wash is a fund raiser staffed by eager amateurs that work on one car at a time and can finish it in about 4 minutes (their time is governed by the Poisson distribution).Customer arrivals at both car washes are Poisson distributed with a mean of 10 per hour.How long does it take the average customer to work his way through either system? How many customers are in the systems on average?
There is but one difference between a waiting line system with a constant service time and one with a Poisson distributed service time.Customers using the system with the constant service time will have half the waiting time of the customers using the system with Poisson distributed service times.
A customer enters a business and has the opportunity to select any one of three lines to receive service.The service is performed by one customer service representative after which the customer leaves the establishment.Which description of this waiting line system is appropriate?
Patrons line up to spin the giant slot machine at the entrance to Ace Rothstein's Tangiers casino.They pour in the door at the rate of 300 per hour and it takes exactly ten seconds every time for the wheels to spin and inform the unlucky patron that they have lost a dollar rather than win a new Corvette.How many customers are in line on average?
Regulars line up to spin the giant slot machine at the entrance to Ace Rothstein's Tangiers casino.They pour in the door at the rate of 300 per hour and it takes exactly ten seconds every time for the wheels to spin and inform the unlucky patron that they have lost a dollar rather than win a new Corvette.How long do customers wait in line on average?
Frenzied cruise vacationers besiege Tatiana,their excursion coordinator,and her fourteen assistants at the Port of Cozumel when they realize that all water excursions have been cancelled for no reason in particular.It takes them 4 minutes to find the customers an alternative excursion activity and customers cluster around them at the rate of 200 per hour.About how many customers are clustered around them,either receiving service or waiting in line to receive their valuable service if the service times are exponentially distributed and the arrivals follow a Poisson distribution?
Barber College is the best deal in town! For only $5,you can get a shampoo and cut by any one of four untrained stylists completed in 7.5 minutes on average.Perhaps this is why customers show up on average two minutes apart (both arrival times and service times are exponentially distributed). Management is concerned about the waiting time for customers and decides to train one more student.If the arrival and service rates remain the same as in the original scenario,what happens to the number of customers in the system?
Nervous cruise vacationers besiege Tatiana,their excursion coordinator,at the Port of Cozumel when they realize that all water excursions have been cancelled for no reason in particular.It takes her 2.5 minutes to find the customers an alternative excursion activity and customers cluster around her at the rate of 20 per hour.About how long does a customer spend waiting in line and receiving her valuable service if the service times are exponentially distributed and the arrivals follow a Poisson distribution?
Customers enter the stadium and purchase refreshments before they are shown to their seats by experienced ushers.The customers are considered objects in the simulation model.
In most waiting line models,customers are assumed to arrive at random intervals,based on a normal distribution.
Customers that leave the system after waiting in line for a while are ________ but customers that don't even join the line because it looks too long are ________.
Barber College is the best deal in town! For only $5,you can get a shampoo and cut by any one of four untrained stylists completed in 7.5 minutes on average.Perhaps this is why customers show up on average two minutes apart (both arrival times and service times are exponentially distributed). On average,how many customers are waiting in line?
The department chair is out of town at a conference and you,as the assistant department chair,find yourself besieged by dozens of students needing permission to get into a very popular (but closed)class.Student arrivals are governed by the Poisson distribution with a mean of 5 minutes.Telling the students that they can't get into the closed class takes about 3 minutes,and this average is exponentially distributed.About how many students are waiting outside your office door and in your office?
________ is an Excel function that generates a uniformly distributed random number between 0 and 1.
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