Exam 6: S: Advanced Waiting Line Theory and Simulation Modeling

Customers enter the stadium and purchase refreshments before they are shown to their seats by experienced ushers. The concession stand lines are considered elements in the simulation model.

Frenzied 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. Calculate system performance characteristics if service times are exponentially distributed and the arrivals follow a Poisson distribution.

A customer enters a business and joins the one line that snakes back and forth through the lobby in order to receive service. The initial part of the service is performed by one customer service representative, after which the customer enters a second, shorter line to complete the service before leaving the establishment. Which description of this waiting line system is appropriate?

Figure 6S-1 Customers enter a haberdashery that sells only ascots, cufflinks and suspenders and are served by the owner operator. The owner is the only employee, so if customer B arrives while customer A is being served, customer B must patiently wait until customer A exits the system. Customers are always willing to wait regardless of how long their wait is. The interarrival and service times are uniformly distributed and shown in the table below. Range Interarrival (min) Service (min) 0.000-0.200 3 6 0.201-0.400 6 7 0.401-0.600 9 8 0.601-0.800 12 9 0.801-1.000 15 10 The stream of random number for a Monte Carlo simulation of the system appear in this table> Interarrival Service .114 .979 .899 .297 .925 .162 .085 .574 .824 .235 .151 .593 .223 .956 .477 .845 -Use the data from Figure 6S-1. How many customers are in the haberdashery at 8:38?

Why would someone choose to use simulation to analyze a waiting line problem rather than use a formula? What are the advantages and disadvantages of a simulation approach?

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. What is the probability that there are no customers awaiting service or being served if the service times are exponentially distributed and the arrivals follow a Poisson distribution?

Anxious 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 many customers are clustered around her, either receiving service or waiting in line to receive her valuable service if the service times are exponentially distributed and the arrivals follow a Poisson distribution?

One of the differences between a waiting line system with a constant service time and one with exponentially distributed service times. 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.

Figure 6S-1 Customers enter a haberdashery that sells only ascots, cufflinks and suspenders and are served by the owner operator. The owner is the only employee, so if customer B arrives while customer A is being served, customer B must patiently wait until customer A exits the system. Customers are always willing to wait regardless of how long their wait is. The interarrival and service times are uniformly distributed and shown in the table below. Range Interarrival (min) Service (min) 0.000-0.200 3 6 0.201-0.400 6 7 0.401-0.600 9 8 0.601-0.800 12 9 0.801-1.000 15 10 The stream of random number for a Monte Carlo simulation of the system appear in this table> Interarrival Service .114 .979 .899 .297 .925 .162 .085 .574 .824 .235 .151 .593 .223 .956 .477 .845 -Use the data from Figure 6S-1. What is the total time that customers must wait from 8:00 am to 9:15 am?

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 10 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?

If 5 minutes passes between customer arrivals then the ________ is 12/hour.

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 ________.

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?

The effect of the Excel formula =20*RAND()

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?

With only a half hour for lunch I screamed into the parking lot of the nearest Golden Arches Supper Club at 40 miles an hour. When I saw the drive-through line was 15 cars deep, I didn't bother getting in line; I was off to visit the Colonel. This behavior might be described as balking.

Anxious 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. Calculate system performance characteristics if service times are exponentially distributed and the arrivals follow a Poisson distribution.

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 of 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 system utilization?

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 many customers are waiting in line to receive her valuable service if the service times are exponentially distributed and the arrivals follow a Poisson distribution?

Many complex waiting line situations cannot be analyzed through neatly derived formulas. In these cases, ________ is the best method of analysis.