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

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 60 seconds (Poisson distributed)and it took a teller 20 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 waiting time for the customers?

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. Which customers wait and how long does each one wait? How many minutes of idle time does the owner/operator enjoy from opening time at 8:00 am until his eighth customer departs?

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. About how long does a customer wait in line to receive their valuable service if the service times are exponentially distributed and the arrivals follow a Poisson distribution?

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 time does the last customer exit the haberdashery if it opens at 8:00 a.m.?

One assumption in most waiting line analyses is that the number of customers is ________.

Which of the following statements about simulation is BEST?

Hopeful 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 long do customers spend waiting in line and finding out the unhappy news on average?

A process is ________ if the outcome of one trial does not have any impact on the next trial.

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 long does a customer wait in line to receive her valuable service if the service times are exponentially distributed and the arrivals follow a Poisson distribution?

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 the owner/operator is idle (has no customers)from 8:00 am to 9:15 am?