QUESTION 1 Consider the Edmonton International Airport on a busy summer day. Whi
ID: 3150708 • Letter: Q
Question
QUESTION 1
Consider the Edmonton International Airport on a busy summer day. Which of the following arrival patterns would be LEAST likely to follow a Poisson arrival process:
taxi cabs arriving at the taxi stand at the Edmonton International Airport, hoping to find a waiting passenger
travellers requiring the use of emergency medical services within the main terminal at the Edmonton International Airport
passengers arriving at the taxi stand at the Edmonton International Airport hoping to find a waiting cab
flights landing at the Edmonton International Airport
1 points
QUESTION 2
A worker at an information booth at the O’Hare Airport in Chicago has found (by collecting data) that he serves an average of 24 customers per hour and notes that he is pretty sure that the arrivals follow a Poisson distribution. He asks his friend to cover for him for an hour while he goes to get a massage. When he returns, his friend insists that he be paid double for the work he did because he is sure that he helped at least 40 customers. According to the Poisson distribution, if the mean is 24 customers/hour, then what is the probability that 40 or more customers arrived in a given hour? (Note - this is not a 'Waiting Lines' question that uses the Excel template, but rather is a question about Poisson arrivals and would use the Poisson equation seen in the lab, text and in class. You will most likely require a spreadsheet to be efficient in answering this question).
0.07% probability
4.6% probability
12.4% probability
0.17% probability
1 points
QUESTION 3
Customers seeking help with technical problems can often opt for a Live Chat with an agent, by way of an online chat mechanism. Assume that a seller of wireless routers staffs three online chat agents during business hours and that each service encounter with a customer requires an average of 4.25 minutes (assume exponential service times). If an average of 31 customers per hour require the service (assume Poisson arrivals), and they wait in a common queue for the first available agent, what is the average amount of time that a customer waits before being served, in minutes? (rounded to two decimals)
0.25 mins
2.85 mins
1.47 mins
14.1 mins
1 points
QUESTION 4
At a car rental kiosk at a busy airport, customers arrive and wait in a common line for the first available of two sales agents. The agents can serve a customer in an average of 2.5 minutes (assume negative exponential distribution). On average, 21 customers per hour will arrive to be served (assume Poisson arrivals). However, on this day, assume that one of the computers is not working, so the two sales agents work together helping one customer at a time. The new average service time per customer is now 1.9 minutes. What is the average time a customer spends waiting in line before being served (in minutes, rounded to two decimals)?
0.12 mins
0.24 mins
0.47 mins
3.77 mins
1 points
QUESTION 5
During the lunch hour at a busy downtown cafeteria, customers arrive at a rate of approximately 274/hour (assume Poisson arrival rate and a single line, for simplicity); a clerk can serve a customer in an average time of 45 seconds (assume service times are negative exponentially distributed). What is the minimum number of clerks needed to keep the average queue length to less than two?
4
5
6
7
1 points
QUESTION 6
It is common in banks for bank tellers to have to access a single central cash window in order to get cash for customers. Consider such a bank, which has seven tellers, each requiring service from the cash window approximately 19 times per hour (assume Poisson arrivals) and an average time being served at the window (assume negative exponential distribution) of 40 seconds. How busy will the server at the central cash window be, on average (i.e., what percentage of the time should they expect to be serving someone)?
50%
60%
70%
80%
90%
1 points
QUESTION 7
A conference is being held at a centre that has three different entrances. A registration desk is being set up at each entrance. Assume that each desk will have its own queue and will see an equal portion of the expected 125 total customers per hour arriving at the conference (assume Poisson arrivals), and that customers will not line jockey between registration desks since they are significant distances apart. If each registration desk can serve one customer at a time, and the average time to serve a customer is 0.75 minutes, then what will be the average time that a customer waits in a line (in minutes) before being able to register?
0.13 mins
0.47 mins
0.82 mins
2.41 mins
4.98 mins
1 points
QUESTION 8
Consider a large distribution centre (DC) that sees the arrival of, on average, 40 trucks per 8-hour workday (assume a Poisson distribution). The unloading of a truck at one of the unloading docks takes on average 45 minutes (assume exponential distribution). The docks operate for 8 hours per day. If a dock is not available, trucks wait in a common line for the next available dock. The truckers charge the DC $30 per hour (or portion thereof) for waiting (not including unloading). The cost to operate a dock is $50 per hour (assume this to be a fixed cost that does not depend on utilization of the dock). Determine the total average cost (dock costs plus truck waiting costs) per hour, if six docks are operated.
between $300 and $305 per hour
between $305 and $310 per hour
between $310 and $315 per hour
between $315 and $320 per hour
more than $320 per hour
1 points
QUESTION 9
Twelve nurses work the fourth floor at a hospital, monitoring, and assisting patients. The nurses are regularly (average 1.3 times per hour each) required to access a drug dispenser on a different floor. Average time (including travel, but not including waiting) for getting drugs from the dispenser is 3.4 minutes. The supervisor has noticed that on occasion more than one nurse is using or waiting for the drug dispenser which reduces the number of nurses that are monitoring the patients on the fourth floor. The supervisor is considering setting up a process to ensure that nurses do not go to the dispenser if there is more than one nurse there already. The goal is to ensure that there is always at least 10 nurses on the fourth floor. Under current conditions, what percentage of the time is there at least 10 nurses on the fourth floor?
0%
57%
67%
86%
99%
1 points
QUESTION 10
With a single-server model, increasing the arrival rate by 10 percent and also increasing the service rate by 10 percent will result in:
an increase in the average number of customers in the system
a decrease in the average time spent in the system, including service
an increase in the waiting-line time
an increase in the utilization of the server
a.taxi cabs arriving at the taxi stand at the Edmonton International Airport, hoping to find a waiting passenger
b.travellers requiring the use of emergency medical services within the main terminal at the Edmonton International Airport
c.passengers arriving at the taxi stand at the Edmonton International Airport hoping to find a waiting cab
d.flights landing at the Edmonton International Airport
Explanation / Answer
1.
Many taxis are there, so it's not rare to find a waiting cab. Hence, as Poisson process is for rare events,
OPTION C: passengers arriving at the taxi stand at the Edmonton International Airport hoping to find a waiting cab [ANSWER]
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2.
Note that P(at least x) = 1 - P(at most x - 1).
Using a cumulative poisson distribution table or technology, matching
u = the mean number of successes = 24
x = our critical value of successes = 40
Then the cumulative probability of P(at most x - 1) from a table/technology is
P(at most 39 ) = 0.998265706
Thus, the probability of at least 40 successes is
P(at least 40 ) = 0.001734294 = 0.17% [ANSWER, D]
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