51) With a multiple-server model, increasing the arrival rate by 10 percent and also increasing the service rate of each server by 10 percent will result in: A) a decrease in the utilization of the system. B) no change in the average number of customers in the waiting line. C) a decrease in the average number of customers in the waiting line. D) an increase in the waiting time in line. 52) With a finite-source model, increasing the arrival rate by 10 percent and also increasing the service rate by 10 percent will result in a(n): A) increase in the utilization of the server. B) increase in the average number of customers in the service system. C) decrease in the average time spent in the system, including service. D) increase in the waiting time in line. 53) With a finite-source model, increasing the arrival rate by 10 percent and also increasing the service rate by 10 percent will result in: A) a decrease in the utilization of the server. B) no change in the average number of customers in the system. C) an increase in the average number of customers in the waiting line. D) an increase in the waiting time in line. Scenario B.1 A single ticket taker can tear tickets and direct movie patrons to their seats at a rate of 90 per hour. Customers arrive every minute for assistance and always wait, regardless of how long the line gets. Arrivals are governed by the Poisson distribution and service is governed by the exponential distribution. 54) Use the information in Scenario B.1. What is the utilization of the ticket taker? A) 0.66 B) 0.55 C) 0.44 D) 0.33 55) Use the information in Scenario B.1. What is the probability that customers with tickets arrive and the ticket taker is not helping another patron? A) 0.011 B) 0.11 C) 0.22 D) 0.33 56) Use the information in Scenario B.1. What is the average number of customers in line? A) 0.33 B) 0.66 C) 1.33 D) 2.00 57) Use the information in Scenario B.1. What is the average number of people waiting in line and being seated? A) 0.66 B) 1.00 C) 2.00 D) 3.00 58) Use the information in Scenario B.1. What is the average time a customer must wait in line? A) 0.66 minute B) 1.33 minutes C) 2.00 minutes D) 3.00 minutes 59) Use the information in Scenario B.1. What is the average combined time a customer waits in line and spends being seated by the ticket taker? A) 1.00 minute B) 1.50 minutes C) 2.00 minutes D) 3.00 minutes Scenario B.2 Weary travelers arrive at Will Rogers International Airport, pick up their luggage, stumble to their cars, and proceed to the parking lot attendant to pay for their parking. Traveler interarrival times are exponentially distributed, as are the service times of the attendant. On average, travelers arrive every 25 seconds. The attendant can process three travelers per minute, and processing rates follow a Poisson distribution. 60) Use the information in Scenario B.2. How many minutes per hour is the attendant not serving customers? A) fewer than or equal to 13 B) greater than 13 but fewer than or equal to 17 C) greater than 17 but fewer than or equal to 21 D) greater than 21
51) With a multiple-server model, increasing the arrival rate by 10 percent and also increasing the service rate of each server by 10 percent will result in:
A) a decrease in the utilization of the system.
B) no change in the average number of customers in the waiting line.
C) a decrease in the average number of customers in the waiting line.
D) an increase in the waiting time in line.
52) With a finite-source model, increasing the arrival rate by 10 percent and also increasing the service rate by 10 percent will result in a(n):
A) increase in the utilization of the server.
B) increase in the average number of customers in the service system.
C) decrease in the average time spent in the system, including service.
D) increase in the waiting time in line.
53) With a finite-source model, increasing the arrival rate by 10 percent and also increasing the service rate by 10 percent will result in:
A) a decrease in the utilization of the server.
B) no change in the average number of customers in the system.
C) an increase in the average number of customers in the waiting line.
D) an increase in the waiting time in line.
Scenario B.1
A single ticket taker can tear tickets and direct movie patrons to their seats at a rate of 90 per hour. Customers arrive every minute for assistance and always wait, regardless of how long the line gets. Arrivals are governed by the Poisson distribution and service is governed by the exponential distribution.
54) Use the information in Scenario B.1. What is the utilization of the ticket taker?
A) 0.66
B) 0.55
C) 0.44
D) 0.33
55) Use the information in Scenario B.1. What is the probability that customers with tickets arrive and the ticket taker is not helping another patron?
A) 0.011
B) 0.11
C) 0.22
D) 0.33
56) Use the information in Scenario B.1. What is the average number of customers in line?
A) 0.33
B) 0.66
C) 1.33
D) 2.00
57) Use the information in Scenario B.1. What is the average number of people waiting in line and being seated?
A) 0.66
B) 1.00
C) 2.00
D) 3.00
58) Use the information in Scenario B.1. What is the average time a customer must wait in line?
A) 0.66 minute
B) 1.33 minutes
C) 2.00 minutes
D) 3.00 minutes
59) Use the information in Scenario B.1. What is the average combined time a customer waits in line and spends being seated by the ticket taker?
A) 1.00 minute
B) 1.50 minutes
C) 2.00 minutes
D) 3.00 minutes
Scenario B.2
Weary travelers arrive at Will Rogers International Airport, pick up their luggage, stumble to their cars, and proceed to the parking lot attendant to pay for their parking. Traveler interarrival times are exponentially distributed, as are the service times of the attendant. On average, travelers arrive every 25 seconds. The attendant can process three travelers per minute, and processing rates follow a Poisson distribution.
60) Use the information in Scenario B.2. How many minutes per hour is the attendant not serving customers?
A) fewer than or equal to 13
B) greater than 13 but fewer than or equal to 17
C) greater than 17 but fewer than or equal to 21
D) greater than 21
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