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Exam 11: Queueing Models

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Question 41

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Customers arrive at a video rental desk at the rate of one per minute (exponential interarrival times) . Each server can handle 0.4 customers per minute (exponential service times) . If there are 4 servers, what is the probability of three or fewer customers in the system?

A) 0.19
B) 0.23
C) 0.63
D) 0.68
E) 0.79

F) C) and D)
G) A) and B)

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Question 42

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The reason for using priorities is to decrease the waiting times for high-priority customers.

A) True
B) False

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Question 43

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A queueing system has four crews with three members each. The number of "servers" is:

For a single-server queueing system, which of the following is TRUE? I. A high utilization factor will result in a system that performs well. II. A high utilization factor will result in a system that performs poorly. III. A low utilization factor will result in a system that performs efficiently.

The expected waiting time in line is equal to the expected number of customers in line divided by the arrival rate.

As the ratio of arrival rate to service rate is increased, which of the following is likely?

Queueing models conventionally assume that the queue can hold an unlimited number of customers.

$\begin{array}{l}\begin{array}{|l|l|}\hline \text { Priority }&\text { Average Arrival Rate (exponential interarrival times) }\\\hline \text { High } & 3 \text { per hour } \\\hline \text { Low } & 5 \text { per hour } \\\hline\end{array}\end{array}$ $\begin{array}{|l|l|}\hline Nurrber~ of~ servers:&5\\\hline Service~ rate:&2~ per~ hour ~(exponential ~service~ times) \\\hline \end{array}$ What is the average time in the system (in minutes) for a high priority item?

$\begin{array}{l}\begin{array}{|l|l|}\hline \text { Priority }&\text { Average Arrival Rate (exponential interarrival times) }\\\hline \text { High } & 3 \text { per hour } \\\hline \text { Low } & 5 \text { per hour } \\\hline\end{array}\end{array}$ $\begin{array}{|l|l|}\hline Nurrber~ of~ servers:&5\\\hline Service~ rate:&2~ per~ hour ~(exponential ~service~ times) \\\hline \end{array}$ What is the system utilization factor?

There are 5 servers in a system with an arrival rate of 6 per hour and a service time of 20 minutes. What is the system utilization?

The lack-of-memory property refers to a customer's willingness to wait in line even though there are other customers that will be served first.

Which of the following is not an assumption of a multiple priority queueing model?

Queue discipline refers to the willingness of customers to wait in line for service.

Customers arrive at a suburban ticket outlet at the rate of 14 per hour on Monday mornings (exponential interarrival times) . Selling the tickets and providing general information takes an average of 3 minutes per customer, and varies exponentially. There is 1 ticket agent on duty on Mondays. How many minutes does the average customer spend in the system?

Which of the following is not an example of a commercial service system?

For a single-server queueing system, which of the following is FALSE? I. Decreasing the variability of service times improves the performance of the system. II. Decreasing the variability of service times reduces the performance of the system. III. Increasing the variability of arrival times improves the performance of the system.

A multiple priority queueing model assumes that:

Customers filter into a record shop at an average of 1 per minute (exponential interarrivals) where the service rate is 15 per hour (exponential service times) . What is the average number of customers in the system with 8 servers?