UCCC Waiting Line Practice Quiz

Which of the following represents an unlimited queue?

• drive-through lane at a fast-food restaurant

• small barbershop with only 5 chairs for waiting customers

• toll booth serving automobiles on an interstate

• faculty office with limited seating during office hours

• E) restaurant with no outside seating and limited capacity due to fire department restrictions

Which of the following is most likely to violate a FIFO queue?

• supermarket with no express lanes

• car repair garage

• emergency room

• fast-food restaurant

• All of these are equally likely to violate a FIFO queue.

Suppose that, on average, 4 customers arrive each minute in a Poisson distribution. What is the probability that 2 customers will arrive in a particular minute?

• 0.500

• 0.147

• 0.018

• 0.073

• 0.195

A waiting line meeting the assumptions of M/M/1 has an average time between arrivals of 15 minutes, and it services items in an average of 10 minutes each. What is the utilization factor?

• 0.25

• 0.33

• 0.50

• 0.67

• 1.50

A single-phase waiting-line system meets the assumptions of constant service time or M/D/1. Units arrive at this system every 12 minutes on average. Service takes a constant 8 minutes. What is the average length of the queue, Lq, in units?

• 0.67

• 2.5

• 4.5

• 0.75

• 5.0

17) A single-phase waiting-line system meets the assumptions of constant service time or M/D/1. Units arrive at this system every 10 minutes on average. Service takes a constant 8 minutes. What is the average number in the system, Ls, in units?

• 1.60

• 2.40

• 0.80

• 1.33

A queuing model that follows the M/M/1 assumptions has λ = 2 and μ = 5. What is the average number of units in the system?

• 2/3

• 1

• 1.5

• 2

Students arrive randomly at the help desk of the computer lab. There is only one service agent, and the time required for inquiry varies from student to student. Arrival rates have been found to follow the Poisson distribution, and the service times follow the negative exponential distribution. The average arrival rate is 12 students per hour, and the average service rate is 20 students per hour. On average, how long does it take to service each student?

• 1 minute

• 3 minutes

• 5 minutes

• 20 minutes

A mechanic for Mr. Plow makes minor repairs to snowplows during the winter. The snowplows break down at an average rate of 5 vehicles per day and breakdowns are distributed according to the Poisson distribution. The mechanic can service an average of 7 vehicles per day with a repair time distribution that approximates a negative exponential distribution. Assume an 8-hour day.

The mechanic's utilization is:

• .60

• .65

• .70

• .75

A goal of many waiting line problems is to help a firm find the ideal level of services that minimize the cost of waiting and the cost of providing the service.

• True

• False