Exam 25: Waiting-Line Models

A crew of mechanics at the Highway Department Garage repair vehicles that break down at an average of λ = 8 vehicles per day (approximately Poisson in nature).The mechanic crew can service an average of μ = 11 vehicles per day with a repair time distribution that approximates an exponential distribution.The crew cost is approximately $300 per day.The cost associated with lost productivity from the breakdown is estimated at $150 per vehicle per day (or any fraction thereof).What is the expected cost of this system?

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.What is the utilization factor?

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.A student has just entered the system.How long is she expected to stay in the system?

Which of the following occurs as the level of service decreases?

Which of the following is most likely to be served in a last-in,first-served (LIFS)queue discipline?

A crew of mechanics at the Highway Department Garage repair vehicles that break down at an average of λ = 7 vehicles per day (approximately Poisson in nature).The mechanic crew can service an average of μ = 11 vehicles per day with a repair time distribution that approximates an exponential distribution. a.What is the utilization rate for this service system? b.What is the average time before the facility can return a breakdown to service? c.How much of that time is spent waiting for service? d.How many vehicles are likely to be waiting for service at any one time?

Four of the most widely used waiting line models-M/M/1 or A,M/M/S or B,M/D/1 or C,and Finite population or D-all share which of the following three characteristics?

In queuing problems,which of the following probability distributions is typically used to describe the time to perform the service?

A dental clinic at which only one dentist works is open only two days a week.During those two days,the traffic arrivals follow a Poisson distribution with patients arriving at the rate of three per hour.The doctor serves patients at the rate of one every 15 minutes. a.What is the probability that the clinic is empty (except for the dentist and staff)? b.What is the probability that there are one or more patients in the system? c.What is the probability that there are four patients in the system? d.What is the probability that there are four or more patients in the system?

What are the six assumptions underlying the M/M/1 waiting line model? Which of these also hold for the M/D/1 model?

A waiting-line system that meets the assumptions of M/M/S has λ = 5,μ = 4,and M = 2.For these values,Po is approximately 0.23077,and Ls is approximately 2.05128.What is the average time a unit spends in this system?

A(n)________ occurs when an arrival refuses to enter a waiting line;a(n)________ occurs when an arrival joins a waiting line,then leaves it before being served.

A McDonald's single-lane drive-through that has one window for making the payment and a second window for receiving the food behaves most like which of the following?

A concert hall,employing both ticket takers and ushers to seat patrons,behaves typically as which of the following?

A waiting line meeting the M/M/1 assumptions has an arrival rate of 10 per hour and a service rate of 12 per hour.What is the average time a unit spends in the system and the average time a unit spends waiting (in hours)?

Which one of the following is NOT a characteristic of a Model C or M/D/1 system?

A waiting line has a(n)________ population if,as arrivals take place,the likelihood of additional arrivals is decreased.

The greater the margin by which the arrival rate exceeds the service rate,the better the performance of the waiting line.

A waiting line meeting the assumptions of M/M/1 has an average time between arrivals of 20 minutes,and it services items in an average of 10 minutes each.What is the utilization factor?