Exam 21: Waiting-Line Models

At the order fulfillment center of a major mail-order firm, customer orders, already packaged for shipment, arrive at the sorting machine to be sorted for loading onto the appropriate truck for the parcel's address. The arrival rate at the sorting machine is at the rate of 100 per hour following a Poisson distribution. The machine sorts at the constant rate of 150 per hour. a. What is the utilization rate of the system? b. What is the average number of packages waiting to be sorted? c. What is the average number of packages in the sorting system? d. How long must the average package wait until it gets sorted? e. What would L_q and W_q be if the service rate were exponential, not constant?

What are L_s and L_q, as used in waiting line terminology? Which is larger, L_s or L_q? Explain.

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

A waiting-line system that meets the assumptions of M/M/1 has λ = 1, μ = 4. For this system, the probability of fewer than two units in the system is approximately

Suppose that a fast food restaurant wants the average line to be 5 customers and that 80 customers arrive each hours. How many minutes will the average customer be forced to wait in line?

On a typical Monday, an average of 8 customers per hour arrive at the bank to transact business. There is one teller at the bank, and the average time required to transact business is five minutes. It is assumed that service times may be described by the exponential distribution. A single line would be used, and the customer at the front of the line would go to the first available bank teller. If a single teller is used, find: a) The average time in the line. b) The average number in the line. c) The average time in the system. d) The average number in the system. e) The probability that the bank is empty. f) If the business is considering adding a second teller (who would work at the same rate as the first) to reduce the waiting time for customers. She assumes that this will cut the waiting time in half. If a second teller is added, find the new answers to parts (a) to (e).

Suppose that a fast food restaurant wants the average line to be 5 customers and that 90 customers arrive each hours. How many minutes will the average customer be forced to wait in line?

In queuing problems, arrival rates are generally described by the normal probability distribution.

A waiting line, or queuing, system has three parts, which are

A college registrar's office requires you to first visit with one of three advisors and then with one of two financial professionals. This system is best described as

Which part of a waiting line has characteristics that involve statistical distribution?

Provide an example of a limited or finite population for a queue.

Which of the following is not a common queuing situation?

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

A crew of mechanics at the Highway Department garage repair vehicles which break down at an average of λ = 5 vehicles per day (approximately Poisson in nature). The mechanic crew can service an average of μ = 10 vehicles per day with a repair time distribution that approximates an exponential distribution. a. What is the probability that the system is empty? b. What is the probability that there is precisely one vehicle in the system? c. What is the probability that there is more than one vehicle in the system? d. What is the probability of 5 or more vehicles in the system?

A waiting line model meeting the assumptions of M/M/1 has an arrival rate of 2 per hour and a service rate of 6 per hour; the utilization factor for the system is approximately

A system in which the customer receives service from only one station and then exits the system is

The source population is considered to be either ________ in its size.

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 probability that the waiting line is empty?

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?