Exam 21: The Modi and Vam Methods of Solving Transportation Problems

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.

You have seen that, in an M/D/1 problem, the average queue length is exactly one-half the average queue length of an otherwise identical M/M/1 problem. Are all other performance statistics one-half as large also? Explain.

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. The average number in the system L_s is approximately

Balk and renege are elements of queue discipline.

In a finite or limited population waiting line, the __________ is calculated from the average service time and average time between service requirements before the problem can be completed.

In the basic queuing model (M/M/1), service times are described by

A(n) __________ queuing system has one waiting line, but several servers; a(n) __________ queuing system is one in which the customer receives services from several stations before exiting the system

Describe the difference between FIFO and LIFO queue disciplines.

The two characteristics of the waiting line itself are whether its length is limited or unlimited and the discipline of the people or items in it.

A queuing model which follows the M/M/1 assumptions has λ = 2 and μ = 8. The average number in the system L_s is __________ and the utilization of the system is __________.

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?

In a repetitive focus factory, the number of phases found in the system might refer to

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?

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. The average length of the queue L_q is approximately

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?

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 manufacturing plant is trying to determine how long the average line for a repair process will be. If 10 machines arrive each hour and must wait 6 minutes in the line, how long will the line be, on average?

A queuing model which follows the M/M/1 assumptions has λ = 10 and μ = 12. The average number in the system is

Which one of the following is not a characteristic of a Model B or M/M/S system?

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