Exam 11: Waiting Line Models

A company has tool cribs where workmen draw parts. Two men have applied for the position of distributing parts to the workmen. George Fuller is fresh out of trade school and expects a $6 per hour salary. His average service time is 4 minutes. John Cox is a veteran who expects $12 per hour. His average service time is 2 minutes. A workman's time is figured at $10 per hour. Workmen arrive to draw parts at an average rate of 12 per hour. a.What is the average waiting time a workman would spend in the system under each applicant? b.Which applicant should be hired?

The manner in which units receive their service, such as FCFS, is the

For a single-channel waiting line, the utilization factor is the probability that an arriving unit must wait for service.

The Quick Snap photo machine at the Lemon County bus station takes four snapshots in exactly 75 seconds. Customers arrive at the machine according to a Poisson distribution at the mean rate of 20 per hour. On the basis of this information, determine the following: a.the average number of customers waiting to use the photo machine b.the average time a customer spends in the system c.the probability an arriving customer must wait for service.

Little's flow equations indicate that the relationship of L to L_q is the same as that of W to W_q.

In a waiting line situation, arrivals occur around the clock at a rate of six per day, and the service occurs at one every three hours. Assume the Poisson and exponential distributions. a.What is λ? b.What is μ? c.Find probability of no units in the system. d.Find average number of units in the system. e.Find average time in the waiting line. f. Find average time in the system. g. Find probability that there is one person waiting. h. Find probability an arrival will have to wait.

In a multiple channel system

In waiting line systems where the length of the waiting line is limited, the mean number of units entering the system might be less than the arrival rate.

The post office uses a multiple channel queue, where customers wait in a single line for the first available window. If the average service time is 1 minute and the arrival rate is 7 customers every five minutes, find, when two service windows are open, a.the probability both windows are idle. b.the probability a customer will have to wait. c.the average time a customer is in line. d.the average time a customer is in the post office.

For an M/G/1 system with λ = 20 and μ = 35, with σ = .005, find a.the probability the system is idle. b.the average length of the queue. c.the average number in the system.

The arrival rate in queuing formulas is expressed as

When blocked customers are cleared, an important decision is how many channels to provide.

Adding more channels always improves the operating characteristics of the waiting line and reduces the waiting cost.

Decision makers in queuing situations attempt to balance

Performance measures dealing with the number of units in line and the time spent waiting are called

If service time follows an exponential probability distribution, approximately 63% of the service times are less than the mean service time.

If some maximum number of customers is allowed in a queuing system at one time, the system has a finite calling population.

During summer weekdays, boats arrive at the inlet drawbridge according to the Poisson distribution at a rate of 3 per hour. In a 2-hour period, a.what is the probability that no boats arrive? b.what is the probability that 2 boats arrive? c.what is the probability that 8 boats arrive?

In waiting line applications, the exponential probability distribution indicates that approximately 63 percent of the service times are less than the mean service time.

If arrivals occur according to the Poisson distribution every 20 minutes, then which is NOT true?