Exam 15: Waiting Line Models

Arrivals at a box office in the hour before the show follow the Poisson distribution with $\lambda$ = 7 per minute.Service times are constant at 7.5 seconds.Find the average length of the waiting line.

In a waiting line situation,arrivals occur,on average,every 10 minutes,and 10 units can be received every hour.What are $\lambda$ and $\mu$ ?

For a single-server queuing system,the average number of customers in the waiting line is one less than the average number in the system.

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

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?

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

Two new checkout scanning systems are under consideration by a retail store.Arrivals to the checkout stand follow the Poisson distribution with $\lambda$ = 2 per minute.The cost for waiting is $18 per hour.The first system has an exponential service rate of 5 per minute and costs $10 per hour to operate.The second system has an exponential service rate of 8 per minute and costs $20 per hour to operate.Which system should be chosen?

Which of the following can NOT be found by the queuing formulas presented in the textbook?

Decision makers in queuing situations attempt to balance

Models with a finite calling population

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

Andy Archer,Ph.D. ,is a training consultant for six mid-sized manufacturing firms.On the average,each of his six clients calls him for consulting assistance once every 25 days.Andy typically spends an average of five days at the client's firm during each consultation. Assuming that the time between client calls follows an exponential distribution,determine the following: a.the average number of clients Andy has on backlog b.the average time a client must wait before Andy arrives to it c.the proportion of the time Andy is busy

For many waiting line situations,the arrivals occur randomly and independently of other arrivals and it has been found that a good description of the arrival pattern is provided by

In a multiple channel system it is more efficient to have a separate waiting line for each channel.

In developing the total cost for a waiting line,waiting cost takes into consideration both the time spent waiting in line and the time spent being served.

For all waiting lines,P₀ + P_w = 1.

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 $\lambda$ = 6 and $\mu$ = 9,with $\sigma$ = .03,find a.the probability the system is idle. b.the average length of the queue. c.the average number in the system.

When a waiting system is in steady-state operation,the number of units in the system is not changing.

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?