Exam 15: Waiting Line Models

Models with a finite calling population

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

​With no waiting allowed,operating characteristics L_q and W_q are automatically zero regardless of the number of servers.

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.

What queue discipline is assumed by the waiting line models presented in the textbook?

For an M/M/k system,the average number of customers in the system equals the customer arrival rate times the average time a customer spends waiting in the system.

The total cost for a waiting line does NOT specifically depend on

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

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

​Give examples of systems you have seen in which a)blocked arrivals are cleared,and b)there is a finite calling population.

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?

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.

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

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.

Waiting line models describe the transient-period operating characteristics of a waiting line.

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

Circle Electric Supply is considering opening a second service counter to better serve the electrical contractor customers.The arrival rate is 10 per hour.The service rate is 14 per hour.If the cost of waiting is $30 and the cost of each service counter is $22 per hour,then should the second counter be opened?

The arrival rate in queuing formulas is expressed as

​Explain what is meant by the following statement,"operating characteristics are non-optimizing."

The 8 students in a seminar class must come to the professor's office to turn in a paper and give a 5-minute oral summary.Assume there is a service rate of 10 per hour and adequate time is available for all.The arrival rate for each unit is 5 per hour.What is the probability there is no one in the office or waiting when you come?