Exam 11: Waiting Line Models

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

Operating characteristics formulas for the single-channel queue do NOT require

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?

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.

The Sea View Resort uses a multiple-channel queue registration system. If the average service time is 8 minutes, there are three registration clerks, and guests arrive at the rate of one every 5 minutes, find a. $\lambda$ and $\mu$ . b.the probability all three clerks are idle. c.the probability a guest will have to wait. d.the average time a customer is in line. e.the average number of customers in line.

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

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

The time to process a registration at the Sea View Resort follows the exponential distribution and has a mean of 6 minutes. a.What is the probability of a registration time shorter than 3 minutes? b.What is the probability of a registration time shorter than 6 minutes? c.What is the probability of a registration time between 3 and 6 minutes?

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

The arrival rate in queuing formulas is expressed as

For an M/M/1 queuing system, if the service rate, µ, is doubled, the average wait in the system, W, is cut in half.

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?

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

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

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

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?

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

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

Diagram the servers and arrivals in the single and multiple channel models. Designate the line and the system.