Exam 13: Queuing Analysis

The number of servers multiplied by the service rate is the ________ for a multiple-server system.

In a bank drive-through, there is a single service window and room only for two cars to line-up to wait for service. The mean time between arrivals for drive through customers is 5 minutes. The mean time to complete a customer transaction is 3 minutes. The number of arrivals is distributed according to a Poisson distribution and the service times are exponentially distributed. -What is the probability that there are no vehicles in the system?

A crew of mechanics at the Department of Transportation garage make minor repairs to snowplows during the winter. The snowplows break down at an average rate of 4 vehicles per day and breakdowns are distributed according to the Poisson distribution. The mechanic can service an average of 7 vehicles per day with a repair time distribution that approximates a negative exponential distribution. Assume an 8 hour day. -Approximately how many vehicles are in the garage, waiting for repairs or being repaired?

Pickmeup is a drive through coffee house that has room for 3 cars in the driveway. The line cannot exceed 3 cars, and because they are exclusively drive through, customers may be turned away. In the morning, the arrival rate is 40 cars per hour (Poisson distributed) and with the servers working in teams, they can process 50 cars per hour (the service rate is exponential). What is the probability of turning customers away?

In a factory, machines breakdown at an average of 6 machines per hour according to a Poisson distribution. The time a repair person takes to repair the machine is not defined by any probability distribution, but has a mean of 8 minutes and a standard deviation of 3 minutes. -On average, how long will a machine have to wait before it is fixed?

The arrival rate is the

The service rate is the average time it takes to serve a customer.

What happens to the customer waiting time if system utilization increases?

A single-bay car wash with a Poisson arrival rate and an exponential service time has cars arriving an average of 15 minutes apart. It takes approximately 9 minutes to wash a car. What is the system utilization?

In real-world queuing applications, the multiple-server system analysis techniques are the same whether customers wait in one line or in separate lines due to customer balking.

Poultry Processing processes chickens for fast food restaurants. The Majestic chickens arrive from the farms on trucks, in cages, at a rate of 8 trucks per hour according to the Poisson distribution. The quality standards of Poultry Processing require that the chickens be processed within 30 minutes, which includes the time from when the trucks arrive until the chickens are finished processing. Determine the maximum average processing rate (in truckloads per hour) that must be designed for the machine, in order to ensure that the cages will be processed, on the average, in 30 minutes or less. Assume processing time is exponentially distributed.

A single-server waiting line system has an arrival pattern characterized by a Poisson distribution with 3 customers per hour. The average service time is 12 minutes. The service times are distributed according to the negative exponential distribution. -The expected number of customers in the system is:

A single-channel queuing system has an average service time of 8 minutes and an average time between arrivals of 10 minutes. What is the hourly arrival rate?

The calling population is the source of customers.

In a single-server queuing system, if 12 customers arrive per hour and 30 customers are served per hour, what is the probability that there are no customers in the system?

The queue discipline is the order in which waiting customers are served.

If it takes 5 minutes to serve a customer at a fast food restaurant the service rate is ________.

In multiple-server models, two or more servers work as a team to serve a single waiting line.

A crew of mechanics at the Department of Transportation garage make minor repairs to snowplows during the winter. The snowplows break down at an average rate of 4 vehicles per day and breakdowns are distributed according to the Poisson distribution. The mechanic can service an average of 7 vehicles per day with a repair time distribution that approximates a negative exponential distribution. Assume an 8 hour day. -What is the expected average number of snowplows in the garage (waiting for repair and being repaired)?

The ________ is the frequency at which the customers arrive at a waiting line according to a probability distribution.