Exam 13: Queuing Analysis

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 the system is full and new arrival must drive on?

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. -A system has 5 servers. Customers arrive at a rate of 6 per hour and service time is 20 minutes. What is the system utilization?

Cars arrive at a single-bay car wash at an average of 6 per hour according to the Poisson distribution. The wash time is a constant 4 minutes. What is the average number of cars in line?

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

A situation in which a mechanic is responsible for repairing a pool of fleet vehicles should be analyzed for a waiting line system with a ________ calling population

If λ = 24 and μ = 30, then utilization is equal to ________.

Movement by customers between two or more queues in a system is called ________.

The basic single-server queuing model assumes an infinite calling population.

A single-server queuing system has average time between arrivals of 20 minutes and a service time of 10 minutes each. Assuming Poisson arrivals and exponential service times, the utilization factor is approximately:

A system has one service facility that can service 10 customers per hour. The customers arrive at an average rate of 6 per hour. Utilization is ________.

Queuing system operating statistics are constant over time.

At Joe's Pool Hall they rent tables by the hour and also rent Balabushka pool cues for purists that can't afford their own. The rental process for these cues is exhaustive and takes an hour and a half for each application. There are three leasing agents that conduct these interviews, and on average, it is one hour between customer arrivals. -On average, how many people are either waiting in line or currently being served?

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. -On average, how many customers are waiting to be served?

Waiting lines form because people or things arrive at the servicing function, or server, faster than they can be served.

Lenny, a graduate research assistant, "moonlights" at the short order counter in the student union snack bar in the evenings. He is the only one on duty at the counter during the hours he works. Arrivals to the counter seem to follow the Poisson distribution with a mean of 8 per hour. Each customer is served one at a time and the service time follows an exponential distribution with a mean of 5 minutes. -The manager thinks that students will go elsewhere for lunch if they have to wait more than 5 minutes. Therefore he's thinking of hiring another server to help Lenny, reducing the customer service time to 4 minutes. How long will students wait in line if Lenny gets help?

The ________ is the average number of customers who can be served during a given time period.

Operating characteristics for a waiting line system include

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. -On average, how long does a plow wait before the mechanic begins the repair?

In a single-server queuing model, L represents the

In multiple-server models, ________ independent servers in parallel serve a single waiting line.