Exam 13: Queuing Analysis

Queuing models provide optimal solutions to waiting line problems.

Server utilization in a multiple-server system is calculated the same as in a single-server system.

Customers arrive at a candy shop every 8 minutes on average. The arrival rate is ________.

Queuing system operating statistics

Operating characteristics describe the methods used by the service process.

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. -Instead of having another student help Lenny, the manager is thinking of having two lines instead. Customers will equally divide themselves between the two lines. How long will students wait in line if there's a second server? (Assume that the service time is 5 minutes.)

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. -What is the likelihood there are more than three customers in the system?

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 probability that the system is idle is:

A manager is trying to improve a single-server queueing system through automation. The average service time is 20 minutes per customer, exponentially distributed, and the arrival rate is 16 customers per 8-hour day (Poisson arrivals). The automated system will have a constant service time of 16 minutes. The effect of this change will

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 snowplow wait before the mechanic can begin his repair?

Utilization of 100% is necessary for a queuing system to reach a steady state.

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 average time a customer spends in the line waiting to be served?

Components of a waiting line system include arrivals, servers, and the calling population.

A car wash with two attendants who work together as a team would be an example of a multiple-server system.

In a single-server system, if λ = 24 and μ = 30, then L is equal to ________.

The local grocery store consists of two cashiers. The customers arrive at the checkout according to the Poisson distribution and the service times are based on negative exponential distribution. The average customer service time is 4 minutes and the average time between the arrivals of successive customers is 3 minutes. Assume that customers equally divide themselves between the two cashiers. -How much time is a customer expected to spend waiting in line and checking out?

Customers arrive at a music store at an average of 1 per minute (Poisson arrivals). The service rate is 15 customers per hour (exponential service times). What is the minimum number of servers needed to keep the waiting time in the system under 5 minutes?

Constant service times occur with

A single-channel queuing system has an average service time of 10 minutes and an average time between arrivals of 15 minutes. What is the arrival rate?

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. -Determine the average time that a snowplow is out of service.