Exam 13: Queuing Analysis

The service time can most often be described by the ________ distribution.

The number of servers, c, in a multiple-server queuing system must be greater than the average queue length.

Customers may be served

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

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. -On average, how much time will the customer spend in line waiting to be served?

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 average time a customer spends in the system?

Cars arrive at a single-bay car wash at an average of 6 per hour according to the Poisson distribution. The wash time averages 4 minutes with a standard deviation of 1 minute, but the wash time is not defined by any distribution. What is the average number of cars in line?

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 cars are in the system?

The service time can often be described by the Poisson distribution.

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

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 being checked out?

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. -How busy are the servers on average?

Poultry Processing processes chickens for fast food restaurants. The 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. What is the minimum 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 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. -The utilization is:

Queue discipline refers to the willingness of customers to wait in line for service.

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 busy are the servers and how likely is it that they have nothing to do?

A multiple channel queuing system with a Poisson arrival rate and exponential service time has an average arrival rate of 6 customers per hour and an average service time of 20 minutes per customer. What is the minimum number of servers required to avoid an overloaded system?

In the ________ queuing system, which is a variation of the single-phase single-channel model, the service rate does not have to exceed the arrival rate.

All single-server queuing models require the utilization factor to be less than 1.

The arrival rate can generally be described by a(n) ________ distribution.