Exam 13: Queuing Analysis

The multiple-server system models have been developed on the assumption that the service times are normally distributed.

A single-bay car wash with a Poisson arrival rate and an exponential service time has cars arriving at an average of 10 minutes apart with an average service time of 4 minutes. What is the system utilization?

Providing quick service is an important aspect of quality customer service.

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 utilization rate for the mechanic?

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. -What is the probability that there are no customers in the grocery store?

An aggressive advertising campaign increases demand for the service by 50%. By what percentage do the average queue length and average time in queue increase?

An important factor to consider in analyzing a queuing system is the

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 percentage of the time is the system completely empty?

A multiple-channel system has customers arriving at an average rate of 5 per hour and an average service time of 40 minutes. What minimum number of servers is required to ensure that the system is not overloaded?

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 be down and out of service?

The local grocery store consists of two cashiers. The customers arrive according to a Poisson distribution and the service times are based on a negative exponential distribution. The average customer service time is 5 minutes and the average time between the arrivals of successive customers is 3 minutes. What is the probability that there are no customers in the grocery store?

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 average time that a snowplow is out of service?

In a multiple-server system, the ratio of the mean effective service rate for the system to the arrival rate to the system must be greater than 1 for customers to be served in a reasonable time.

Which of the following will not decrease system utilization?

________ is the act of a customer refusing to enter a service system because the wait is too lengthy.

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 system?

The basic single-server model assumes that customers who arrive first are served first.

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. -What is the average number of customers waiting in each line and being checked out?

In systems with finite queue length, the service rate does not have to exceed the arrival rate.

The basic single-server model assumes that arrival rates are normally distributed.