Exam 13: Waiting Lines and Queuing Theory Models

At an automatic car wash, cars arrive randomly at a rate of 7 every 30 minutes. The car wash takes exactly 4 minutes (this is constant). On average, how many customers would be at the car wash (waiting in line or being serviced)?

At a local fast food joint, cars arrive randomly at a rate of 12 every 30 minutes. The fast food joint takes exactly 2 minutes (this is constant). The average total time in the system is

Table 13-5 -According to the information provided in Table 13-5, which presents a queuing problem solution for a queuing problem with a constant service rate, on average, how many customers arrive per time period?

Which of the following is not true about arrivals?

Table 13-3 -According to the information provided in Table 13-3, which presents a queuing problem solution, what proportion of time is the system totally empty?

Two characteristics of arrivals are the line length and queue discipline.

When waiting time is based on time in the queue, which of the following is the correct equation for total cost?

A professor decides to hold a three hour window open for student advising. The professor has 15 advisees. He's unsure if each advisee will show up, and its possible that a single advisee could show up multiple times during the 3 hour window. On average, the professor will spend 12 minutes with each student. He usually expects each student to arrive once during the 3 hour window. (a) What proportion of the time can the professor expect to be busy during the window? (b) What is the expected number of students in queue during the window? (c) What is the expected wait time in queue during the window?

A bank with a single queue to move customers to several tellers is an example of a single-channel system.

Table 13-4 -According to the information provided in Table 13-4, which presents a queuing problem solution for a queuing problem with a constant service rate, on average, how many customers arrive per time period?

Sam the Vet is running a rabies vaccination clinic for dogs at the local grade school. Sam can vaccinate a dog every 3 minutes. It is estimated that the dogs will arrive independently and randomly throughout the day at a rate of 1 dog every 6 minutes, according to a Poisson distribution. Also assume that Sam's vaccinating times are exponentially distributed. Sam would like to have each waiting dog placed in a holding pen. If Sam wants to be certain he has enough cages to accommodate all dogs at least 90 percent of the time, how many cages should he prepare?

One difficulty in waiting line analysis is that it is sometimes difficult to place a value on customer waiting time.

Sam the Vet is running a rabies vaccination clinic for dogs at the local grade school. Sam can vaccinate a dog every 3 minutes. It is estimated that the dogs will arrive independently and randomly throughout the day at a rate of 1 dog every 6 minutes, according to a Poisson distribution. Also assume that Sam's vaccinating times are exponentially distributed. (a) Find the probability that Sam is idle. (b) Find the proportion of time that Sam is busy. (c) Find the average number of dogs receiving or waiting to be vaccinated. (d) Find the average number of dogs waiting to be vaccinated. (e) Find the average time a dog waits before getting vaccinated. (f) Find the average amount (mean) of time a dog spends between waiting in line and getting vaccinated.