Exam 12: Waiting Lines and Queuing Theory Models

On a practical note-we should probably view the checkout counters in a grocery store as a set of single channel systems.

Table 12-1 -According to the information provided in Table 12-1, on average, how many customers are in the line?

Bank Boston has a branch at Bryant College.The branch is busiest at the beginning of the college year when freshmen and transfer students open accounts.This year, freshmen arrived at the office at a rate of 40 per day (8-hour day).On average, it takes the Bank Boston staff person about ten minutes to process each account application.The bank is considering having one or two tellers.Each teller is paid $12 per hour and the cost of waiting in line is assumed to be $8 per hour. (a)What is the total daily waiting cost for the single teller model? (b)What is the total daily waiting cost for the two-teller model? (c)What is the total daily service cost for the single teller model? (d)What is the total daily service cost for the two-teller model? (e)Which model is preferred?

A post office has a single line for customers waiting for the next available postal clerk.There are two postal clerks who work at the same rate.The arrival rate of customers follows a Poisson distribution, while the service time follows an exponential distribution.The average arrival rate is three per minute and the average service rate is two per minute for each of the two clerks.How long does the average person spend waiting for a clerk?

Thanks to a generous and eccentric donor, the school of business has 3 fax machines.The toner in each machine needs to be changed after about 5 hours of use.There is one unit secretary who is responsible for the fax machine maintenance.It takes him 15 minutes to replace the toner cartridge.What is the probability that one of the fax machines needs toner?

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 long would each driver have to wait before receiving service?

A post office has a single line for customers waiting for the next available postal clerk.There are two postal clerks who work at the same rate.The arrival rate of customers follows a Poisson distribution, while the service time follows an exponential distribution.What type of queuing model applies here?

The customer who arrives at a bank, sees a long line, and leaves to return another time is

In the multichannel model (M/M/m), we must assume that the average service time for all channels is the same.

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)?

What is meant by a multichannel queuing system?

A vendor selling newspapers on a street corner is an example of a

If we are studying the arrival of automobiles at a highway toll station, we can assume an infinite calling population.

The initial state of a queuing system (for example, when a restaurant first opens), is referred to as the ________ state.

The rule of thumb for employing a finite population queuing model is if the calling population is eight or fewer.

A single automatic car wash with one bay and a service time that is normally distributed is what type of model?

A professor holds office hours during final exam week and discovers much to his dismay that his sudden popularity affords him little time to engage in his favorite activity, watching cat videos.Fifteen students per hour arrive at his office and he patiently answers questions, averaging three minutes per student.On average, how many students are waiting to ask questions?

At an automatic car wash, cars arrive randomly at a rate of 7 cars every 30 minutes.The car wash takes exactly 4 minutes (this is constant).On average, what would be the length of the line?

Using a simulation model allows one to ignore the common assumptions required to use analytical models.

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 4 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.