Exam 12: Waiting Lines and Queuing Theory Models

The customer who arrives at a bank, enters a line, and decides to leave is

Table 12-3 -According to the information provided in Table 12-3, which presents a queuing problem solution, on average, how long does each customer spend waiting in line?

Table 12-5 -According to the information provided in Table 12-5, which presents the solution for a queuing problem with a constant service rate, on average, how many minutes does a customer spend in the system?

Table 12-6 Customers arrive at coffee shop at a rate of 40 per hour.There are 2 servers available and it takes an average of 1 minute to serve each customer. -Using Table 12-6, what proportion of time are the servers busy?

Table 12-1 -According to the information provided in Table 12-1, how long does a customer wait on average?

An M/M/2 model has Poisson arrivals exponential service times and two channels.

A suburban specialty restaurant has developed a single drive-thru window.Customers order, pay, and pick up their food at the same window.Arrivals follow a Poisson distribution, while service times follow an exponential distribution.What type of queuing model is exhibited in this problem?

Table 12-1 -Using the information provided in Table 12-1, counting each person being served and the people in line, on average, how many customers would be in this system?

On a practical note-if we were to study the waiting lines in a hair salon that had only five chairs for patrons waiting, we should use an infinite queue waiting line model.

Customers enter the waiting line at a cafeteria on a first-come, first-served basis.The arrival rate follows a Poisson distribution, while service times follow an exponential distribution.If the average number of arrivals is four per minute and the average service rate of a single server is seven per minute, what is the average number of customers waiting in line behind the person being served?

What is meant by a single-channel queuing system?

In order to analyze a queue using a single channel single phase model, customer arrivals must be independent of one another but the average arrival rate is invariant.

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

Table 12-6 Customers arrive at coffee shop at a rate of 40 per hour.There are 2 servers available and it takes an average of 1 minute to serve each customer. -Using Table 12-6, what is the average number of customers waiting in line?

A single automatic car wash with one bay and a cycle time of 2.5 minutes is what type of model?

Table 12-4 The sentient car wash in Luther knows she is in for a busy day when dawn breaks on a gorgeous spring morning.She is capable of washing a car every four minutes, and by the looks of things, it is reasonable to expect a steady stream of twelve cars per hour arriving.Because she is fully automatic, she knows that the four-minute estimate is accurate and invariant.She values her time at $10 per hour.Yes, it seems low, but as a single bay car wash, there are few other jobs in town she is qualified for.(We won't get into her unsuccessful turn at the beauty salon.)She estimates that customer time can be valued at $15 per hour. -According to the information provided in Table 12-4, on average, how many customers are in line?

Consider a single-server queuing system with Poisson arrivals of 10 units per hour and a constant service time of 2 minutes per unit.How long will the customer waiting time be in seconds, on average?

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?

In order to analyze a queue using a single channel single phase model, customer interarrival time must be lower than service time.

Service times often follow a Poisson distribution.