Exam 13: Waiting Lines and Queuing Theory Models

A goal of many waiting line problems is to help a firm find the ideal level of services that minimize the cost of waiting and the cost of providing the service.

Table 13-3 -According to the information provided in Table 13-3, which presents a queuing problem solution what is the utilization rate of the service facility?

At the start of football season, the ticket office gets busy the day before the first game. Customers arrive at the rate of four every ten minutes. A ticket seller can service a customer in four minutes. Traditionally, there are two ticket sellers working. The university is considering an automated ticket machine similar to the airlines' e-ticket system. The automated ticket machine can service a customer in 2 minutes. (a) What is the average length of the queue for the in-person model? (b) What is the average length of the queue for the automated system model? (c) What is the average time in the system for the in-person model? (d) What is the average time in the system for the automated system model? (e) Assume the ticket sellers earn $8 per hour and the machine costs $20 per hour (amortized over 5 years). The wait time is only $4 per hour because students are patient. What is the total cost of each model?

Cars arrive at a local JLUBE franchise at the rate of 1 every 12 minutes. Service times are exponentially distributed with an average of 15 minutes. Jack Burns, the JLUBE owner, has decided to open a second work bay, i.e., make the shop into a two-channel system. Under this new scheme, the total time an average customer spends in the system will be

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 car spend at the car wash?

Customers enter the waiting line to pay for food as they leave 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, on average, how much time will elapse from the time a customer enters the line until he/she leaves the cafeteria?

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 much time is spent waiting in line?

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. If the average number of arrivals is 6 per hour and the service rate is 2 every 15 minutes, what is the average number of customers in the system?

At a local fast-food joint, cars arrive randomly at a rate of 12 every 30 minutes. The fast food joint takes an average of 2 minutes to serve each arrival. The utilization factor for this system is

What is meant by a single-channel queuing system?

Table 13-1 -According to the information provided in Table 13-1, what is the average time spent by a person in this system?

Which of the following distributions is most often used to estimate service times?

A finite population model differs from an infinite population model because there is a random relationship between the length of the queue and the arrival rate.

What is meant by a multiphase system?

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

Cars arrive at a local JLUBE franchise at the rate of 1 every 12 minutes. Service times are exponentially distributed with an average of 15 minutes. Jack Burns, the JLUBE owner, has decided to open a second work bay, i.e., make the shop into a two-channel system. Under this new scheme, the average customer will wait in an ________ line

An "infinite calling population" occurs when the likelihood of a new arrival depends upon the number of past arrivals.

Little's Flow Equations are transferable to a production environment. Which of the following would be a proper interpretation of Little's Flow Equations?

Table 13-1 -Using the information provided in Table 13-1 and counting each person being served and the people in line, on average, how many people would be in this system?

Table 13-2 -According to the information provided in Table 13-2, which presents a queuing problem solution, what proportion of time is at least one server busy?