Exam 13: Waiting Lines and Queuing Theory Models

Table 13-5 -According to the information provided in Table 13-5, 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 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 are in the system?

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 average time spent in the system?

A dry cleaner has a single drive-thru window for customers. The arrival rate of cars follows a Poisson distribution, while the service time follows an exponential distribution. The average arrival rate is 16 per hour and the average service time is three minutes. If the dry cleaner wants to accommodate (have enough room for) All of the waiting cars at least 96 percent of the time, how many car-lengths should they make the driveway leading to the window?

Table 13-2 -According to the information provided in Table 13-2, which presents a queuing problem solution, there are two servers in this system. Counting each person being served and the people in line, on average, how many people would be in this system?

A new shopping mall is considering setting up an information desk manned by one employee. Based upon information obtained from similar information desks, it is believed that people will arrive at the desk at the rate of 15 per hour. It takes an average of two minutes to answer a question. It is assumed that arrivals are Poisson and answer times are exponentially distributed. (a) Find the probability that the employee is idle. (b) Find the proportion of time that the employee is busy. (c) Find the average number of people receiving and waiting to receive information. (d) Find the average number of people waiting in line to get information. (e) Find the average time a person seeking information spends at the desk. (f) Find the expected time a person spends waiting in line to have his question answered.

If we are using a simulation queuing model, we still have to abide by the assumption of a Poisson arrival rate, and negative exponential service rate.

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 2 fax machines need toner at the same time?

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

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 dry cleaner has a single drive-thru window for customers. The arrival rate of cars follows a Poisson distribution, while the service time follows an exponential distribution. The average arrival rate is 16 per hour and the average service time is three minutes. (a) What is the average number of cars in the line? (b) What is the average time spent waiting to get to the service window? (c) What percentage of time is the dry cleaner's drive-thru window idle? (d) What is the probability there are more than 2 cars at the drive-thru window?

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

The "utilization factor" is defined as the

A queuing system with a normally distributed arrival pattern, exponential service times, and three servers would be described as ________.

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 proportion of the time is the server busy?

Most systems use a queue discipline known as ________.

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

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 average number of fax machines in the queue?

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

There is a tutoring lab at a university that holds 20 students. Due to the popularity of the 3 tutors, the lab is always at capacity. Each student approaches a tutor an average of 2 times per hour, and a tutor spends on average 5 minutes per question from a student. The service time follows an exponential distribution. (a) What proportion of the time are the tutors busy? (b) What is the average waiting time for students in queue?