Exam 12: Waiting Lines and Queuing Theory Models

If inventory increases, then flow rate must also increase.

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?

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.

The goal of most waiting line problems is to identify the service level that minimizes service cost.

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?

Moving from a single channel queuing system to a multichannel queuing system with two servers will cut the queue length and waiting time in half.

Table 12-5 -According to the information provided in Table 12-5, which presents a queuing problem solution for a queuing problem with a constant service rate, on average, how many customers arrive per time period?