# Waiting Line and Queuing Theory Models Essay examples

4889 Words Apr 9th, 2013 20 Pages
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M14_REND6289_10_IM_C14.QXD 5/12/08 1:01 PM Page 218

218

CHAPTER 14

WAITING LINE

AND

QUEUING THEORY MODELS

Alternative Example 14.3: A new shopping mall is considering setting up an information desk manned by two employees. Based on information obtained from similar information desks, it is believed that people will arrive at the desk at the rate of 20 per hour. It takes an average of 2 minutes to answer a question. It is assumed that arrivals are Poisson and answer times are exponentially distributed. a. Find the proportion of the time that the employees are idle. b. Find the average number of people waiting in the system. c. Find the expected time a person spends waiting in the system. ANSWER: (servers). a. P
Arrivals Waiting time Service dirty cars or trucks cars in one line (or more lines if there are service parallel wash systems); always FIFO either multiphase (if car ﬁrst vacuumed, then soaped, then sent through automatic cleaner, then dried by hand) or single-phase if all automatic or performed by one person

14-8. The waiting time cost should be based on time in the queue in situations where the customer does not mind how long it takes to complete service once the service starts. The classic example of this is waiting in line for an amusement park ride. Waiting time cost should be based on the time in the system when the entire time is important to the customer. When a computer or an automobile is taken into the shop to be repaired, the customer is without use of the item until the service is ﬁnished. In such a situation, the time in the system is the relevant time. 14-9. The use of Poisson to describe arrivals: a. Cafeteria: probably not. Most people arrive in groups and eat at the same time. b. Barbershop: probably acceptable, especially on a weekend, in which case people arrive at the same rate all day long. c. Hardware store: okay. d. Dentist’s ofﬁce: usually not. Patients are most likely scheduled at 15- to 30-minute intervals and do not arrive randomly. e. College class: number of students come in groups at the beginning of class period; very few arrive during the class or

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