Queuing theory

Assistant Professor Krung Sinapiromsaran, Ph. D.
17 November 2017

Agenda

  • Queue
  • Why we want to study queuing theory?
  • Different queue discipline
  • Queueing theory
  • Contact me

\[ p_i = \left\{\begin{array}{ll}\displaystyle 1 + \sum_{k = 1}^{\infty} \frac{\lambda_0 \cdot \lambda_1 \cdot ... \cdot \lambda_{k-1}}{\mu_1 \cdot \mu_2 \cdot ... \cdot \mu_k} & \mbox{if } i = 0 \\ \frac{\lambda_0 \cdot \lambda_1 \cdot ... \cdot \lambda_{i-1}}{\mu_1 \cdot \mu_2 \cdot ... \cdot \mu_i} p_0 & \mbox{if } i > 0\end{array} \right. \]

Queue

Queue example

Queue appears everywhere that people want the service.

Queue example

Why Queue?

QoS

  • Business owners (1) know how their customers have been treated, (2) improve their services

  • Customers (1) know the service level of the business, (2) optimize their valuable time.

Multiple queue

http://www.leda-tutorial.org/en/official

A single queue

http://www.leda-tutorial.org/en/official

Queuing theory

= mathematical study of waiting lines, or queues.

Queue length

  • Aim to predict queue lengths and waiting times

http://en.wikibooks.org/wiki/Fundamentals_of_Transportation/Queueing

Queue resources

  • Help making business decisions about the resources needed to provide a service.

Queue history

Telephone exchange

  • Queuing theory has its origins in research by Agner Krarup Erlang when he created models to describe the Copenhagen telephone exchange.

http://www.swindonviewpoint.com/content/gwr-works-telephone-exchange

  • Currently used in
    • telecommunication
    • traffic engineering
    • computing
    • the design of factories, shops, offices and hospitals.

Concerns

Conceptual Queue

http://web.augsburg.edu/~crockett/210/

Queue Structure

Contact me