1 / 8

Queuing theory

operations research ..waiting lines

jituvvv
Download Presentation

Queuing theory

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. QUEUES:INTRODUCTION LT COL JITHESH

  2. Murphy’s Law on Queues • If anything can go wrong, it will. • If you change queues, the one you have left will start to move faster than the one you are in now. • Your queue always goes the slowest. • Whatever queue you join, no matter how short it looks, it will always take the longest for you to get served.

  3. Queuing Theory • Waiting!!! • The aim of all investigations in queueing theory is to get the main performance measures of the system which are the probabilistic properties ( distribution function, density function, mean, variance ) of the following random variables: • number of customers in the system, • number of waiting customers, • utilization of the server/s, • response time of a customer, • waiting time of a customer, • idle time of the server, • busy time of a server • Agnes KrarupErlang: 1909 • http://web2.uwindsor.ca/math/hlynka/queue.html • Kendal Notation

  4. Performance measures of Queuing System • Interarrival time • Service time • Capacity of System • Structure of service • Number of servers • Service discipline • FIFO - First In First Out: who comes earlier leaves earlier • LIFO - Last Come First Out: who comes later leaves earlier • RS - Random Service: the customer is selected randomly • Priority • Queue length • Number of customers in the system • Waiting time • Response time

  5. Kendal Notation A / B / m / K / n/ D Where A: distribution function of the interarrival times, B: distribution function of the service times, m: number of servers, K: capacity of the system, the maximum number of customers in the system including the one being serviced, n: population size, number of sources of customers, D: service discipline. (David George Kendal)

  6. Markovian Process • Andrey Markov, 1906 • Stochastic Process • is a sequence of events in which the outcome at any stage depends on some probability. • Markov Process • is a stochastic process with the following properties: • The number of possible outcomes or states is finite. • The outcome at any stage depends only on the outcome of the previous stage. • The probabilities are constant over time. • Memoryless • M Exponentially distributed random variables

  7. Poisson Distribution • Denise Poisson • The Poisson distribution is a discrete probability distribution for the counts of events that occur randomly in a given interval of time (or space). • The number of cases of a disease in different towns • The number of mutations in set sized regions of a chromosome • The number of dolphin pod sightings along a flight path through a region • The number of particles emitted by a radioactive source in a given time • The number of births per hour during a given day

  8. Questions!!!!!!!!!!!

More Related