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Unformatted text preview: Queueing Systems: Lecture 3 Amedeo R. Odoni October 18, 2006 Announcements • PS #3 due tomorrow by 3 PM • Office hours – Odoni: Wed, 10/18, 2:304:30; next week: Tue, 10/24 • Quiz #1: October 25, open book, in class; options: 1012 or 10:3012:30 • Old quiz problems and solutions: posted Thu evening along with PS #3 solutions • Quiz coverage for Chapter 4: Sections 4.0 – 4.6 (inclusive); Prof. Barnett’s lecture NOT included Lecture Outline • Remarks on Markovian queues • M/E 2 /1 example • M/G/1: introduction, epochs and transition probabilities • M/G/1: derivation of important expected values • Numerical example • Introduction to M/G/1 systems with priorities Reference: Section 4.7 Variations and extensions of birthanddeath queueing systems • Huge number of extensions on the previous models • Most common is arrival rates and service rates that depend on state of the system; some lead to closedform expressions • Systems which are not birthanddeath, but can be modeled by continuous time, discrete state Markov processes can also be analyzed [“phase systems”] • State representation is the key (e.g. M/E k /1 or more than one state variables – P.S. #3) M/G/1: Background • Poisson arrivals; rate λ • General service times, S ; f S (s); E[S]=1/ μ ; σ S • Infinite queue capacity • The system is NOT a continuous time Markov process (most of the time “it has memory”) • We can, however, identify certain instants of time (“epochs”) at which all we need to know is the number of customers in the system to determine the probability that at the next epoch there will be 0, 1, 2, …, n...
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This note was uploaded on 11/08/2011 for the course AERO 16.72 taught by Professor Hansman during the Fall '06 term at MIT.
 Fall '06
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