lec8 (1)

Lec8(1) - Queueing Systems Lecture 4 Amedeo R Odoni Lecture Outline • M/G/1 a simple example • Introduction to systems with priorities •

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Queueing Systems: Lecture 4 Amedeo R. Odoni October 20, 2006 Lecture Outline • M/G/1: a simple example • Introduction to systems with priorities • Representation of a priority queuing system • The M/G/1 non-preemptive priority system • An important optimization theorem • … and an important corollary • Brief mention of other priority systems • Bounds for G/G/1 systems Reference: Chapter 4, pp. 222-239 (just skim Sections 4.8.2 and 4.8.4) Expected values for M/G/1 ρ 2 + λ 2 ⋅ σ S 2 L = ρ + ( ρ < 1) 2(1 − ρ ) 1 ρ 2 + λ 2 ⋅ σ S 2 W = + μ 2 λ (1 − ρ ) W q = ρ 2 + λ 2 ⋅ σ S 2 = ρ 2 (1 + C S 2 ) = 1 ⋅ ρ ⋅ (1 + C S 2 ) 2 λ (1 − ρ ) 2 λ (1 − ρ ) μ (1 − ρ ) 2 L q = ρ 2 2 + (1 λ − 2 ρ ⋅ σ ) S 2 Note : C S = E σ [ S S ] = μ ⋅ σ S Runway Example • Single runway, mixed operations • E[S] = 75 seconds; σ S = 25 seconds μ = 3600 / 75 = 48 per hour • Assume demand is relatively constant for a sufficiently long period of time to have approximately steady-state conditions • Assume Poisson process is reasonable approximation for instants when demands occur Estimated expected queue length and expected waiting time L q L q W q W q λ (per hour) ρ (% change) (seconds) (% change) 30 0.625 0.58 69 30.3 0.63125 0.60 3.4% 71 2.9% 36 0.75 1.25 125 36.36 0.7575 1.31 4.8% 130 4% 42 0.875 3.40 292 42.42 0.88375 3.73 9.7% 317 8.6% 45 0.9375 7.81 625 45.45 0.946875 9.38 20.1% 743 18.9% Can also estimate PHCAP ≅ 40.9 per hour Announcements • Quiz #1: October 25, open book, in class; quiz begins at 10:00, ends at 12:30; pick any TWO hours (10-12 or 10:30-12:30) • Odoni: Office hrs Tu 10-12 • Old quiz problems and solutions: posted • Quiz coverage for Chapter 4: Sections 4.0 – 4.6 (inclusive) Background and observations...
View Full Document

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.

Page1 / 10

Lec8(1) - Queueing Systems Lecture 4 Amedeo R Odoni Lecture Outline • M/G/1 a simple example • Introduction to systems with priorities •

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online