{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# qlec3 - Queueing Systems Lecture 3 Amedeo R Odoni...

This preview shows pages 1–5. Sign up to view the full content.

October 18, 2004 Queueing Systems: Lecture 3 Amedeo R. Odoni Announcements PS #3 due today Office hours – Odoni: Tue. 10-12 AM or send me a message for an appointment Quiz #1: October 25, open book, in class Old quiz problems and solutions: posted Quiz coverage for Chapter 4: Sections 4.0 – 4.6 (inclusive)

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

View Full Document
Lecture Outline M/M/m: finite system capacity, K M/M/m: finite system capacity, K=m M/G/1: epochs and transition probabilities M/G/1: derivation of L Why M/G/m, G/G/1, etc. are difficult Reference: Sections 4.7 and 4.8.1 M/M/m: finite system capacity, K; customers finding system full are lost 0 1 2 m λ λ λ λ λ λ 3 µ 2 µ µ m µ m µ m µ K λ m µ m µ λ …… …… closed form expressions for P n , L , W , L q , W q Often useful in practice m+1 K-1 Can write system balance equations and obtain
M/M/m: finite system capacity, m; special case! …… 0 1 2 m λ λ λ λ λ 3 µ 2 µ µ ) µ m µ m i n P m i i n n ! ) ( ! ) ( 0 = = = µ λ µ λ P m P n of M/ m-1 (m-1 n for ,... 2 , 1 , 0 Probability of full system, , is “Erlang’s loss formula” Exactly same expression for G/m system with K=m M/M/ (infinite no. of servers) 0 1 2 m λ λ λ λ λ λ λ 3 µ 2 µ µ ) µ m µ µ µ ! ) ( ) ( = = n e P n n µ λ µ λ N is Poisson distributed! L = λ / µ ; W = 1 / L q = 0; W q = 0 m-1 m+1 (m-1 (m+1} (m+2) , ..... 2 , 1 , 0 n for µ ; Many applications

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

View Full Document
Variations and extensions of birth-and-death queueing systems Huge number of extensions on the previous models Most common is arrival rates and service
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}