{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Ch3_queue_theory-2008-7

# Ch3_queue_theory-2008-7 - Queueing Theory(Delay Models...

This preview shows pages 1–6. Sign up to view the full content.

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

View Full Document

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

View Full Document

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Queueing Theory (Delay Models) Sunghyun Choi Adopted from Prof. Saewoong Bahk’s material Closed Queueing Networks – No customers are allowed to arrive or depart – M : the number of customers in the system – : the state dependent service rate at queue j when there are m customers : the total arrival rates (need to be found) : the constant related with M : a particular solution ) m ( j μ 1 1 1 K ij j p i , , K = = = & ) m ( j λ 1 1, , ( ) ( ) K j i ij i j j p j K m m λ λ λ α λ = = = = ) m ( α where j λ ⋅ ⋅ ⋅ = = = if ) ( ) 2 ( ) 1 ( if 1 ) ( ˆ ) ( ) ( Let j j j j j j j j j j j n n n n P m m ρ ρ ρ μ λ ρ Closed queueing networks – states for the network of K queues: n =(n 1 ,n 2 , …,n K ) – total of M customers in the system: where G(M) is a normalization constant that ensures that P[ n ] is a probability distribution P n P n P n G M K K [ ] ( ) ( ) ( ) = 1 1 G M P n P n K K n n n n M K K ( ) ( ) ( ) {( , , ) } = + + = ∑ 1 1 1 1 • Example ( closed queueing networks) –...
View Full Document

{[ snackBarMessage ]}

### Page1 / 10

Ch3_queue_theory-2008-7 - Queueing Theory(Delay Models...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online