EE555_spr08_Lect04_Basic_Queueing_Models

# EE555_spr08_Lect04_Basic_Queueing_Models - Basic Queueing...

This preview shows pages 1–3. Sign up to view the full content.

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: Basic Queueing Models EE555-Spring 2008, Silvester 3-1 3 Basic Queueing Concepts We think of a stream of packets arriving to a multiplexer as the customers in a queueing system. x n is service time for customer n t n+1 is inter-arrival time for customer n (between customer n and customer n+1) w n is waiting time for customer n s n = w n +x n is total system time for customer n See diagram on next page. Basic Queueing Models EE555-Spring 2008, Silvester 3-2 c n c n+1 c n+2 c n+3 c n c n+1 c n+2 c n+3 Departures Arrivals Queue In Service x n t n+1 w n+2 x n+2 x n+1 s n+2 IDLE BUSY PERIOD c n c n+1 c n+2 c n+3 c n c n+1 c n+2 c n+3 Departures Arrivals Queue In Service x n t n+1 w n+2 x n+2 x n+1 s n+2 IDLE BUSY PERIOD We note that: 1 1 , max{ + + − + = n n n n t x w w } which is useful for studying system behaviour since x and t are random variables that can be simulated to drive system evolution. Basic Queueing Models EE555-Spring 2008, Silvester 3-3 ) ( ) ( ) ( n a n − = which is the number in system at time t Consider the area: ∫ = t dt t n t A ) ( ) ( Then: ) ( / ) ( t N t t A = is the average number (packets) in system in (0, t ). We can compute this area another way: ∑ = = ) ( 1 ) ( t a n n s t A (assume for simplicity that t is in an idle period). a ( t )= number of arrivals in (0, t ) d ( t )= number of departures in (0, t ) n ( t ) s n a ( t )= number of arrivals in (0, t ) d ( t )= number of departures in (0, t ) n ( t ) s n Basic Queueing Models EE555-Spring 2008, Silvester 3-4 So, ) ( ) ( ) ( ) ( 1 ) ( ) ( 1 t T t t a s t t a s t t N n t a n n λ = = = ∑ ∑ = = Arrival rate in (0, t ) * Average time in system for packets up to time t Dropping the time parameter...
View Full Document

{[ snackBarMessage ]}

### Page1 / 6

EE555_spr08_Lect04_Basic_Queueing_Models - Basic Queueing...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online