Discussion Notes 10

Discussion Notes 10 - EE132B - Recitation 10 Queueing...

Info iconThis preview shows pages 1–7. 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

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: EE132B - Recitation 10 Queueing Systems Prof. Izhak Rubin rubin@ee.ucla.edu Electrical Engineering Department UCLA Outline Birth & Death Process Discrete Time Queueing System Geometric Distribution The Geom/Geom/1 QS Example Continuous Time Queueing System The M/M/1 QS Example Birth & Death Process A process is said to be a birth & death process if the TPF is given by: , for 1 , for 1 ( , ) 1 , for 0, otherwise i i i i X j i j i P i j i j = + = - = -- = 1 2 3 1 2 3 1 2 3 Birth & Death Process (cont.) Balanced equations Flow into a node = flow out of a node 1 1 1 1 1 1 At node 0: (0) (1) At any other node : ( ) ( ) ( 1) ( 1) Node 0: (0) (1) (1) (0) ( 1) ( ), j j j j j j P P j P j P j P j P P P P P j P j j - + + = + =- + + = = + = 1 1 2 1 2 Node 1: ( ) (1) (0) (2) (2) (1) P P P P P + = + = Birth & Death Process (cont.) 1 1-2-1-2-3-1-1-1 1-1-2-3-1-1 1 ... ( ) ( 1) ( 2) .... (0) ..... ... Define ..... A unique stationary distribution exists for ( ) (0) j j j j j j j j j j j j j j j j j j j j j j P j P j P j P a a P j P -- = = =- =- = = < = -1-2-3 1-1-1 1 1 ... (0) .. (0) ... 1 ..... (0) 1, (0) ( ) , 0,1,2,.. j j j j j j j j j j j i i P P P a P a a P j j a - = = = + + + + = = = = = Discrete Time Queueing Systems Example: Geom/Geom/1 Geometric Distribution Recall the following properties for geometric distribution It is the only discrete memoryless distribution Let p = probability of success And 1-p = probability of failure If T n is a geometrically distributed random variable, P(T n = j) = p(1-p) j-1 The Geom/Geom/1 QS...
View Full Document

Page1 / 18

Discussion Notes 10 - EE132B - Recitation 10 Queueing...

This preview shows document pages 1 - 7. Sign up to view the full document.

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