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132B_1_Recitation9_Queueing_Systems

# 132B_1_Recitation9_Queueing_Systems - EE132B Recitation 9...

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EE132B - Recitation 9 Queueing Systems Prof. Izhak Rubin [email protected] Electrical Engineering Department UCLA

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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 2
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 0 1 2 3 λ 0 λ 1 λ 2 λ 3 μ 1 μ 2 μ 3 3

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Birth & Death Process (cont.) Balanced equations Flow into a node = flow out of a node 0 1 1 1 0 1 0 1 1 At node 0: (0) (1) At any other node : ( ) ( ) ( 1) ( 1) Node 0: (0) (1) (1) (0) ( 1) ( ), 0 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 0 2 1 2 Node 1: ( ) (1) (0) (2) (2) (1) P P P P P 4