lec6 - Queueing Systems: Lecture 2 Amedeo R. Odoni October...

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Unformatted text preview: Queueing Systems: Lecture 2 Amedeo R. Odoni October 11, 2006 Lecture Outline M/M/m M/M/ M/M/1: finite system capacity, K M/M/m: finite system capacity, K M/M/m: finite system capacity, K=m Related observations and extensions M/E 2 /1 example M/G/1: epochs and transition probabilities Reference: Chapter 4, pp. 203-217 M/M/m (infinite queue capacity) ( ) n P n = P for n = 0, 1, 2,...., m 1 n ! ( ) n P n = n m P for n = m , m + 1, m + 2,.... m m ! Condition for steady state? 1 2 m-1 m m+1 3 2 (m-1) m m m . M/M/ (infinite no. of servers) 1 2 m-1 m m+1 3 2 (m-1) m (m+1} (m+2) ( ) n e ( ) P n = for n = 0, 1, 2,..... n ! N is Poisson distributed! L = / ; W = 1 / ; L q = 0; W q = 0 Many applications M/M/1: finite system capacity, K; customers finding system full are lost...
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This note was uploaded on 11/08/2011 for the course AERO 16.72 taught by Professor Hansman during the Fall '06 term at MIT.

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lec6 - Queueing Systems: Lecture 2 Amedeo R. Odoni October...

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