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# class16 - Spatially Distributed Queues M/G/1 2 Servers N...

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Unformatted text preview: Spatially Distributed Queues M/G/1 2 Servers N servers Approximations M/G/1 Directions Of Travel (0,Y Y A Ambulance ) (0,0) X A (X ,0) M/G/1 M/G/1 Ambulance (0,0) (0,Y ) (X ,0) Directions Of Travel X A Y A M/G/1 a Ambulance always returns home with each service; standard M/G/1 applies a But suppose we have an emergency repair vehicle that travels directly from one customer to the next?... M/G/1with different 1st service time S 1 , S 1 2 = expected value and variance,respectively, of the 1st service time in a busy period S 2 , S 2 2 = expected value and variance,respectively, of the 2nd & all succeeding service times in a busy period S 2 < 1 = 1 P 0 = fraction of time server is busy M/G/1with different 1st service time S 1 = 1 ( S 2 S 1 ) 2 2 2 2 2 2 L = + [ S 1 + S 1 + { S 1 ( + S 2 ) S 2 ( + S 1 2 ) ] S 2 S 1 1 ( S 2 S 1 ) 2(1 S 2 ) M/G/1with different 1st service time Little' s Law : Buy one, get three others for free! L = W L q = W q See the book, Eqs. (5.0) - (5.5) M/G/1with different 1st service time a Does this new more general M/G/1 model apply exactly to the ambulance problem?...
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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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class16 - Spatially Distributed Queues M/G/1 2 Servers N...

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