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Unformatted text preview: Spatially Distributed Queues M/G/1 2 Servers N servers Approximations hy Spatial Queues? a Demand responsive transportation systems a Organ donation queues a Warehouses a Supply chains a Cell phone systems a People waiting to be evacuated in a hurricane M/G/1 Ambulance (0,0) (0,Y ) (X ,0) Directions Of Travel X A Y A 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, 2 of the 1st service time in a busy period S , S 2 2 = expected value and variance,respectively, & all succeeding service times in a busy period S 2 of the 2nd < 1 = 1 P = fraction of time server is busy M/G/1with different 1st service time = S 1 1 ( S 2 S 1 ) L = + 2 1 ( S 2 S 1 ) [ S 1 2 + S 1 2 + { S 1 ( S 2 2 + S 2 2 ) S 2 ( S 1 2 + S 1 2 ) 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.
 Fall '06
 hansman

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