que_for_sys_desn

que_for_sys_desn - Queuing Formula: Single Server...

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Copyright 2005 Stephen C. Graves All Rights Reserved Queuing Formula: Single Server Utilization : = = λ ρ λτ µ Little's law : L= W λ 1 W expected wait time in system D D == + = + τ µ () as D expected wait time in queue for G1/G/1 SCV SCV 1 12 SCV SCV = ⎛⎞ + ρ ⎜⎟ −ρ µ ⎝⎠ + ρ ≅τ −ρ
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Copyright 2005 Stephen C. Graves All Rights Reserved Queuing Formula: Multiple Servers () kk 1 00 0 ki k1 i0 11 For M/M/k system: D k !1 - 1 k ! 1 where and k 1k ! i ! = ⎛⎞ ρρ ρ = π= π ⎜⎟ µ−λ −ρ ρ µ ⎝⎠ λ ρ= µ + s as D expected wait time in queue for M/G/k 1S C V expected wait time in queue for M/M/k 2 SCV SCV A quick approx. is D 2 = + + ρτ
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Copyright 2005 Stephen C. Graves All Rights Reserved Queuing Formula: Multiple Servers, No Queue ( ) () n i k i0 n! For M/G/k/k: Pr [ # in system = n ] = and i! Pr[ # in system = k ] = "loss probability" = λτ or M/G/ , number in the system is Poisson with mean = ith variance = ∞λ τ
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Copyright 2005 Stephen C. Graves All Rights Reserved Emergency Care Cool off OK Not OK Triage Blisters & Cramps Dehydration Recovery Services Finish line
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Copyright 2005 Stephen C. Graves
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This note was uploaded on 12/06/2011 for the course ESD 15.763j taught by Professor Davidsimchi-levi during the Spring '05 term at MIT.

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que_for_sys_desn - Queuing Formula: Single Server...

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