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 ( ) a s a s D expected wait time in queue for G1/G/1 SCV SCV 1 1 2 SCV SCV 1 2 = + ρ −ρ µ + ρ τ −ρ

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Copyright 2005 Stephen C. Graves All Rights Reserved Queuing Formula: Multiple Servers ( ) ( ) ( ) ( ) ( ) ( ) ( ) k k 1 0 0 0 k i k 1 i 0 k k 1 1 For M/M/k system: D k 1 k! 1- 1 k! 1 where and k k k 1 k! i! = ρ ρ ⎞⎛ ρ = π = π ⎟⎜ µ−λ −ρ ρ µ −ρ ⎠⎝ λ π = ρ= µ ρ ρ + −ρ ( ) s a s D expected wait time in queue for M/G/k 1 SCV expected wait time in queue for M/M/k 2 SCV SCV A quick approx. is D 1 k 2 = + + ρ τ −ρ

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