Ch3_queue_theory-2008-3

# Ch3_queue_theory-2008-3 - Queueing Theory(Delay Models...

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Unformatted text preview: Queueing Theory (Delay Models) Sunghyun Choi Adopted from Prof. Saewoong Bahk’s material Priority Queueing • M/G/1 with n priority classes of customers – For class k , – Independent Poisson arrival processes • Non preemptive priority – Complete the on-going service without interruption – Separate queue for each priority class – : avg. number of customers in queue for priority k : avg. queueing time for priority k : R : mean residual service time k Q N k W k ρ k k μ λ = 2 , 1 , k k k k X X μ λ = – – for class 1 (highest priority) and 2 1 1 < ρ ∑ = n i i ( 29 ( 29 2 1 1 2 1 1 1 2 2 1 2 2 1 1 2 1 1 2 2 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Then 1 queue in waiting is customer 2 class a while arrive that 1 class of customers to due delay queueing additional ρ- ρ- ρ- = ρ- ρ- ρ + = ρ + ρ + ρ + = λ μ + μ + μ + = ρ- = ρ + = μ + = R W R W W W W R W N N R W R W W R N R W Q Q Q – For class k – System delay for class k – Mean residual service time – finally...
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Ch3_queue_theory-2008-3 - Queueing Theory(Delay Models...

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