September_25th_Lecture_3000

September_25th_Lecture_3000 - September 25th Lecture CEE...

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September 25 th Lecture CEE 3000 Queuing Theory Ex. Soda Machine μ = service rate λ = arrival rate avg. time in system = 1/ (μ- λ) avg. of units in the queue= (λ/ μ)^2/ (1 – λ/μ) avg. time in queue = λ/ (μ (μ- λ)) probability of “n” units in the system = (λ /μ)^n (1- λ/ μ) Avg. number of units in the system = (λ/ μ)/ (1- λ /μ) Ex.1 μ = 16 planes/hr λ = 12 planes/hr a. prob(0) = (0.75)^0*(1-0.75) 0.25 or 25% b. avg. time = 1/(16-12) 0.25 hr 15 minutes c. avg. number of units in system = 0.75/(1- 0.75) Ex. 2 μ = 600 pax/hr λ = 500 pax/hr a. avg. # of ppl in queue (5/6)/(1/6)= 4.17 pax. (don’t round) b. avg. time in queue
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September_25th_Lecture_3000 - September 25th Lecture CEE...

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