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3325p11hs d waiting line

# Queue waiting utilization factor for the system d

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Unformatted text preview: e time a unit spends Average waiting in the queue waiting λ µ(µ – = ) µ(µ λ ρ λ µ = Utilization factor for the system = D – 27 Model A – Single-Channel P0 = Probability of 0 units in the Probability system (that is, the service unit is idle) system λ =µ 1– Pn > k = Probability of more than k units in the Probability system, where n is the number of units in the system the k+1 λ µ= D – 28 Single-Channel Example λ λ µ–λ 2 3-2 1 µ–λ 1 3-2 λ2 µ(µ – λ ) µ(µ = 2 cars arriving/hour µ = 3 cars serviced/hour Ls = = = 2 cars cars in the system on average in Ws = = =1 22 hour average waiting time in the system s 3(3 - 2) ystem Lq = = 1.33 cars waiting in line 1.33 = D – 29 Single-Channel Example λ λ µ(µ – λ ) µ(µ λ µ 2 3(3 - 2) = 2 cars arriving/hour µ = 3 cars serviced/hour Wq = = = 2/3 hour = 40 minute average waiting time average ρ = λ /µ = 2/3 = 66.6% /µ of P0 = 1 of time mechanic is busy = .33 probability .33 there are 0 cars in the s...
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