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Problem 4 Average time a ticket buyer must wait From the information provided; λ 10 µ 12 Average waiting time = λ/µ(µ-λ) µ-λ 2 Thus, Wa 0.416666667 hrs or 25 mins Portion of time the ticket seller is busy Portion of busy time, Ƿ = λ/µ Hence, Ƿ 0.833333333 hrs or 50 mins Problem 6 Let arrival rate be λ, service rate be µ, average number of the products waiting be L q, percentage of time the mach From the question; µ 10 parts per hour λ 8 parts per hour Average number of parts waiting to be worked on L q is given by λ^2/µ(µ-λ) λ^2 64 (µ-λ) 2 Thus, L q 3.2 parts Percentage of time the operator is working U = λ/µ Hence, U 80% Percentage of time the machine is idle I = 1- λ/ µ Hence, I 20% Problem 8 Let arrival rate be λ, service rate be µ, average number of the planes in the waiting line be L q, average time a plane From the provided information; I 12 min λ 4 planes per hour. µ 5 a) Average number of planes that will be stack up, waiting to land L q =λ^2/µ(µ-λ) (µ-λ) 1 λ^2 16 Thus, L q 3.2 average number of planes waiting to land b) Average time a plane must wait in line before it can land Wq = λ/µ(µ-λ) Hence, Wq 0.8 hrs or 48 mins c) Average time it takes a plane to clear the runway W = 1/ (µ-λ) Thus, W 1 hour d) FAA rule on idle time for air traffic controllers is 15 minutes (25%). To determine if the airport have to hire an ex U =λ/µ Hence, U 0.8 This probability exceeds 75% busy time implying that planes will wait longer t ...
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