推 littlewei328:太感謝你了 02/23 16:55
※ 引述《littlewei328 (wei)》之銘言：
: 今天寫考古題，對這題答案有疑問，請求板上高手幫忙解!
: 題目是:
: Consider a system of two infinite queues in series,where each of the two
: service facilities has a single server.All service times are independent
: and have an exponential distribution,with a mean of 3 minutes at facility
: 1 and 4 minutes at facility 2.Facility 1 has a Poisson input process with
: a mean rate of 10 per hour:
1.Jackson network ,two facilities : F1,F2
2.Rate diagram
λ
—○ ─○
μ1 μ2
We know F1 is M/M/1 , F2 is M/M/1
λ= 10 unit/hr = 1/6 unit per min
μ1=3 ,μ2=4
: (a) Find the steady-state distribution of the number of customers at
: facility 1 and then at facility 2 .
1.F1
L - Lq = ... =ρ = 1/18
2.F2 (F2's arrival rate = μ1 = 3)
ρ = 3/4
: (b)Show the product form solution for the joint distribution of the number
: at the respective facilities.
ρ of F1 * ρ of F2 = 1/18 * 3/4 = 1/24
: (c)What is the probability that both servers are idle?
1.F1
P0 =...= 1- ρ =17/18
2.F2
P0 = 1/4
: (d)Find the expected total number of customers in the system and expected
: total waiting time (include service times) for a customer.
1.F1
L= ΣnPn =...= ρ/(1-ρ) = 1/17
W= L / λ = 1/17 * 6 = 6/17
2.F2
L = 3
W = 1
: 感謝再感謝~~
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※ 編輯: vity 來自: 59.112.132.213 (02/22 23:02)
※ 編輯: vity 來自: 59.112.132.213 (02/22 23:27)