class13 - -Queue can be finite or infinite infinite queue...

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Sheet1 Page 1 04/08/07 HW6 and HW7 due thursday HW6 Assume infinite queue 1) what is the max arival rate such that the average response time R<0.05 if the service demand is S_d = 0.01 ANSWER 80 2) a)what is the average number of jobs in the system,for the above system,at its "maximum" arival rate Nbar=4 customers b) @2 lambda doesnt work c) at lambda/2 2/3 .66 3) what is the average response time for this system at 2lambda and lambda/2 lambda/2 = 1/60 0.0166 s/job HW7 Find P0, U, X,Nbar,R for a closed system with three jobs assume uniform lambda 1=1.5, 2=1, 3=.75 1) for think time =0.75 2) for think time 0.25 3) for Z=.5,BUT mew1=mew2=mew3=1 generalized system level model -arival rates and service rates need not be uniform --they may depend on the state
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Unformatted text preview: -Queue can be finite or infinite infinite queue U=1-p_0 X=sum(mew_k*P_k,1,infinity) Nbar=sum(k*P_k,1,infinity) what is product(lambda_i/mew_(i+1).i=0 to k-1) K=0? product(lambda_i/mew_(i+1).i=0 to -1) define it as 1 K=1? product(lambda_i/mew_(i+1).i=0 to 0) lambda_0/mew-1 K=2? product(lambda_i/mew_(i+1).i=0 to 1) Sheet1 Page 2 (lambda_0/mew_1) * (lambda_1/mew_2) ect. remember 1st Example lambda=30 mew=50 Queue is infinite derived P_0=[sum((lambda/mew)^k,k=0to inf.)]^-1=1-lambda/mew = 40% U=1-P_0=60% for homework 8 due tuesday 1)for 30,50 calculate Nbar,X,R using first 6 terms 2) redo example using 5 terms (k=0->4) with lambda 020 110 2,35 mew 140 2,3,450 calculate P0,P1,P2,Nbar...
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class13 - -Queue can be finite or infinite infinite queue...

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