class14 - calulate the average queue for a system with a...

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Unformatted text preview: calulate the average queue for a system with a finite queue, such that: @ most 4 jobs are in the system assume uniform arival rate of 25 jobs/sec and a service rate of 50*N jobs/sec for 0<n<4 and 50*3 jobs/sec for N4 where N is the state ----------------------------------------------- so find Nbar W=4 lambda = 25 1=50 2=100 3=150 4=150 draw state diagram 25 25 25 25 ͻͻͻͻ Ĵ д д д п 0 1 2 3 4 ;;;; 50 100 150 150 P0*L0=P1 P1=P0*L0 -- 1 P2=P0*L0*L1 ----- 1*2 P3=P0*L0*L1*L2 -------- 1*2*3 P4=P0*L0*L1*L2*L3 ----------- 1*2*3*4 P0+P1+P2+P3+P4=1 1= P0*[1 + L/1 + L^2/1*2 + L^3/1*2*3 + L^4/1*2*3*4] L=25 1=50 2=100 3=150 4=150 P0=1/[1 + 25/50 + 25^2/(50*100) + 25^3/(50*100*150) + 25^3/(50*100*150*150)] P0=.6 or 60% Nbar=(k*Pk,1,4) P1=.6*25/50 = 0.3 P2=.6*25^2/(50*100) = 0.045 P3=.6*25^3/(50*100*150) = 0.02 P4=.6*25^3/(50*100*150*150) = 0.0024 Nbar=1*.3 + 2*.045 + 3*.02 + 4*.0024 0.31 -------------------------------------------------------------------------------- ...
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